- #1

garylau

- 70

- 3

## Homework Statement

The sketch shows, from two views, a simple pulley system for raising large masses. A light, inextensible cord attached to a mass m is wound, without slipping, on a cylinder of radius r. Rigidly joined to this cylinder and mounted on the same central shaft is a cylinder of radius R. The friction between the cylinders and the shaft is negligible. The two cylinders together have mass M, moment of inertia, I and radius of gyration k. Around the larger cylinder is wound, without slipping, anther light, inextensible cord, as shown. An operator pulls with tension T1 on this cord to raise the mass m.The mass m accelerates upwards with vertical acceleration a. (i) Using Newton's laws or otherwise, write an expression for T2, the tension in the cord attached to mass m, in terms of m, g and a. (ii) Using Newton's laws for rotation or otherwise, derive an expression for the angular acceleration, α, of the cylinders, in terms of variables given in the diagram. (iii) Showing all working, derive an expression for the acceleration a of mass m in terms of some or all of the parameters T1, m, M, I, r, R and the gravitational acceleration g.

## Homework Equations

F=mg

Torque=maR=I*alpha

## The Attempt at a Solution

i have done my work in the paper but i found the answer get wrong in(iii)and i don't know whether it is correct or notcan i write the answer like this?

the correct answer is a =( RT1 – rmg)/( I/r + rm)

but my answer is something like...(I/r-rm)...

Do i do it wrong?thank you

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