Question

A heavy steel ball is hung from a cord to make a pendulum. The ball is pulled to the side so that the cord makes a 5 ∘ angle with the vertical. Holding the ball in place takes a force of 40 N . If the ball is pulled farther to the side so that the cord makes a 10 ∘ angle, what force is required to hold the ball?

Answer 1

The required force is calculated as 79.69 N

Solution:

As per the question:

Angle,
`\theta = 5^(\circ)`

Force, F = 40 N

The angle after the ball is being pulled,
`\theta' = 10^(\circ)`

Now,

To calculate the required force:

The tension in the string can be calculated by considering the vertical component:

`F = Tsin\theta`

where

T = Tension in the cord

Now,

`T = (F)/(sin\theta) = (40)/(sin5^(\circ)) = 458.94\ N`

Now, after the cord is being pulled, the force exerted is given by:

`F' = Tsin\theta' = 458.94* sin10^(\circ) = 79.69\ N`