Question

A ball of mass 1.26 kilograms is attached to a cord 1.55 meters long and swung in a vertical circle at a constant speed of 7.28 meters per second.a. What is the centripetal force acting on the ball? b. What is the tension in the cord when the ball is at the bottom of its path?c. What is the tension in the cord when the ball is at the top of its path?

Answer 1

Given:

The mass of the ball is m = 1.26 kg

The radius of the cord is r = 1.55 m

The speed of the ball is v = 7.28 m/s

To find

(a) Centripetal force acting on the ball

(b) Tension in the cord when the ball is at the bottom of its path

(c) Tension in the cord when the ball is at the top of its path

Step-by-step explanation:

(a) Centripetal force acting on the ball will be

`\begin{gathered} F=(mv^2)/(r) \\ =\text{ }(1.26*(7.28)^2)/(1.55) \\ =\text{ 43.08 N} \end{gathered}`

(b) Tension in the cord when the ball is at the bottom of its path will be

`\begin{gathered} T_b=F+mg \\ =\text{ 43.08 +\lparen1.26}*9.8\text{\rparen} \\ =\text{ 55.428 N} \end{gathered}`

(c) Tension in the cord when the ball is at the top of its path will be

`\begin{gathered} T_t=\text{ F-mg} \\ =43.08+(1.26*9.8) \\ =30.732\text{ N} \end{gathered}`

Final Answer:

(a) Centripetal force acting on the ball is 43.08 N

(b) Tension in the cord when the ball is at the bottom of its path is 55.428 N

(c) Tension in the cord when the ball is at the top of its path is 30.732 N