# Physics problem about μk and friction?

Assume the mass of the cart is m, and the mass hanging on the end of the string is M.

Suppose m = 2940 g and M = 784 g, and the cart accelerates at 0.43 m/s2. Find μk, the coefficient of kinetic friction between the cart and the track.

### 2 Answers

- RickBLv 78 years agoFavorite Answer
Hey Jake, next time you want help, explain the scenario a little better. Like: "A string connects a cart and a mass. The cart sits on a table, the string runs over a frictionless pulley, and the mass hangs down over the edge of the table."

I ASSUME that's the story here.

So to solve this, write separate "F=ma" equations for the cart and the mass, and then the rest is just algebra.

It's useful to start by writing down variables for the things you know and the things you don't know.

m = mass of cart = 2940 grams

M = mass of hanging mass = 784 grams

μk = coefficient of friction = ??

T = tension in the rope = ??

a = acceleration = 0.43 meters/s² (same number for both the cart and the hanging mass, since they're connected)

Write "F=ma" equation for cart:

The cart is pulled to the right(?) by the tension "T", and to the left by friction "mgμk". So the net force on the cart is "T−mgμk". So:

Net force = ma

T−mgμk = ma

Write "F=ma" equation for the hanging mass:

The mass is pulled up by the tension "T", and down by the force of gravity "Mg". So the net force on the mass is: "Mg−T". So:

Mg−T = Ma

Recap: You have these equations:

T−mgμk = ma

Mg−T = Ma

These are two equations in two unknowns ("T" and "μk"). Use the algebra of simultaneous equations to solve for μk, then plug in the given values for "m", "M", and "a".

- PearlsawmeLv 78 years ago
μmg = Mg - (M + m) a

μ 2.940*g = 0.784g – 3.724*0.43

μ 2.940*9.8 = 0.784*9.8 – 3.724*0.43

μ = 0.211

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Note that both M and m have the same acceleration a.

The gravitational force Mg pulls both the masses (M + m).

Frictional force μmg opposes this.

Net force acting on both of them is [Mg - μmg]

Acceleration = net force/mass = [Mg – μmg] / (M + m).

Solve for μ

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