Deprecated: preg_match(): Passing null to parameter #2 ($subject) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/lbfactory/LBFactory.php on line 759

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 262

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: Return type of MediaWiki\Session\PHPSessionHandler::open($save_path, $session_name) should either be compatible with SessionHandlerInterface::open(string $path, string $name): bool, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/session/PHPSessionHandler.php on line 181

Deprecated: Return type of MediaWiki\Session\PHPSessionHandler::close() should either be compatible with SessionHandlerInterface::close(): bool, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/session/PHPSessionHandler.php on line 196

Deprecated: Return type of MediaWiki\Session\PHPSessionHandler::read($id) should either be compatible with SessionHandlerInterface::read(string $id): string|false, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/session/PHPSessionHandler.php on line 210

Deprecated: Return type of MediaWiki\Session\PHPSessionHandler::write($id, $dataStr) should either be compatible with SessionHandlerInterface::write(string $id, string $data): bool, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/session/PHPSessionHandler.php on line 238

Deprecated: Return type of MediaWiki\Session\PHPSessionHandler::destroy($id) should either be compatible with SessionHandlerInterface::destroy(string $id): bool, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/session/PHPSessionHandler.php on line 344

Deprecated: Return type of MediaWiki\Session\PHPSessionHandler::gc($maxlifetime) should either be compatible with SessionHandlerInterface::gc(int $max_lifetime): int|false, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/session/PHPSessionHandler.php on line 365

Deprecated: strcasecmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/session/CookieSessionProvider.php on line 101

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 262

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: Return type of MediaWiki\Session\Session::count() should either be compatible with Countable::count(): int, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/session/Session.php on line 593

Deprecated: Return type of MediaWiki\Session\Session::current() should either be compatible with Iterator::current(): mixed, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/session/Session.php on line 599

Deprecated: Return type of MediaWiki\Session\Session::next() should either be compatible with Iterator::next(): void, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/session/Session.php on line 611

Deprecated: Return type of MediaWiki\Session\Session::key() should either be compatible with Iterator::key(): mixed, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/session/Session.php on line 605

Deprecated: Return type of MediaWiki\Session\Session::valid() should either be compatible with Iterator::valid(): bool, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/session/Session.php on line 623

Deprecated: Return type of MediaWiki\Session\Session::rewind() should either be compatible with Iterator::rewind(): void, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/session/Session.php on line 617

Deprecated: Return type of MediaWiki\Session\Session::offsetExists($offset) should either be compatible with ArrayAccess::offsetExists(mixed $offset): bool, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/session/Session.php on line 633

Deprecated: Return type of & MediaWiki\Session\Session::offsetGet($offset) should either be compatible with ArrayAccess::offsetGet(mixed $offset): mixed, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/session/Session.php on line 646

Deprecated: Return type of MediaWiki\Session\Session::offsetSet($offset, $value) should either be compatible with ArrayAccess::offsetSet(mixed $offset, mixed $value): void, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/session/Session.php on line 656

Deprecated: Return type of MediaWiki\Session\Session::offsetUnset($offset) should either be compatible with ArrayAccess::offsetUnset(mixed $offset): void, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/session/Session.php on line 661

Deprecated: Message implements the Serializable interface, which is deprecated. Implement __serialize() and __unserialize() instead (or in addition, if support for old PHP versions is necessary) in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/language/Message.php on line 161

Deprecated: MapCacheLRU implements the Serializable interface, which is deprecated. Implement __serialize() and __unserialize() instead (or in addition, if support for old PHP versions is necessary) in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/MapCacheLRU.php on line 38

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: RawMessage implements the Serializable interface, which is deprecated. Implement __serialize() and __unserialize() instead (or in addition, if support for old PHP versions is necessary) in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/RawMessage.php on line 35

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: Creation of dynamic property Parser::$scribunto_engine is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/extensions/Scribunto/includes/common/Hooks.php on line 81

