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 bowling ball is at its highest point, it has maximum potential energy. This is because the ball is lifted against the force of gravity by the person pulling it back. As the ball is released and starts swinging, the potential energy is converted into kinetic energy. At the lowest point of the swing, the ball has maximum kinetic energy and minimum potential energy. As the ball swings back towards its highest point, the kinetic energy is gradually converted back into potential energy.
2. The bowling ball will not hit the person's nose if the pendulum is set up correctly. This is because the total mechanical energy of the system remains constant throughout the motion. As the ball swings back and forth, the potential and kinetic energies continuously transfer between each other, but the total energy remains the same. Therefore, the ball will swing to the same height on the other side as it was released from, without hitting the person's nose.
3. If the person gives the bowling ball a small push as it is released, it will have an additional initial velocity. This results in an increase in the ball's kinetic energy. As a result, the ball will swing higher on each side and have greater potential energy at its highest point. However, since the total mechanical energy remains constant, the kinetic energy will be converted back into potential energy as the ball swings back in the opposite direction. Therefore, the ball will swing to a higher point, but it will not hit the person's nose as long as the original setup was correct.
1. The potential energy of the bowling ball changes as it swings back and forth in the pendulum. When the ball is at its highest point, the potential energy is at its maximum because it is furthest from the ground. As the ball starts to swing downwards, the potential energy decreases and gets converted into kinetic energy. At the lowest point of the swing, the potential energy is at its minimum because the ball is closest to the ground. At this point, the kinetic energy is at its maximum because the ball is moving at its fastest. As the ball swings back upwards, the process repeats, with potential energy increasing while kinetic energy decreases until it reaches the highest point again.
2. The bowling ball will not hit the person's nose as long as we assume an ideal situation with no external factors like air resistance or friction. This is because of the conservation of energy principle. At the highest point of the swing, the ball has maximum potential energy, which is converted to kinetic energy as it swings downwards. This kinetic energy will be sufficient to carry the ball across the lowest point of the swing and up to an equal height on the other side. As the ball swings back and forth, it will continue to oscillate with a decreasing amplitude but never reach the person's nose.
3. If the person gives the bowling ball a small push as it is released, it will affect the energy changes in the system. The additional initial kinetic energy from the push will cause the ball to swing with greater amplitude but will not change the total energy of the system. As the ball swings back and forth, the additional kinetic energy will be continuously converted into potential energy as it moves upwards, and vice versa. This will result in a slightly higher maximum height reached by the ball during each swing, but it will not affect the overall pattern of the swinging motion. The ball will still not hit the person's nose if the push is small enough to maintain the energy balance during the swings.