How do you determine the coefficient of kinetic friction?

Question

If a 20kg sled is being pulled across a horizontal surface at a constant velocity. The pulling force has a magnitud of 80N and is directed at an angle of 30 degrees above the horizontal.

Answer 1

The horizontal force component counteracts friction exactly

Fx=80*cos(30)

Normal force,
N=20*9.8-80*sin(30)

so
80*cos(30)=(20*9.8-80*sin(30))*u

solve for u
u=4*cos(30)/(9.8-4*sin(30))
u=0.44

j

Answer 2

You might use a variable angle incline with a block of wood on the incline, to determine the coefficient of static friction ms between the surface of the incline & the wood block. First find the angle of repose, qR. Then, as shown in class:

ms = tan qR.
Lower the incline so that it is horizontal.


Determine the largest value of m that can be hung on the string in the above configuration such that the above system remains static. By applying Newton's Second Law, you should be able to show that for the largest value of m, fs=fs,max=msMg, so that

ma = 0 = mg-msMg
=ms.
Thus, the theoretical value mt= msM should be compared to the experimental value me.

x 100
Next, add more weight to m and allow the system above to accelerate from rest. How much more weight should you add? Experiment & see if there is an optimal m that gives the best results! The coefficient of kinetic friction between the block & tabletop is mk. Allow the block to slide through a distance s in a time t. Adjust the parameters M, m, & s so that t can be read with some accuracy. Since the frictional force is nonconservative, the mechanical energy E = K+V of the system will not be conserved. Then the work done by friction is

Wf = -fks = -mkMgs = DE
Calculate the mechanical energy loss of the system: DE=Ef-E0

Calculate mk: mk=

Compare mk and ms. These are NOT the same, so you can NOT use a % error or % difference calculation. You must use a subjective type comparison. Which is theoretically larger? Did you find this to be the case?