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Warning: Cannot modify header information - headers already sent by (output started at /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/session/PHPSessionHandler.php:35) in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/changes/ChannelFeed.php on line 95

Warning: Cannot modify header information - headers already sent by (output started at /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/session/PHPSessionHandler.php:35) in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/changes/ChannelFeed.php on line 100

Warning: Cannot modify header information - headers already sent by (output started at /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/session/PHPSessionHandler.php:35) in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/WebResponse.php on line 74

Warning: Cannot modify header information - headers already sent by (output started at /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/session/PHPSessionHandler.php:35) in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/WebResponse.php on line 74

Warning: Cannot modify header information - headers already sent by (output started at /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/session/PHPSessionHandler.php:35) in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/WebResponse.php on line 74

Warning: Cannot modify header information - headers already sent by (output started at /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/session/PHPSessionHandler.php:35) in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/WebResponse.php on line 74

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578
http://www.mysolutions.tecnico.ulisboa.pt//mysolutions/wiki/index.php?action=history&feed=atom&title=Plano_inclinado%2C_Disco_vs_Anel 2025-08-18T21:38:02Z Histórico de edições para esta página nesta wiki MediaWiki 1.35.2
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http://www.mysolutions.tecnico.ulisboa.pt//wiki/index.php?title=Plano_inclinado,_Disco_vs_Anel&diff=558&oldid=prev 2015-10-28T11:48:55Z

<p></p> <table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="pt"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Revisão anterior</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revisão das 11h48min de 28 de outubro de 2015</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l50" >Linha 50:</td> <td colspan="2" class="diff-lineno">Linha 50:</td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;div class=&quot;mw-collapsible-content&quot;&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;div class=&quot;mw-collapsible-content&quot;&gt;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>\( \<del class="diffchange diffchange-inline">alpha = </del>\<del class="diffchange diffchange-inline">frac{a}{R} = - </del>\<del class="diffchange diffchange-inline">frac</del>{<del class="diffchange diffchange-inline">m_1 </del>- <del class="diffchange diffchange-inline">m_2</del>}<del class="diffchange diffchange-inline">{m_1 + m_2 + </del>\<del class="diffchange diffchange-inline">frac</del>{<del class="diffchange diffchange-inline">m_R</del>}{2<del class="diffchange diffchange-inline">}} \frac{g}{R</del>} \)</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">*</ins>\( <ins class="diffchange diffchange-inline">a_{anel} </ins>\<ins class="diffchange diffchange-inline">simeq 1.27 </ins>\<ins class="diffchange diffchange-inline">) m s</ins>\<ins class="diffchange diffchange-inline">(^</ins>{-<ins class="diffchange diffchange-inline">2</ins>}\<ins class="diffchange diffchange-inline">)</ins></div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">*\( a_</ins>{<ins class="diffchange diffchange-inline">disco</ins>} <ins class="diffchange diffchange-inline">\simeq 1.69 \) m s\(^</ins>{<ins class="diffchange diffchange-inline">-</ins>2}\)</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;/div&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;/div&gt;</div></td></tr> <tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l61" >Linha 61:</td> <td colspan="2" class="diff-lineno">Linha 62:</td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;div class=&quot;mw-collapsible-content&quot;&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;div class=&quot;mw-collapsible-content&quot;&gt;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>\( \<del class="diffchange diffchange-inline">alpha = </del>\<del class="diffchange diffchange-inline">frac</del>{<del class="diffchange diffchange-inline">a</del>}{<del class="diffchange diffchange-inline">R</del>} <del class="diffchange diffchange-inline">= - </del>\<del class="diffchange diffchange-inline">frac{m_1 - m_2}{m_1 + m_2 + </del>\<del class="diffchange diffchange-inline">frac</del>{<del class="diffchange diffchange-inline">m_R}{2}</del>} \<del class="diffchange diffchange-inline">frac{g}{R} </del>\)</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">Para o anel:</ins></div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">*</ins>\(<ins class="diffchange diffchange-inline">E_{c t} \simeq 0.51</ins>\<ins class="diffchange diffchange-inline">) J</ins></div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">*</ins>\<ins class="diffchange diffchange-inline">(E_</ins>{<ins class="diffchange diffchange-inline">c r</ins>} <ins class="diffchange diffchange-inline">\simeq 0.51\) J</ins></div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">Para o disco:</ins></div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">*\(E_</ins>{<ins class="diffchange diffchange-inline">c t</ins>} \<ins class="diffchange diffchange-inline">simeq 0.68\) J</ins></div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">*</ins>\<ins class="diffchange diffchange-inline">(E_</ins>{<ins class="diffchange diffchange-inline">c r</ins>} \<ins class="diffchange diffchange-inline">simeq 0.34</ins>\) <ins class="diffchange diffchange-inline">J</ins></div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;/div&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;/div&gt;</div></td></tr> <tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l72" >Linha 72:</td> <td colspan="2" class="diff-lineno">Linha 79:</td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;div class=&quot;mw-collapsible-content&quot;&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;div class=&quot;mw-collapsible-content&quot;&gt;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">\( \alpha = \frac{a}{R} = - \frac{m_1 - m_2}{m_1 + m_2 + \frac{m_R}{2}} \frac{g}{R} \)</del></div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">O que chega primeiro é o disco pois, uma vez que tem um momento de inércia mais pequeno, consegue que uma percentagem maior da energia potencial gravítica se transforme em energia cinética de translação.</ins></div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;/div&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;/div&gt;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;/div&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;/div&gt;</div></td></tr> </table>

