A cart full of whistles and bells rolls down a slope (ignore friction) and impac

Question

A cart full of whistles and bells rolls down a slope (ignore friction) and impacts a spring at the base of the hill. The initial height and velocity of the car are given. By how much, x, does the cart compress the spring before coming to a complete stop? The spring rebounds and the cart is sent back up the hill. What is the maximum height, h_max of the cart above the ground when it comes to a momentary stop? In the absence of friction this exchange will just go on forever. But in the real world where does the cart end up?

Explanation / Answer

a)

using conservation of energy

spring potential energy due to compression = initial potential energy of cart

(0.5) k x2 = mgh

(0.5) (630) x2 = 3 x 9.8 x 1.2

x = 0.335 m

b)

using conservation of energy again

final potential energy of cart = spring potential energy due to compression

(0.5) k x2 = mgh

hmax = 1.2 m

c)

in real work , the cart will loose some energy and hence comes to a stop finally after moving several times

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