Question

A 390 g block is dropped onto a relaxed vertical spring that has a spring constant of k = 1.7 N/cm (see the figure). The block becomes attached to the spring and compresses the spring 14 cm before momentarily stopping. While the spring is being compressed, what work is done on the block by (a) the gravitational force on it and (b) the spring force? (c) What is the speed of the block just before it hits the spring? (Assume that friction is negligible.) (d) If the speed at impact is doubled, what is the maximum compression of the spring?

Answer 1

A)

The work done by gravity is the weight of the block times the distance the spring is compressed.

W_g=mgΔx

W_g=(0.390)(9.8)(0.14)

W_g= 0.535 J

the work done by gravity on the block is 0.535 J.

B)

The work done by the spring force is the negative potential energy stored in the spring when it is compressed.

W_s=−1/2*kΔx²

W_s=−1/2*(170)(0.14²)

W_s=−1.66J

Thus, the work done by the spring force is -1.66 J

C)

compression of the spring

x = 0.253 m or x= 25.3cm