Question

A heavy ball with a weight of $100N$ $(m=10.2kg)$ is hung from the ceiling of a lecture hall on a $4.5-m$-long rope. The ball is pulled to one side and released to swing as a pendulum, reaching a speed of $5.5m/s$ as it passes through the lowest point. What is the tension in the rope at that point?

Short answer

The tension in the rope at that point is$T=169N$.

Step-by-step solution

Given Information

A heavy ball with a weight of $100N$$(m=10.2kg)$is hung from the ceiling of a lecture hall on a $4.5$-m-long rope.

Explanation

To find the tension in the rope at the point

$T-mg=\frac{m{v}^2}{r}$

Where,

$T-$is the tension in the string

$m-$mass of the ball

$g-$is the acceleration due to gravity

$v-$is the velocity

$r-$is the radius

Here,

$T=10.2\times 9.8+\frac{10.2\times {(5.5)}^2}{4.5}$

$T=169N$

Final Answer

The tension in the rope at that point is $T=169N$.