a 3.5 kg block is accelerated from rest by a compressed spring of spring constant 640 N/m. The block leaves the spring at the springs relaxation length.The block then travels over a horizontal floor with coefficient of kinetic friction 0.25. The friction force stops the block in a distance D = 7.8 m.

Question

What is the increase in the thermal energy of the block+floor system?

Answer 1

All of the stored potential energy of the spring, (1/2)kX^2, winds up as heat. X is the spring compression, which they don't tell you.

You can compute the heat generated another way:
Friction work = M*g*Uk*X = 66.9 J

Answer 2

What is the original compression distance of the spring?
Thought it would be zero but that isn't right.

Answer 3

You can calculate the spring compression X from
66.9 J = (1/2)kX^2, but you don't need it. 66.9 J is the thermal energy increease.

They gave you more information than you need to answer the question

Answer 4

(a) W=F*X
W= u*Fn*X
=>M*g*uk*X -> 4.3kg*0.26*7.8m

(b) same as (a)

(c) Us=0.5*k*x^2
=> (a)=0.5*640N/m*x^2
figure out X from that

[very late but someone might benefit from this]