Ball hanging from string, what is tension when at its lowest point?

[racer98jc]

Homework Statement

A heavy ball with a weight of 130 is hung from the ceiling of a lecture hall on a 4.6--long rope. The ball is pulled to one side and released to swing as a pendulum, reaching a speed of 5.6 as it passes through the lowest point.

What is the tension in the rope?

Homework Equations

The Attempt at a Solution

 

[rl.bhat]

Hi racer98jc, welcome to PF.

What are the forces acting on the ball at the lowest point of the swing?

 

[racer98jc]

Hello,

at the bottom: tension and the balls own weight are acting on it. Correct?

 

[Dadface]

Hello,

at the bottom: tension and the balls own weight are acting on it. Correct?

Correct(the question probably wants you to ignore frictional forces)

 

[rwisz]

The tension in the rope at the lowest point can be calculated using the equation T = mg + ma, where T is the tension, m is the mass of the ball, g is the acceleration due to gravity, and a is the acceleration of the ball at the lowest point.

In this case, the mass of the ball is 130 kg, the acceleration due to gravity is 9.8 m/s^2, and the acceleration of the ball at the lowest point is 5.6 m/s^2 (since it is moving at a constant speed).

Therefore, the tension in the rope at the lowest point is T = (130 kg)(9.8 m/s^2) + (130 kg)(5.6 m/s^2) = 2284 N.

This means that the rope is experiencing a tension of 2284 N when the ball is at its lowest point. This is the minimum amount of tension required to keep the ball at that position and prevent it from falling. As the ball swings back and forth, the tension in the rope will vary depending on the position of the ball.