Physics: A heavy ball with a weight of 110 N is hung from the ceiling of a lecture hall on a 4.4-m-long rope. The ball is pulled to one side and released to swing as a pendulum, reaching a speed of 5.3 m/s as it passes through the lowest point. What is the tension in the rope at that point?

A heavy ball with a weight of 110 N is hung from

symaria

20.01.2022

The tension in the rope is T = 180.225N.

Explanation:

The forces acting on the ball is the tension on the string and the force of gravity . Their sum contributes to the centripetal force:

$T -mg = \dfrac{mv^2}{R}$

Solving for tension we get:

$\boxed{T = \dfrac{mv^2}{R} +mg}$

Putting in numerical values

$m = \dfrac{110N}{10ms^{-2}} =11kg$

v = 5.3m/s

R = 4.4m

$T = \dfrac{(11kg)(5.3m/s)^2}{4.4m} +(11kg)(10ms^{-2})$

$\boxed{T = 180.225N}$

which is the tension in the rope.

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