Question

What is the tension in the string when the ball is at the top? A 300 g ball moves in a vertical circle on a Express your answer with the appropriate units. 109 m-long string. If the speed at the top is 4.70 m/s, then the speed at the bottom will be 8.05 m/s. What is the tension in the string when the ball is at the bottom?

Answer 1

The tension in the string at the bottom is calculated by summing the forces of gravity and centripetal force. Using the formula T = mg + Fc, where Fc = mv^2/r, allows the determination of the string's tension for a given mass, velocity, and radius.

Step-by-step explanation:

The tension in the string when the ball is at the bottom can be found by using the centripetal force formula and Newton's second law. The centripetal force needed to keep the ball moving in a circular path is provided by the tension in the string, along with the weight of the ball at the bottom of the circle. The formula for centripetal force is Fc = mv2/r, where m is the mass of the object, v is the tangential velocity, and r is the radius of the circle.

Additionally, at the bottom of the circle, the tension has to support the weight of the ball as well as provide the centripetal force. So, the total tension T at the bottom would be T = mg + Fc. Here, g is the acceleration due to gravity (9.81 m/s2).

By plugging in the values, we would get the tension at the bottom. Remember to convert the mass into kilograms by dividing by 1000 since mass is given in grams, and use the radius in meters.