A pallet slides over a loading-dock floor. A force sensor reads the kinetic friction on it: 30 N. A scale check gives the normal force: 150 N.
Nobody knows this surface pair's coefficient yet. How do you get it?
Well, the same equation holds the answer: f = μN. When a question hands you f and one other quantity, you rearrange for the one you need.
To find the coefficient, make μ the subject.
Start from f = μN. Divide both sides by N: f/N = μ. So μ = f/N.
To find the normal force, make N the subject.
Start from f = μN. Divide both sides by μ: f/μ = N. So N = f/μ.
A quick unit check: f and N are both in newtons, so f/N is a newton divided by a newton. The units cancel, which is why μ has no unit.
For the pallet: μ_k = f_k/N = 30/150 = 0.20. This surface pair's kinetic coefficient is 0.20.
A sliding pallet feels 30 N of kinetic friction under a 150 N normal force. Calculate μ_k for the surface pair.
Write down the values in the question:
f_k = 30 N
N = 150 N
μ_k = ?
Write down the equation:
f_k = μ_k N
Make μ_k the subject:
μ_k = f_k/N
Substitute in the values:
μ_k = 30 ÷ 150
Simplify:
μ_k = 0.20
The pair's kinetic coefficient is 0.20. It has no unit.
A sliding crate feels 54 N of kinetic friction under a 135 N normal force. Enter μ_k for the surface pair.
A sliding cart feels 72 N of kinetic friction, and the surface pair has μ_k = 0.45. Calculate the normal force on the cart.
Write down the values in the question:
f_k = 72 N
μ_k = 0.45
N = ?
Write down the equation:
f_k = μ_k N
Make N the subject:
N = f_k/μ_k
Substitute in the values:
N = 72 ÷ 0.45
Simplify:
N = 160 N
The normal force on the cart is 160 N.
A sliding bin feels 48 N of kinetic friction, and the surface pair has μ_k = 0.24. Enter the normal force on the bin in N.
The same two rearrangements work at the verge of sliding. There the friction equals the maximum static friction, μ_s N, so the coefficient they recover is μ_s.
A mat sits on the verge of sliding when the friction on it reaches 66 N. The normal force is 120 N. Enter μ_s for the surface pair.
A sliding dolly feels 45 N of kinetic friction under a 250 N normal force. Enter μ_k for the surface pair.
A sliding cooler feels 91 N of kinetic friction, and the surface pair has μ_k = 0.35. Enter the normal force on the cooler in N.
A generator crate sits on the verge of sliding when the friction on it reaches 117 N. The surface pair has μ_s = 0.65. Enter the normal force on the crate in N.