In the figures at the right are shown two systems: a cart moving back and forth

Question

In the figures at the right are shown two systems: a cart moving back and forth on a spring and a swinging pendulum. The graph below can be used to show the back and forth displacement of both systems as a function of time as long as the pendulum is kept at a small angle. Three instants of time are marked on the graph: A, B, and C. A. Specify the directions of the quantities below for the cart by choosing one of the following symbols: L (Left), R (Right), U (Up), D (Down), 0 (Zero), or S (Some other direction). V_cart(at A): V_cart(at C): a_cart(at B): F^net_cart(at B): B. Specify the directions of the quantities below for the pendulum by choosing one of the following symbols: L (Left), R (Right), U (Up), D (Down), 0 (Zero), or S (Some other direction). v_pendulum(at A): v_pendulum(at C): a_pendulum(at B): F^net_cart(at B): C. If you knew m, could you calculate the length of the pendulum, L? If yes, explain how. If no, explain why not.

Explanation / Answer

a) at point A the displcement of the cart is maximum so it gets stopped momentarily to change its direction. So its velocity at point A is zero.

b) at B, the position is zero and the object has maximum velocity and it is moving along the positive x-axis i.e. right.

The acceleration is zero at point B as F = -kx and x =0. The net force also equals to zero.

c) The velocity of cart at C is also towards right as it has positive slope.

Same answers for pendulum also.

If we know the mass we cannot be determined the length. Actually length can affectes the timeperiod.

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