Chapter 2: Q 875865-2-3 (page 81)

$Y o u o b s e r v e t h r e e c a r t s m o v i n g t o t h e l e f t . C a r t A m o v e s t o t h e l e f t a t n e a r l y c o n s \tan t s p e e d . C a r t B m o v e s t o t h e l e f t, g r a d u a l l y s p e e d i n g u p . C a r t C m o v e s t o t h e l e f t, g r a d u a l l y s l o w i n g d o w n . W h i c h c a r t o r c a r t s, i f a n y, e x p e r i e n c e a n e t f o r c e t o t h e l e f t ?$

Short Answer

Expert verified

Thus, the Cart ' $B$ ' is the cart that is being pushed to the left by the net force.

Step by step solution

Definition of net force

The net force, also known as the resultant force, is the sum of all forces acting on an item at the same time.

Find that when there is a net force to the left, whichever cart or carts are it?

$C a r t' A' a c c e l e r a t e s t o t h e l e f t a t a n e a r - c o n s \tan t r a t e . C a r t' B' a c c e l e r a t e s a s i t a d v a n c e s t o t h e l e f t . C a r t ‘ C' m o v e s t o t h e l e f t, s w o o p i n g d o w n g r a d u a l l y . T h e n e t f o r c e a c t i n g o n a n o b j e c t m o v i n g a t c o n s \tan t s p e e d i s z e r o, h e n c e t h e r e i s n o n e t f o r c e a c t i n g o n c a r t' A' t o w a r d t h e l e f t . W h e n t h e i t e m' s v e l o c i t y a n d f o r c e a r e i n t h e s a m e d i r e c t i o n, t h e o b j e c t w i l l a c c e l e r a t e . B e c a u s e t h e C a r t B i s s p e e d i n g u p a n d t r a v e l l i n g t o t h e l e f t, t h e r e i s a n e t f o r c e o p e r a t i n g o n t h e c a r t' B' t o t h e l e f t . W h e n t h e v e l o c i t y a n d f o r c e d i r e c t i o n s a r e o p p o s i t e, t h e i t e m s l o w s d o w n . B e c a u s e t h e c a r t C i s s l o w i n g d o w n a n d t r a v e l l i n g t o t h e l e f t, t h e r e i s a n e t f o r c e o p e r a t i n g o n t h e c a r t' C' t o t h e r i g h t .$ uncaught exception: Invalid chunk

in file: /var/www/html/integration/lib/com/wiris/plugin/impl/HttpImpl.class.php line 68
#0 /var/www/html/integration/lib/php/Boot.class.php(769): com_wiris_plugin_impl_HttpImpl_1(Object(com_wiris_plugin_impl_HttpImpl), NULL, 'http://www.wiri...', 'Invalid chunk') #1 /var/www/html/integration/lib/haxe/Http.class.php(532): _hx_lambda->execute('Invalid chunk') #2 /var/www/html/integration/lib/php/Boot.class.php(769): haxe_Http_5(true, Object(com_wiris_plugin_impl_HttpImpl), Object(com_wiris_plugin_impl_HttpImpl), Array, Object(haxe_io_BytesOutput), true, 'Invalid chunk') #3 /var/www/html/integration/lib/com/wiris/plugin/impl/HttpImpl.class.php(30): _hx_lambda->execute('Invalid chunk') #4 /var/www/html/integration/lib/haxe/Http.class.php(444): com_wiris_plugin_impl_HttpImpl->onError('Invalid chunk') #5 /var/www/html/integration/lib/haxe/Http.class.php(458): haxe_Http->customRequest(true, Object(haxe_io_BytesOutput), Object(sys_net_Socket), NULL) #6 /var/www/html/integration/lib/com/wiris/plugin/impl/HttpImpl.class.php(43): haxe_Http->request(true) #7 /var/www/html/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(268): com_wiris_plugin_impl_HttpImpl->request(true) #8 /var/www/html/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(307): com_wiris_plugin_impl_RenderImpl->showImage('a7e34b9a1d77800...', NULL, Object(PhpParamsProvider)) #9 /var/www/html/integration/createimage.php(17): com_wiris_plugin_impl_RenderImpl->createImage(' $" width="0" height="0" role="math"> C a r t' A' a c c e l e r a t e s t o t h e l e f t a t a n e a r - c o n s \tan t r a t e . C a r t' B' a c c e l e r a t e s a s i t a d v a n c e s t o t h e l e f t . C a r t ‘ C' m o v e s t o t h e l e f t, s w o o p i n g d o w n g r a d u a l l y . T h e n e t f o r c e a c t i n g o n a n o b j e c t m o v i n g a t c o n s \tan t s p e e d i s z e r o, h e n c e t h e r e i s n o n e t f o r c e a c t i n g o n c a r t' A' t o w a r d t h e l e f t . W h e n t h e i t e m' s v e l o c i t y a n d f o r c e a r e i n t h e s a m e d i r e c t i o n, t h e o b j e c t w i l l a c c e l e r a t e . B e c a u s e t h e C a r t B i s s p e e d i n g u p a n d t r a v e l l i n g t o t h e l e f t, t h e r e i s a n e t f o r c e o p e r a t i n g o n t h e c a r t' B' t o t h e l e f t . W h e n t h e v e l o c i t y a n d f o r c e d i r e c t i o n s a r e o p p o s i t e, t h e i t e m s l o w s d o w n . B e c a u s e t h e c a r t C i s s l o w i n g d o w n a n d t r a v e l l i n g t o t h e l e f t, t h e r e i s a n e t f o r c e o p e r a t i n g o n t h e c a r t' C' t o t h e r i g h t .$ uncaught exception: Invalid chunk

