# Energy Conservation: Block & Spring

#### mrnastytime

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.

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#### Delphi51

Homework Helper
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.

"Energy Conservation: Block & Spring"

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