- #1

Muthumanimaran

- 81

- 2

## Homework Statement

A force F is applied on the bigger mass 'M', which results in the prevention of smaller masses M1 and M2 moving with respect to larger mass M. The mass 'M' slides smoothly on the frictionless surface. Find the magnitude of the force. The pulley is ideal also consider the reaction force of pulley onto mass 'M'.

## Homework Equations

## The Attempt at a Solution

The normal force on the pulley is

$$R=2T \sin(\frac{\pi}{4})$$

The force on the system is

$$F=F_{1}+F_{2}+F_{3}$$

F1, F2, F3 are the forces on the masses M, M1 and M2 respectively.

The force F1

$$F_{1}=Ma-R\cos(\frac{\pi}{4})$$

$$F_{2}=M_{1}a$$

$$F_{3}=M_{2}a$$

If the masses M1 and M2 are at rest

$$T=M_{1}g$$

$$M_{2}a=M_{1}g$$

The force on the system is

$$F=(M+M_{1}+M_{2})\frac{M_{1}}{M_{2}}g-2M_{1}g\sin(\frac{\pi}{4})\cos(\frac{\pi}{4})$$

or

$$F=(M+M_{1})\frac{M_{1}}{M_{2}}g$$

I don't know whether my solution is correct. If I made an error, please give me a hint.