Question

- 13. A ball attached to a string of length r rotates in a vertical circle. When the string is parallel to the ground and the ball is moving upward, the ball's velocity is v. What is the rate of change in the ball's speed at this point? asla (A) Vg2 + (04/r2) ((B)) - √g²+ (v4/72) (C) +g (D)-g (E) Not enough information is given. Fc-my²

Answer 1

Solution

To solve this problem, we apply Newton's second law, at the point where the rope is horizontally

In the following scheme, the mass free body diagram is illustrated

The forces acting on the object are, the weight of the body and the tension of the rope, which goes in the direction of the center of the circle

Then

The tension of the rope, is what keeps the body in a circular trajectory, therefore it is a centripetal force

Now, the rate of change of the speed of the ball is acceleration. Therefore, at that point of study, two accelerations act: radial or centripetal acceleration and tangential, which is gravity

Then

In our case

Now, if the body is not attached to the rope, the centripetal acceleration is zero, therefore, the ball describes a movement with acceleration of the negative gravity(-g), until it reaches its maximum displacement and returns to the ground

Then, the rate of change of the speed of the ball is option B