Ist172693
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http://www.mysolutions.tecnico.ulisboa.pt//wiki/index.php?title=Plano_inclinado,_Disco_vs_Anel&diff=557&oldid=prev 2015-10-28T11:26:06Z

<p></p> <table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="pt"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Revisão anterior</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revisão das 11h26min de 28 de outubro de 2015</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l20" >Linha 20:</td> <td colspan="2" class="diff-lineno">Linha 20:</td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Um disco e um anel rodam sem deslizar por um plano inclinado, partindo ambos de uma altura \(h\). Considere as massas do anel e do disco iguais e \(m=200\) g, e os raios do anel e do disco iguais a \(r=10\) cm. O plano inclinado faz um ângulo de \(\theta = 15^º\) com a horizontal.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Um disco e um anel rodam sem deslizar por um plano inclinado, partindo ambos de uma altura \(h\). Considere as massas do anel e do disco iguais e \(m=200\) g, e os raios do anel e do disco iguais a \(r=10\) cm. O plano inclinado faz um ângulo de \(\theta = 15^º\) com a horizontal.</div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Considere \(g = 9.81 \) m s\(^{-2}\)</ins></div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Quais as forças que actuam no anel durante o movimento ao longo do plano? E no disco?</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Quais as forças que actuam no anel durante o movimento ao longo do plano? E no disco?</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l37" >Linha 37:</td> <td colspan="2" class="diff-lineno">Linha 38:</td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;div class=&quot;mw-collapsible-content&quot;&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;div class=&quot;mw-collapsible-content&quot;&gt;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>\( <del class="diffchange diffchange-inline">\alpha = \frac{a}</del>{<del class="diffchange diffchange-inline">R</del>} = <del class="diffchange diffchange-inline">- </del>\<del class="diffchange diffchange-inline">frac{m_1 - m_2}{m_1 + m_2 + </del>\<del class="diffchange diffchange-inline">frac{m_R}{</del>2<del class="diffchange diffchange-inline">}} </del>\<del class="diffchange diffchange-inline">frac</del>{<del class="diffchange diffchange-inline">g}{R</del>} \)</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">*</ins>\( <ins class="diffchange diffchange-inline">I_</ins>{<ins class="diffchange diffchange-inline">anel</ins>} = <ins class="diffchange diffchange-inline">0.002 </ins>\<ins class="diffchange diffchange-inline">) Kg m</ins>\<ins class="diffchange diffchange-inline">(^</ins>2\<ins class="diffchange diffchange-inline">)</ins></div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">*\( I_</ins>{<ins class="diffchange diffchange-inline">disco</ins>} <ins class="diffchange diffchange-inline">= 0.001 \) Kg m\(^2</ins>\)</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;/div&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;/div&gt;</div></td></tr> </table>

