Conservation of Energy Problem.

AI Thread Summary
When a cart slides down a frictionless ramp from height h and compresses a spring by distance D, the energy conservation equation is mgh = 0.5 k D^2. If the height is increased to 2h, the new equation becomes mg(2h) = 0.5 k (2D)^2. Solving this leads to the conclusion that the spring compresses by 4D. The initial calculations appear to be correct, confirming that the spring will compress four times the original distance. This demonstrates the relationship between gravitational potential energy and spring compression in a frictionless system.
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A cart, initially at rest, slides down a frictionless ramp onto a horizontal frictionless surface which is a distance h below the original position of the cart. It then collides with the free end of a relaxed horizontal spring, the other end of which is fixed to a wall. As a result the spring compresses a distance D.

Suppose now the initial height is changed to 2h. How far will the spring now compress?

A) sqrt(2)D
B) 2D
C) 4D

------

Initially: mgh = 0.5 k D^2

Suppose: mg(2h) = 0.5 k (2D)^2

So... the spring will now compress 4D. Is this correct?
 
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Maybe rework your math again?

And remember D is unknown.
 

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