# Projecting a block up to compress a spring!

1. Dec 7, 2012

### zumi78878

1. The problem statement, all variables and given/known data

A spring( k=200 n/m) is fixed at the top of a frictionless plane inclined at angle θ=40 degrees . A 1.0 kg block is projected up the plane from an initial position that is distance d=0.60m from the end of the relaxed spring with an initial kinetic energy of 16J.

a) what is the kinetic energy of the block at the instant it has compressed the spring 0.20m?

2. Relevant equations

3. The attempt at a solution

Et1 = Et2

Ek1 = Et1 = 16J

Et2 = Ek2 +Eg2 + Es2
16J = Ek2 + (1)(9.8)(0.6 +0.2)(sin40°) + (1/2)(0.2)(0.2)2
16J = Ek2 + 5.04J + 4J
Ek2 = 6.96J

My question is: do we have to account for the increase in gravitational potential when the block compresses the spring? cuz the block moves up higher when it compresses the spring. Thanks

Ug = mgh
= 1(9.8)0.6 sin 40
= 3.80 J
Us = ½ k Δx2
= ½ 200 (0.2)2
= 4 J
And we have
Total Energy before = Total Energy after
K0 + Ug0 + Us0 = K + Ug + Us
16 + 0 + 0 = K + 3.8 + 4
K = 8.2 J

2. Dec 7, 2012