Ist172693
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http://www.mysolutions.tecnico.ulisboa.pt//wiki/index.php?title=Plano_inclinado,_Disco_vs_Anel&diff=556&oldid=prev 2015-10-28T11:20:17Z

<p></p> <table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="pt"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Revisão anterior</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revisão das 11h20min de 28 de outubro de 2015</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l9" >Linha 9:</td> <td colspan="2" class="diff-lineno">Linha 9:</td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*AUTOR: Ana Mourão</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*AUTOR: Ana Mourão</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*MATERIA PRINCIPAL: Momento de Inércia</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*MATERIA PRINCIPAL: Momento de Inércia</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*DESCRICAO: <del class="diffchange diffchange-inline">Máquina de Atwood com roldana</del></div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*DESCRICAO: <ins class="diffchange diffchange-inline">Plano inclinado, Disco vs Anel</ins></div></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*DIFICULDADE: <del class="diffchange diffchange-inline">*</del>**</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*DIFICULDADE: **</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*TEMPO MEDIO DE RESOLUCAO: 1200 [s]</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*TEMPO MEDIO DE RESOLUCAO: 1200 [s]</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*TEMPO MAXIMO DE RESOLUCAO: 2400 [s]</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*TEMPO MAXIMO DE RESOLUCAO: 2400 [s]</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*PALAVRAS CHAVE: <del class="diffchange diffchange-inline">Máquina, atwood, roldana, momento</del>, inércia, rotação, corpo, rígido</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*PALAVRAS CHAVE: <ins class="diffchange diffchange-inline">Momento</ins>, inércia, rotação, corpo, rígido<ins class="diffchange diffchange-inline">, plano, inclinado, angular, disco, anél</ins></div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;/div&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;/div&gt;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;/div&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;/div&gt;</div></td></tr> <tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l26" >Linha 26:</td> <td colspan="2" class="diff-lineno">Linha 26:</td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;div class=&quot;mw-collapsible-content&quot;&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;div class=&quot;mw-collapsible-content&quot;&gt;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">\( \alpha = \frac{</del>a<del class="diffchange diffchange-inline">}{R} = - \frac{m_1 - m_2}{m_1 + m_2 + \frac{m_R}{2}} \frac{g}{R} \)</del></div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">As forças que actuam no anel são iguais às que actuam no disco, nomeadamente o seu peso, </ins>a <ins class="diffchange diffchange-inline">força de atrito e a reacção normal da superfície.</ins></div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;/div&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;/div&gt;</div></td></tr> </table>

Ist172693
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http://www.mysolutions.tecnico.ulisboa.pt//wiki/index.php?title=Plano_inclinado,_Disco_vs_Anel&diff=552&oldid=prev 2015-10-27T14:41:18Z

<p></p> <table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="pt"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Revisão anterior</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revisão das 14h41min de 27 de outubro de 2015</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l19" >Linha 19:</td> <td colspan="2" class="diff-lineno">Linha 19:</td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[File:MO_plano_inclinado_roda_e_anel_esquema.png|thumb|Plano inclinado com roda e anel]]</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[File:MO_plano_inclinado_roda_e_anel_esquema.png|thumb|Plano inclinado com roda e anel]]</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Um disco e um anel rodam sem deslizar por um plano inclinado, partindo ambos de uma altura \(h\). Considere as massas do anel e do disco iguais e \(m=200\) g, e os raios do anel e do disco iguais a \(r=10\) cm. O plano inclinado faz um ângulo de \(15^º\) com a horizontal.</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Um disco e um anel rodam sem deslizar por um plano inclinado, partindo ambos de uma altura \(h\). Considere as massas do anel e do disco iguais e \(m=200\) g, e os raios do anel e do disco iguais a \(r=10\) cm. O plano inclinado faz um ângulo de \(<ins class="diffchange diffchange-inline">\theta = </ins>15^º\) com a horizontal.</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Quais as forças que actuam no anel durante o movimento ao longo do plano? E no disco?</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Quais as forças que actuam no anel durante o movimento ao longo do plano? E no disco?</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> </table>

