Energy Conservation: Block & Spring

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

2. Relevant 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=??

3. 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

Homework Helper
3,407
10
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.
 
thank you, i figured it out.
 

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