A pendulum is made with a bowling ball as the bob and a wire attached to the ceiling, as shown in the illustration below. The person in the illustration pulls the bowling ball back until it touches his nose, then releases the bowling ball. Assume that he does not move.
1.Describe the changes in the potential energy and the kinetic energy of the bowling ball as it swings back and forth.
2.Explain whether the bowling ball will hit the person’s nose. Include a discussion of energy changes in your explanation.
3.Explain what will happen if the person gives the bowling ball a small push as it is released. Include a discussion of energy changes in your explanation.
1. When the person pulls the bowling ball back and releases it, the potential energy of the bowling ball is at its maximum. This is because the ball is at its highest point, farthest away from the ground, and has the potential to gain kinetic energy as it falls. As the ball starts swinging back and forth, it continuously exchanges potential energy and kinetic energy. When the ball reaches its lowest point in its swing, its potential energy is at its minimum, while its kinetic energy is at its maximum. This is because all of the potential energy has been converted into kinetic energy as the ball speeds up. As the ball swings back up in its trajectory, its kinetic energy decreases and potential energy increases, until it reaches its highest point again.
2. The bowling ball will not hit the person's nose. This is because of the conservation of energy. As the ball swings back and forth, its total mechanical energy (the sum of potential and kinetic energy) remains constant, neglecting any energy losses due to friction or air resistance. At the highest point of each swing, when the ball has its maximum potential energy, it has no kinetic energy. As the ball swings down, its potential energy decreases and is converted into kinetic energy, increasing its speed. At the lowest point of each swing, when the potential energy is at its minimum, the kinetic energy is at its maximum. However, because the initial release position of the ball is higher than the person's nose, the ball will always reach its highest point before it descends again. Therefore, the ball will not hit the person's nose.
3. If the person gives the bowling ball a small push as it is released, it will add additional kinetic energy to the ball. This will cause the ball to swing with a higher initial speed compared to when it was just released without a push. As the ball swings back and forth, the added kinetic energy from the push will result in a higher maximum kinetic energy during each swing. This means that the ball will have a greater speed at its lowest point and a higher height at its highest point. The additional kinetic energy from the push will be converted into potential energy as the ball swings up and back down. The total mechanical energy of the ball will still be conserved, but the initial push will make the swinging motion more energetic and dynamic.