- #1

shepherd882

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## Homework Statement

A mass M1 is sliding across a table with coefficient of kinetic friction μk. A string is tied to this mass and runs over a pulley, drops vertically and is tied to another mass M2 which is falling. The pulley is connected to the table by a support. The pulley is a solid cylinder of mass M3, radius R. See figure. As the figure indicates, you may assume that the string is tied to the midpoint of both masses, that it runs horizontally from M1 to the pulley and vertically from the pulley to M2. You may also assume that the mass M1 is not tipping over as it slides.

a) Assume the string slips over the pulley with zero friction, and that the pulley is not rotating. Calculate the magnitude of the acceleration of M1 and M2. (This is the same for both masses.) Also find the tensions T1 in the string attached to M1 and T2 in the string attached to M2. Express your answers in terms of g and the various parameters given in the question.

b) Now assume that the string runs over the pulley without slipping, making the pulley rotate with increasing angular speed. Assume the pulley is attached to the table by a support which allows it to rotate on an axle with no friction between the pulley and axle. Calculate the magnitude of the acceleration of the masses M1 and M2 in this case. Also calculate the tensions T1 and T2 in this case.

Thanks for you help!

## Homework Equations

Fnet = ma

Torque net = I*a

I = (MR^2)/2

Ff = uFn

## The Attempt at a Solution

a) [/B]Fnet = ma

Fg2-T2+T1-Ff1 = (M1+M2)a

Fg2 - Ff1 = (M1+M2)a

M2g-uM1g = (M1+M2)a

(M2g-uM1g)/(M1+M2) = a

Fnet1 = T1-Ff1 = M1a

T1 = M1a + Ff1

T1 = M1a + uM1g

Fnet2 = Fg2 - T2 = M2a

T2 = Fg2 - M2a

T2 = M2g - M2a

b) Torque = I*a

T2R-T1R = Ia

a = [R^2/(M3R^2)]*(T2-T1)

a = (T2-T1)(2/M3)

T1 and T2 same as part a)?