Due for labs meeting the week of March 25-27. A 5.0 kg block with a kinetic ener

Question

Due for labs meeting the week of March 25-27. A 5.0 kg block with a kinetic energy of 30 J is about to collide with a spring at its relaxed length. As the block compresses the spring, a frictional force between the block and floor acts on the block. The figure below gives the kinetic energy K(x) of the block and the potential energy U(x) of the spring as functions of position x of the block, as the spring is compressed. What is the increase in thermal energy of the block and floor when the block reaches position x = 0.10 m and the spring reaches its maximum compression? What is the speed of the block at x = 0.80 m?

Explanation / Answer

let the speed be v
conservation of momentum

5 * 3 + 10* 2 = 10 * 2.5 + 5* v

5v = 10

v = 2 m/s ----answer

b)
initial KE
0.5 * 5 * 9 + 0.5 * 10 * 4 = 42.5J
final KE
0.5 * 10 * 6.25 + 0.5* 5 * 4 = 41.25 J

loss of KE = 41.25 - 42.5 = 1.25 J ---ans

c)
5 * 3 + 10* 2 = 10 * 4 + 5* v1

v1 =-1
final KE
0.5 * 10 * 16 + 0.5* 5 * 1 = 82.5 J

change of KE
= 82.5 -42.5
= 40 J ---ans

d) not possible to add on KE after impact unless 10 kg is powered by itself.

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