Energy Conservation: Block & Spring

[mrnastytime]

Homework Statement

An object of mass M = 4 kg slides from rest a distance d = 4 m down a frictionless inclined plane where it encounters a spring. It compresses the spring a distance D = 1 m before stopping. The inclined plane makes an angle q = 20° with the horizontal.

Homework Equations

When the block just touches the spring, how much gravitational potential energy has it lost?
U=53.7 J
After the mass has fully compressed the spring, what is its total loss of gravitational potential energy?
U=67.1 J
What is the value of the spring constant?
k=??

The Attempt at a Solution

U=Ui-Uf
U=53.7-67.1=-13.4
U=(1/2)kx^2
k=2U/x^2
k=2(-13.4)/(5)^2
k=1.07?
the answer is wrong. am i suppose to use the conservation of mechanical energy? because i am lost.

 

[Delphi51]

It is wrong to take the difference between 53.7 and 67.1.
The ramp is frictionless, so all of the PE (67.1 J) goes into the spring energy.

 

[mrnastytime]

thank you, i figured it out.