Projecting a block up to compress a spring

[zumi78878]

Homework Statement

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?

Homework Equations

The Attempt at a Solution

My Answer:

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? because the block moves up higher when it compresses the spring. Thanks

Professor's Answer:

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

 

[Doc Al]

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

Of course you do. Looks like your professor made an error.

 

[zumi78878]

Of course you do. Looks like your professor made an error.

thanks a lot.