[khailing]

A mail bag with a mass of 120 kilogram is suspended by a vertical rope 6.0 meters long. What horizontal force is necessary to hold the bag in a position displaced sideways 3.0 meters from its initial position?

[Abhimanyu Pudi]

This cannot be answered without drawing a free body diagram of the mass. But I will try to tell you as better as I can. Try to draw it as I direct you.

DRAW A MASS SUSPENDED FROM A POINT BY A VERTICAL THREAD. NOW DISPLACE IT BY A CERTAIN ANGLE. DRAW A HORIZONTAL LINE REPRESENTING THE MASS' 3m DISPLACEMENT.YOU CAN FIND A RIGHT ANGLED TRIANGLE FORMED BY THIS LINE, THE LENGTH OF THE THREAD IN THE DISPLACED POSITION AND SOME PART OF THE THREAD'S LENGTH IN ITS INITIAL POSITION.
IF YOU CALCULATE THE SINE OF THAT DISPLACED ANGLE, IT WILL BE 1/2, INDICATING THAT IT WAS DISPLACED AT AN ANGLE OF 30degrees.

Now represent the forces acting on the mass in the displaced position.
1) Weight mg acting vertically downward
2) Tension T of the thread acting along the thread towards the suspension point
3) the required horizontal force F acting towards right.

Resolve the tension into components along horizontal and vertical directions. Since F should bring the mass to rest at that position, the forces in each direction balance one another.

In vertical direction, T*cos30=mg
In horizontal direction, T*sin30=F

Solve to find F.