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(c7p50) A 350-g block is dropped onto a vertical spring with spring constant k =

ID: 1331459 • Letter: #

Question

(c7p50) A 350-g block is dropped onto a vertical spring with spring constant k =140.0 N/m. The block becomes attached to the spring, and the spring compresses 53.5 cm before momentarily stopping. While the spring is being compressed, what work is done on the block by its weight?

While the spring is being compressed, what work is done on the block by the spring force?

What is the speed of the block just before it hits the spring? (Assume that friction is negligible.)

If the speed at impact is doubled, what is the maximum compression of the spring?

Explanation / Answer

a)

The work done by the force of gravity (acting on the block) is

W1 =mgx =0.350*9.8*0.535=1.83505 J

b)

The work done by the spring is

W2=-0.5kx^2 =-0.5*140*0.535^2 =-20.03575 J

c)

The speed vi of the block just before it hits the spring is found from the work-kinetic energy theorem

0-0.5mVi^2=W1+W2

=>Vi=sqrt[-2(W1+W2)/m]

Vi =sqrt(-2(1.83505-20.03575)/0.350]

Vi=10.2 m/s

d)

mgd-0.5kd^2=0.5mv^2

using this solve for d for twice the value of v