Question 1. Assume the mass of the cart is 517 g, and there is no friction anywhere

Suppose that the graph of force vs. time for a very unusual spring has only straight lines. The cart hits the spring at t = 3.00 s, so force F = 0 up to that point. Then, after t = 3.00 s, the force increases linearly until it reaches a maximum at Fmax = 8.25 N at time t = 3.66 s. Then the spring pushes the cart away, and the force decreases linearly until it goes back to F = 0 at time t = 4.07s.

a) Find the magnitude of the impulse exerted by the spring on the cart.

b) Find the speed of the cart just as it leaves the spring.

HINT: Assume the cart is at rest when the force exerted by the spring is a maximum.

c) For the graph described above: what does this graph tell you about the initial speed of the cart vo and the final speed of the cart vf

a) You cannot tell if vo is greater than or less than vf
b) vo must be less than vf
c) vo must be equal than vf
d) vo must be greater than vf

Question 2. Suppose a cart of mass m = 249 g is initial moving at speed v0 = 6.68 m/s. It strikes a spring attached to a fixed wall, comes to a stop, and bounces back at speed vf = 4.20 m/s. Assume the track is frictionless.

a) Find the magnitude of the impulse exerted by the spring on the cart.

b) Find the energy lost in this collision.

c) If the cart was in contact with the spring for 393 ms, find the magnitude of the average force exerted by the spring on the cart.

Question 3. Suppose the cart has mass m = 348 g, and it strikes the clay at speed vo = 1.77 m/s and comes to a dead stop. Assume the track is frictionless, and the clay is crushed inward by 2.04 cm.

a) Find the magnitude of the impulse exerted by the clay on the cart.

b) Find the magnitude of the average force exerted by the clay on the cart.

HINT: Use kinematics, assuming the force is constant during the impulse!

c) Find the time it took for the cart to come to rest while in contact with the clay.