Question

A 900 g ball moves in a vertical circle on a 1.06 m-long string. If the speed at the top is 4.70 m/s, then the speed at the bottom will be ______ m/s. What is the tension in the string when the ball is at the top?

1) 7.98
2) 4.70
3) 1.06
4) cannot be determined

Answer 1

The speed at the bottom of the vertical circle is the same as the speed at the top, which is 4.70 m/s. The tension in the string at the top is approximately 7.98 N.

Step-by-step explanation:

To find the speed at the bottom of the vertical circle, we can use the principle of conservation of energy. At the top of the circle, the ball has potential energy and kinetic energy, given by the equations: mgh + 1/2mv^2. At the bottom of the circle, the ball only has kinetic energy. Since energy is conserved, we can equate the two expressions and solve for the speed at the bottom. In this case, the potential energy and kinetic energy at the top cancel each other out, leaving only the kinetic energy at the bottom. Therefore, the speed at the bottom is the same as the speed at the top, which is 4.70 m/s.

To find the tension in the string at the top, we can use Newton's second law. At the top, the tension and the gravitational force are both acting on the ball. The tension provides the centripetal force needed for the circular motion. Therefore, we can set the sum of the tension and the gravitational force equal to the centripetal force, which is given by the equation: mv^2/r. Solving for the tension, we get: T = mv^2/r - mg. Plugging in the given values, we find that the tension at the top is approximately 7.98 N.