On a clear sunny day (no air friction), a person on a cart (combined mass m of 7

Question

On a clear sunny day (no air friction), a person on a cart (combined mass m of 70kg) begins at the top of a hill 10m high traveling at 2 m/s, and coasts to the bottom along a frictionless surface route. It then bumps into a spring putting the cart to a halt. Experiment shows that a force of 10 N compresses the spring by 0.02 m.

(a) Find the speed of the cart at the bottom of the hill.

v=14.1 m/s

(b) By what length is the spring compressed after the collision?

I'm stuck on question b. I'm guessing that we can use 1/2mv2 = 1/2kx2 ?

This comes out to 5.3m though, and that would be a very large spring. Please help?

Explanation / Answer

Your equation was right, it's conservation of energy, but the answer is 3.73m. Think about this: 10 Newtons is about 2.24 pounds, right? So that gives a k of 500N/m, but more importantly, 2.24 pounds is a TINY force compared to 150 lbs moving at 14m/s (about 31 miles an hour). Darn right it's a big spring just to handle that, and darn right that it would compress way more than if 2.25 lbs pressed it =) Make sense?

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