Ist172693
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http://www.mysolutions.tecnico.ulisboa.pt//wiki/index.php?title=Plano_inclinado,_Disco_vs_Anel&diff=551&oldid=prev 2015-10-27T14:37:11Z

<p></p> <table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="pt"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Revisão anterior</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revisão das 14h37min de 27 de outubro de 2015</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l17" >Linha 17:</td> <td colspan="2" class="diff-lineno">Linha 17:</td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;/div&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;/div&gt;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>[[File:<del class="diffchange diffchange-inline">MO_maquina_de_atwood_esquema</del>.png|thumb|<del class="diffchange diffchange-inline">Máquina de Atwood</del>]]</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>[[File:<ins class="diffchange diffchange-inline">MO_plano_inclinado_roda_e_anel_esquema</ins>.png|thumb|<ins class="diffchange diffchange-inline">Plano inclinado com roda e anel</ins>]]</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Um disco e um anel rodam sem deslizar por um plano inclinado, partindo ambos de uma altura \(h\). Considere as massas do anel e do disco iguais e \(m=200\) g, e os raios do anel e do disco iguais a \(r=10\) cm. O plano inclinado faz um ângulo de \(15^º\) com a horizontal.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Um disco e um anel rodam sem deslizar por um plano inclinado, partindo ambos de uma altura \(h\). Considere as massas do anel e do disco iguais e \(m=200\) g, e os raios do anel e do disco iguais a \(r=10\) cm. O plano inclinado faz um ângulo de \(15^º\) com a horizontal.</div></td></tr> </table>

Ist172693
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Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

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Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578
http://www.mysolutions.tecnico.ulisboa.pt//wiki/index.php?title=Plano_inclinado,_Disco_vs_Anel&diff=548&oldid=prev 2015-10-27T14:30:05Z