in file: /var/www/html/integration/lib/com/wiris/plugin/impl/HttpImpl.class.php line 68
#0 /var/www/html/integration/lib/php/Boot.class.php(769): com_wiris_plugin_impl_HttpImpl_1(Object(com_wiris_plugin_impl_HttpImpl), NULL, 'http://www.wiri...', 'Invalid chunk') #1 /var/www/html/integration/lib/haxe/Http.class.php(532): _hx_lambda->execute('Invalid chunk') #2 /var/www/html/integration/lib/php/Boot.class.php(769): haxe_Http_5(true, Object(com_wiris_plugin_impl_HttpImpl), Object(com_wiris_plugin_impl_HttpImpl), Array, Object(haxe_io_BytesOutput), true, 'Invalid chunk') #3 /var/www/html/integration/lib/com/wiris/plugin/impl/HttpImpl.class.php(30): _hx_lambda->execute('Invalid chunk') #4 /var/www/html/integration/lib/haxe/Http.class.php(444): com_wiris_plugin_impl_HttpImpl->onError('Invalid chunk') #5 /var/www/html/integration/lib/haxe/Http.class.php(458): haxe_Http->customRequest(true, Object(haxe_io_BytesOutput), Object(sys_net_Socket), NULL) #6 /var/www/html/integration/lib/com/wiris/plugin/impl/HttpImpl.class.php(43): haxe_Http->request(true) #7 /var/www/html/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(268): com_wiris_plugin_impl_HttpImpl->request(true) #8 /var/www/html/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(307): com_wiris_plugin_impl_RenderImpl->showImage('a7e34b9a1d77800...', NULL, Object(PhpParamsProvider)) #9 /var/www/html/integration/createimage.php(17): com_wiris_plugin_impl_RenderImpl->createImage(' $" width="0" height="0" role="math"> C a r t' A' a c c e l e r a t e s t o t h e l e f t a t a n e a r - c o n s \tan t r a t e . C a r t' B' a c c e l e r a t e s a s i t a d v a n c e s t o t h e l e f t . C a r t ‘ C' m o v e s t o t h e l e f t, s w o o p i n g d o w n g r a d u a l l y . T h e n e t f o r c e a c t i n g o n a n o b j e c t m o v i n g a t c o n s \tan t s p e e d i s z e r o, h e n c e t h e r e i s n o n e t f o r c e a c t i n g o n c a r t' A' t o w a r d t h e l e f t . W h e n t h e i t e m' s v e l o c i t y a n d f o r c e a r e i n t h e s a m e d i r e c t i o n, t h e o b j e c t w i l l a c c e l e r a t e . B e c a u s e t h e C a r t B i s s p e e d i n g u p a n d t r a v e l l i n g t o t h e l e f t, t h e r e i s a n e t f o r c e o p e r a t i n g o n t h e c a r t' B' t o t h e l e f t . W h e n t h e v e l o c i t y a n d f o r c e d i r e c t i o n s a r e o p p o s i t e, t h e i t e m s l o w s d o w n . B e c a u s e t h e c a r t C i s s l o w i n g d o w n a n d t r a v e l l i n g t o t h e l e f t, t h e r e i s a n e t f o r c e o p e r a t i n g o n t h e c a r t' C' t o t h e r i g h t .$ uncaught exception: Invalid chunk

