Answer:
Step-by-step explanation:
When the ball is dropped and bounces, some of its initial potential energy is transferred to other forms of energy, such as heat and sound. To calculate the energy transferred to heat and sound during the bounce, we need to find the difference in potential energy before and after the bounce.
Energy transferred to heat and sound during the bounce:
The initial potential energy of the ball is given by mass (m) multiplied by gravitational acceleration (g) multiplied by the height (h) above the table. In this case, it is 1 kg × 9.8 m/s² × 10 m = 98 J. When the ball reaches its maximum height of 7 m, the potential energy is 1 kg × 9.8 m/s² × 7 m = 68.6 J. The difference in potential energy is 98 J - 68.6 J = 29.4 J. Therefore, 29.4 J of energy is transferred to heat and sound during the bounce.
The ball cannot bounce to a height of 12 m if it is dropped because some energy is lost during the bounce. When the ball bounces, not all of the energy is converted back into potential energy. Some energy is dissipated as heat and sound due to the internal friction and deformations within the ball and the surface it bounces off. This energy loss reduces the amount of energy available for the ball to reach a higher height on subsequent bounces.
To make the ball bounce to a height of 12 m, you could take several actions:
Use a more elastic material for the ball: Using a material with higher elasticity would allow the ball to store more energy during compression and release it more efficiently during the bounce, resulting in a higher bounce height.
Modify the surface it bounces off: Using a surface with higher rebound characteristics, such as a trampoline or a highly elastic material, would provide a greater impulse to the ball, allowing it to bounce higher.
Increase the initial potential energy: By raising the initial height from which the ball is dropped, you can increase the initial potential energy, which can contribute to a higher bounce height.
It's important to note that these modifications may have limitations based on the physical properties of the ball and the surface it interacts with.