A shopping cart that has an inertia of 12 kg when empty is loaded with 28 kg of

Question

A shopping cart that has an inertia of 12 kg when empty is loaded with 28 kg of groceries. A child pushing the loaded cart loses control, and the cart rolls into a concrete lamppost, which sustains no damage. The cart is moving at 2.0 m/s when it strikes the lamppost, and the groceries all crash forward on impact, moving the center of mass forward by 0.10 m before everything comes to a halt.

Part A: What is the average force exerted by the post on the cart-groceries system?

Express your answer with the appropriate units. Enter positive value if the force is directed toward the front of the cart and negative value if the force is directed toward the rear of the cart.

Part B: What is the work done by the post on the system?

Part C: What is the change in kinetic energy of the system's center of mass?

Explanation / Answer

Total mass of the cart + grocery system, M = 12 + 28 = 40 kg
Total energy of the cart + grocery system before the impact = 1/2 Mv2
= 0.5 x 40 x 4 = 80 J
Total work done to stop the cart = F x distance
= F x 0.1

A)
d = 0.1 m
80 = F x 0.1
F = 800 N
Since it is directed toward the rear,
F = - 800 N

B)
Work done = Fd
= 800 x 0.1 = 80 J

C)
Change in kinetic energy = 1/2 Mv2 - 0
= 80 J - 0 = 80 J

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