in file: /var/www/html/integration/lib/com/wiris/plugin/impl/HttpImpl.class.php line 68
#0 /var/www/html/integration/lib/php/Boot.class.php(769): com_wiris_plugin_impl_HttpImpl_1(Object(com_wiris_plugin_impl_HttpImpl), NULL, 'http://www.wiri...', 'Invalid chunk') #1 /var/www/html/integration/lib/haxe/Http.class.php(532): _hx_lambda->execute('Invalid chunk') #2 /var/www/html/integration/lib/php/Boot.class.php(769): haxe_Http_5(true, Object(com_wiris_plugin_impl_HttpImpl), Object(com_wiris_plugin_impl_HttpImpl), Array, Object(haxe_io_BytesOutput), true, 'Invalid chunk') #3 /var/www/html/integration/lib/com/wiris/plugin/impl/HttpImpl.class.php(30): _hx_lambda->execute('Invalid chunk') #4 /var/www/html/integration/lib/haxe/Http.class.php(444): com_wiris_plugin_impl_HttpImpl->onError('Invalid chunk') #5 /var/www/html/integration/lib/haxe/Http.class.php(458): haxe_Http->customRequest(true, Object(haxe_io_BytesOutput), Object(sys_net_Socket), NULL) #6 /var/www/html/integration/lib/com/wiris/plugin/impl/HttpImpl.class.php(43): haxe_Http->request(true) #7 /var/www/html/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(268): com_wiris_plugin_impl_HttpImpl->request(true) #8 /var/www/html/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(307): com_wiris_plugin_impl_RenderImpl->showImage('a7e34b9a1d77800...', NULL, Object(PhpParamsProvider)) #9 /var/www/html/integration/createimage.php(17): com_wiris_plugin_impl_RenderImpl->createImage(' $" width="0" height="0" role="math">$

- Cart 'A' accelerates to the left at a near-constant rate.

- Cart 'B' accelerates as it advances to the left.

- Cart 'C' moves to the left, swooping down gradually.

- The net force acting on an object moving at constant speed is zero, hence there is no net force acting on cart $' \ m a t h r m {A}$ ' toward the left.

- When the item's velocity and force are in the same direction, the object will accelerate.

- Because the Cart B is speeding up and travelling to the left, there is a net force operating on the cart ' $B$ ' to the left.

- When the velocity and force directions are opposite, the item slows down.

- Because the cart C is slowing down and travelling to the left, there is a net force operating on the cart ' $C$ ' to the right.

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Short Answer

Step by step solution

Definition of net force

Find that when there is a net force to the left, whichever cart or carts are it?

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Youobservethreecartsmovingtotheleft.CartAmovestotheleftatnearlyconstantspeed.CartBmovestotheleft,graduallyspeedingup.CartCmovestotheleft,graduallyslowingdown.Whichcartorcarts,ifany,experienceanetforcetotheleft?

Short Answer

Step by step solution

Definition of net force

Find that when there is a net force to the left, whichever cart or carts are it?

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Engineering Physics

Solid State Physics

Fluids

Linear Momentum

Nuclear Physics

Atoms and Radioactivity

Study anywhere. Anytime. Across all devices.