How do you calculate friction?

Question

I'm a sophomore and i need to calculate friction for a science experiment. Our lab was basically setting up a ramp and covering it with different materials to see how they affected the speed at which the hot wheel slid down it. Is there a formula I can use that will tell me how much friction the car experienced from the different surfaces?
Thank you!

Anonymous · Accepted Answer

draw a force diagram at the center of mass of the hot wheel

N: Normal force, the force of the incline pushing on the hotwheel
W: Weight of the hot wheel vertical pointing at center of earth
Ff: Force of friction, points in the opposite direction of motion parallel to the incline

Ignore all other effects.

N = Wcos(theta), theta the angle of incline
W = m*g, where m is mass of hot wheel
Ff = mu*N

The W force, we have to resolve it into two components:

Wy=Wcos(theta)
Wx=Wsin(theta)

Wy = N
Wx = Ff

so, Wx = muN = mu(Wy)

mu = Wx/Wy = Wsin(theta)/Wcos(theta) =

tan(theta)

So, we can calculate the coefficient of friction and therefore the frictional force operating on the car for each surface material by raising the incline SLOWLY to the point where the car begins to move

For this angle, theta1, tan(theta1) is the coefficient of STATIC friction.  The force of friction (static) the hot wheel overcame is 

Ff = mu*N =

tan(theta1)*(Wcos(theta1)) = Wsin(theta1) = Wx =

mgsin(theta1)

Secondly, start raising the incline SLOWLY and give the hot wheel the slightest tap to make it move at CONSTANT velocity, this theta2, tan(theta2) is the coefficient of KINETIC friction,

Ff = mu*N =

tan(theta2)*(Wcos(theta2)) = Wsin(theta2) = Wx =

mgsin(theta2)

for this angle, theta2 < theta1, will be the result which implies mu(kinetic) < mu(static) as we expect.

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How do you calculate friction?

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