Finding coefficient of kinetic friction on a track with a spring.

[lykwedontcare]

1. The problem statement

A 10 kg block is released from point A on a track ABCD. The track is frictionless except for the portion BC, of length 6 m. The block travels down the track and hits a spring of force constant k = 2250 N/m and compresses it a distance of 0.3 m from its equilibrium position before coming to rest momentarily. Determine the coefficient of kinetic friction between the track portion BC and the block.

***ADDITIONAL INFO

The height is 3 meters from the slope from A>B, while points B>C>D are completely horizontal.

The Attempt at a Solution

PE = KE

I find at point B the velocity of the block is 7.67 m/s. However I'm unable to figure out the next step.

I started with using KE = PE (spring) and found a difference of about 192 N, which I'm not sure has anything to do with the problem (the difference of the block slowing down?) but am not sure.

I do know the answer is 0.327, so I'm not after an answer, I simply just want to know how to do the problem.

Any direction would be appreciated, the more the better,
Thanks

 

[PhanthomJay]

1. The problem statement

A 10 kg block is released from point A on a track ABCD. The track is frictionless except for the portion BC, of length 6 m. The block travels down the track and hits a spring of force constant k = 2250 N/m and compresses it a distance of 0.3 m from its equilibrium position before coming to rest momentarily. Determine the coefficient of kinetic friction between the track portion BC and the block.

***ADDITIONAL INFO

The height is 3 meters from the slope from A>B, while points B>C>D are completely horizontal.

The Attempt at a Solution

PE = KE

I find at point B the velocity of the block is 7.67 m/s. However I'm unable to figure out the next step.

That value is correct, although this step is unnecessary.

I started with using KE = PE (spring) and found a difference of about 192 N, which I'm not sure has anything to do with the problem (the difference of the block slowing down?) but am not sure.

If there is a difference between the KE at point B and the PE at point D, then KE at B does not equal the PE at point D. As you note, 192 J (not N) of energy was 'lost' due to work done by friction. Use the definition of this Work to find the friction force and then the friction coefficient.

Note that you can take the start point at A and the end point at D, and get the same answer using the conservation of total energy law.

Also note that (KE + PE)_initial = (KE + PE)_final, only when conservative forces that do work (such as gravity and springs) are acting. When non-conservative forces (like friction) are acting, energy is transferred out of (or into) the system, due to the work done by such non-conservative forces.