<p>Criou a página com &quot;&lt;div class=&quot;toccolours mw-collapsible mw-collapsed&quot; style=&quot;width:420px&quot;&gt; &#039;&#039;&#039;Metadata&#039;&#039;&#039; &lt;div class=&quot;mw-collapsible-content&quot;&gt; *CONTEXTO : Primeiro ciclo universitário *AREA...&quot;</p> <p><b>Página nova</b></p><div>&lt;div class=&quot;toccolours mw-collapsible mw-collapsed&quot; style=&quot;width:420px&quot;&gt;<br /> &#039;&#039;&#039;Metadata&#039;&#039;&#039;<br /> &lt;div class=&quot;mw-collapsible-content&quot;&gt;<br /> *CONTEXTO : Primeiro ciclo universitário<br /> *AREA: Física<br /> *DISCIPLINA: Mecânica e ondas<br /> *ANO: 1<br /> *LINGUA: pt<br /> *AUTOR: Ana Mourão<br /> *MATERIA PRINCIPAL: Momento de Inércia<br /> *DESCRICAO: Máquina de Atwood com roldana<br /> *DIFICULDADE: ***<br /> *TEMPO MEDIO DE RESOLUCAO: 1200 [s]<br /> *TEMPO MAXIMO DE RESOLUCAO: 2400 [s]<br /> *PALAVRAS CHAVE: Máquina, atwood, roldana, momento, inércia, rotação, corpo, rígido<br /> &lt;/div&gt;<br /> &lt;/div&gt;<br /> <br /> [[File:MO_maquina_de_atwood_esquema.png|thumb|Máquina de Atwood]]<br /> <br /> Um disco e um anel rodam sem deslizar por um plano inclinado, partindo ambos de uma altura \(h\). Considere as massas do anel e do disco iguais e \(m=200\) g, e os raios do anel e do disco iguais a \(r=10\) cm. O plano inclinado faz um ângulo de \(15^º\) com a horizontal.<br /> * Quais as forças que actuam no anel durante o movimento ao longo do plano? E no disco?<br /> <br /> &lt;div class=&quot;toccolours mw-collapsible mw-collapsed&quot; style=&quot;width:260px&quot;&gt;<br /> &#039;&#039;&#039;Respostas&#039;&#039;&#039;<br /> &lt;div class=&quot;mw-collapsible-content&quot;&gt;<br /> <br /> \( \alpha = \frac{a}{R} = - \frac{m_1 - m_2}{m_1 + m_2 + \frac{m_R}{2}} \frac{g}{R} \)<br /> <br /> &lt;/div&gt;<br /> &lt;/div&gt;<br /> <br /> * Calcule os momentos de inércia do disco e do anel relativamente ao ponto que passa no centro de cada um e é perpendicular ao plano de rotação.<br /> <br /> &lt;div class=&quot;toccolours mw-collapsible mw-collapsed&quot; style=&quot;width:260px&quot;&gt;<br /> &#039;&#039;&#039;Respostas&#039;&#039;&#039;<br /> &lt;div class=&quot;mw-collapsible-content&quot;&gt;<br /> <br /> \( \alpha = \frac{a}{R} = - \frac{m_1 - m_2}{m_1 + m_2 + \frac{m_R}{2}} \frac{g}{R} \)<br /> <br /> &lt;/div&gt;<br /> &lt;/div&gt;<br /> <br /> * Calcule a aceleração do anel e a aceleração do disco durante este movimento.<br /> <br /> &lt;div class=&quot;toccolours mw-collapsible mw-collapsed&quot; style=&quot;width:260px&quot;&gt;<br /> &#039;&#039;&#039;Respostas&#039;&#039;&#039;<br /> &lt;div class=&quot;mw-collapsible-content&quot;&gt;<br /> <br /> \( \alpha = \frac{a}{R} = - \frac{m_1 - m_2}{m_1 + m_2 + \frac{m_R}{2}} \frac{g}{R} \)<br /> <br /> &lt;/div&gt;<br /> &lt;/div&gt;<br /> <br /> * Calcule a energia cinética de translação e a energia cinética de rotação do anel e do disco quando se deslocaram 2 metros ao longo do plano inclinado.<br /> <br /> &lt;div class=&quot;toccolours mw-collapsible mw-collapsed&quot; style=&quot;width:260px&quot;&gt;<br /> &#039;&#039;&#039;Respostas&#039;&#039;&#039;<br /> &lt;div class=&quot;mw-collapsible-content&quot;&gt;<br /> <br /> \( \alpha = \frac{a}{R} = - \frac{m_1 - m_2}{m_1 + m_2 + \frac{m_R}{2}} \frac{g}{R} \)<br /> <br /> &lt;/div&gt;<br /> &lt;/div&gt;<br /> <br /> * Qual dos dois (anel ou disco) chega primeiro ao fim do plano inclinado? Justifique.<br /> <br /> &lt;div class=&quot;toccolours mw-collapsible mw-collapsed&quot; style=&quot;width:260px&quot;&gt;<br /> &#039;&#039;&#039;Respostas&#039;&#039;&#039;<br /> &lt;div class=&quot;mw-collapsible-content&quot;&gt;<br /> <br /> \( \alpha = \frac{a}{R} = - \frac{m_1 - m_2}{m_1 + m_2 + \frac{m_R}{2}} \frac{g}{R} \)<br /> <br /> &lt;/div&gt;<br /> &lt;/div&gt;</div>

Ist172693
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