How can we find Force of friction & coefficient of friction, if both are unknown?

Question

the distance, mass, and initial & final velocities are given!

Answer 1

KE1 = KE2 + Ff*d

Where

KE1 = kinetic energy of mass (m) at initial velocity (v1)
= 1/2 * m * v1^2
KE2 = kinetic energy at final velocity
= 1/2 * m * v2^2
Ff*d = work done on mass by friction force (Ff) over distance (d)

Ff = (KE1 - KE2) / d = normal force (Fn) * coefficient of friciton (mu) = Fn * mu

Fn = m * g = mass * gravity assuming Fn vector is vertical

Ff = 1/2 * m * (v1^2 - v2^2) / d = mu * m * g

Solve for Ff and mu knowing m, v1, v2, d, and g

Answer 2

Then you know the force because the difference in velocities is acceleration and F=MA

Answer 3

as we know the formulae :
F = mu x R
you asked that if MU and F are not given.
then the thing that remains is the resultant only.
so what we can do is to.
resolute the resultant(reaction) in its horizontal and vertical components.
thus deriving the F.
when F is known the MU can be got by applying in the formula.

Answer 4

Actually, F=MA

A=dv/dt =ds/dt*dv/ds =V*dv/ds
Therefore, F=M*V*dv/ds

From here integrate and then solve for F
S=integral sign
S2 & V2 = final state
S1&V1= initial state

S(F/ M)ds=S(V)dv

After integrating and solving for F
F=M/(S2-S1)*1/2*((V2)^2-(V1)^2)

Answer 5

It depends on the amount of KY used.