A spring is at the bottom of a frictionless incline. When a box of mass M compre

Question

A spring is at the bottom of a frictionless incline. When a box of mass M compresses the spring distance x and is released from rest, the box slides distance d up the incline (measured from where the box is at rest).

a) Suppose a box of mass 2M is used to compress the spring distance x, and is released from rest. The distance the box will slide up the incline now will be

between d/2 and d

between d and 2d     

4d

d/2

d/4

2d

between d/2 and d/4

d

between 2d and 4d

b) Suppose a box of mass M is used to compress the spring distance 2x, and is released from rest. The distance the box will slide up the incline now (measured from where the box is at rest) is

between 4d and 2d

between d and d/2     

between d and 2d

4d

d/4

d

d/2

between d/4 and d/22d

Explanation / Answer

Spring Potential Energy = Gain in Gravitational Potential Energy
Given , Mass M compresses X m, and moves distance d.

So,
0.5 * kx^2 = M*g*h
h = 0.5 * kx^2 / M*g

(a)
In this Case,
Mass = 2M
Compression = x

0.5*k*x^2 = 2M*g*s
2*s = 0.5*k*x^2/M*g
2*s = h

Therefore, Distance box will slide up = d/2

(b)
In this case,
Mass = M
Compression = 2x

0.5*k*(2x)^2 = M*g*s
s = 0.5*k*4*x^2/M*g
s = 4 * 0.5*k*x^2/M*g
s = 4*h

Therfore, Distance box will slide up = 4*d

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