Question

A metal ball of mass 2 kg is supported by a massless inextensible string, 12 cm long. A

horizontal force displaces the ball by 30o

to the vertical so that the string remains taut. Find:

a) the horizontal force.

b) the tension in the thread.

Answer 1

(a) the horizontal force is 11.3 N

(b) The tension in the thread is 22.6 N

Draw a free body diagram for the suspended metal ball as shown in the figure. The tension T acts along the length of the thread, the force F is the horizontal force and its weight is mg, which acts vertically down wards.

Resolve the tension into two components- T cos 30 along the vertical and T sin30 along the horizontal as shown in the figure.

Apply the condition for equilibrium along the horizontal direction.

`F=Tsin30........(1)`

Apply the condition for equilibrium along the vertical direction.

`mg=Tcos30.......(2)`

Divide equation (1) by equation (2) and write an expression for F.

`(F)/(mg) = tan30\\ F=mgtan30`

Substitute 2 kg for m and 9.81 m/s² for g.

`F=mgtan30\\ =(2kg)(9.81m/s^2)(tan30^o)\\ =11.3N`

The horizontal force required to keep the ball taut is 11.3 N

From equation (2),

`T=(mg)/(sin30) \\ =((2kg)(9.81m/s^2))/(sin30^o) \\ =22.6N`

Thus, the tension in the thread is 22.6 N