# Homework Help: Springs, thermal energy

1. Nov 5, 2014

### PhysicsMan999

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

1. A block with mass m = 1.46 kg is attached to a spring with spring constant k = 52.0 N/m and negligible mass. The coefficient of kinetic friction between the block and the table is µk = 0.349. The block is displaced from its equilibrium position to the left by 0.203 m and released from rest. Calculate the block's displacement when it first comes to rest again.

2. Relevant equations
Thermal energy=Ff * x
Us= 0.5kx^2

3. The attempt at a solution
Ff= MuN= (1.46 x 9.8)(0.349)=4.99 N
Us(initial)= 0.5(52)(-0.203^2)
Us(final)= 0.5(52)Xfinal
initial thermal and spring energy=final thermal and spring energy
(4.99)(-0.203)+26(0.203^2)=4.99x +26x^2
i tried to solve it, plugged it into a quadratic equation but am still getting the wrong answer.

Any ideas on what im doing wrong? Thanks!

2. Nov 5, 2014

### Staff: Mentor

Instead of calling it thermal energy, call it energy dissipated by friction. Note that x is the distance traveled by the mass.

OK. Here x is the displacement from equilibrium. Careful with notation!

Careful! You start and end with pure spring potential energy, the difference being the energy lost to friction.

3. Nov 5, 2014

### PhysicsMan999

Okay, so now I got:
4.99 (0.203+x)=26x^2-26(0.203^2)
plugged everything in and still didn't get the correct answer.

4. Nov 5, 2014

### Staff: Mentor

The two terms on the right hand side are in the wrong order. You want initial U minus final U.

5. Nov 5, 2014

### PhysicsMan999

Okay awesome! Thank you very much haha I had been going at this one for a good 45 minutes! I feel pretty confident I understand it now just needed a bit of guidance. Thanks again!