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.
I dont recommend if she gives it a push and remains motionless.
I will be happy to check your work.
1. The changes in potential energy and kinetic energy of the bowling ball can be described as follows:
When the person pulls the bowling ball back until it touches his nose, potential energy is being stored in the system. The higher the ball is lifted, the more potential energy it possesses with respect to the ground. At this point, the kinetic energy of the ball is zero since it is not in motion.
As the person releases the bowling ball, the potential energy starts converting into kinetic energy. As the ball swings downwards, its potential energy decreases while the kinetic energy increases. At the lowest point of the swing, the potential energy is minimized while the kinetic energy is maximized since the ball is moving at its highest speed.
As the ball swings back upwards, the kinetic energy decreases while the potential energy increases. At the highest point of the swing, the potential energy is maximized while the kinetic energy is minimized since the ball momentarily comes to a stop before changing direction.
This cycle continues back and forth, with potential energy and kinetic energy continuously interchanging but the total mechanical energy (the sum of potential and kinetic energy) remaining constant as long as there are no external forces acting on the system.
2. Whether the bowling ball will hit the person's nose depends on the initial conditions and the length of the pendulum. If the person pulls the ball back exactly to the point where its potential energy is at maximum and releases it from there, the ball will follow a symmetrical trajectory. In this case, the ball will come back to the original position and stop just short of touching the person's nose due to the conservation of mechanical energy. The potential energy it had initially will be converted back into potential energy at the highest point of the swing, preventing the ball from hitting the person's nose.
However, if the initial conditions are such that the ball is released from a point where its potential energy is less than maximum, the ball will not complete a full swing and may reach a lower height on each subsequent swing. In this case, the ball could potentially hit the person's nose if the swings become shorter and the ball's trajectory intersects with 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 system. This extra energy will cause the ball to swing with a slightly higher velocity and thus a higher kinetic energy throughout the swing. Consequently, the ball will reach a higher maximum height on each swing, and the overall motion will become more energetic.
The additional kinetic energy will come from the person's push, but the system will still conserve mechanical energy. The potential energy at the highest point will still be equal to the potential energy at the original release point plus the additional kinetic energy given by the push. Hence, if the person gives the ball a sufficient push, it can reach a height where it may hit the person's nose on subsequent swings, especially if the swings become shorter due to energy losses (e.g., air resistance, friction).