Workenergy theorem problem
Hi everyone,
I have a problem that has me stumped and would appreciate some pointers as to where I am going wrong and maybe point me in the right direction for solving the problem.
The problem is in essence to use the "WorkEnergy Theorem" to find the coefficient of kinetic friction in a pulley system. Problem  We have an 8.00 kgblock on flat horizontal tabletop attached via a rope and pulley to a hanging 6.00 kgblock. The rope and pulley have negligible mass and the pulley is frictionless. Initially the 6.00 kgblock is moving downward and the 8.00 kgblock is moving to the right, both with a speed of 0.900 m/s. The blocks come to rest after moving 2.00 meters.
Use the WorkEnergy Theorem to calculate the coefficient of Kinetic friction between the 8.00 kgblock and the tabletop.
Basically I used the two main equations of the WorkEnergy Theorem to try to solve this. I first calculated the Work used in moving each block using the difference in kinetic energy over the distance travelled that is ...
W= K(2)  K(1) = 1/2 mv(2) sqrd  1/2 mv(1) sqrd for each block, and since both blocks come to rest, each of the equations above reduce to just 1/2mv(1) sqrd for each block.
I then took the difference in the values for the work each block expended to be the work expended by friction force.
Now since (for a constant force) WORK also equals Force x distance, I equated the Work difference above to be equal to the work expended by the Kinetic Friction Force.
And so Work difference = Work(Friction force)=Kinetic friction x distance moved.
From my calculations I got W(8kgblock)=3.24 J, W(6kgblock)=2.43 J giving difference of 0.81 J as the Work of Friction force.
Now since W=f x distance then f=w/distance =0.81/2.0 = 0.405 J
I now have a value for Friction force (f) and I then used the relationship Friction = Coefficient of Friction x Normal force .. in this case 0.405=coefficient x mg (Normal force for 8kgblock = weight of block ie. 'mg')
So we have coefficient = w/mg = 0.405/(8x9.8) = 0.405/78.8 = 0.02 .
However the answer at the back of the book gives coefficient = 0.786.
I have tried doing this in slightly different ways and the nearest I get to the correct answer is .. 0.75 (which if you notice is just the massratio between the 2 blocks) ???
So where have I gone wrong ?
can anyone help ?
