Final answer:
To find the energy converted to heat, calculate the difference between the initial potential energy (19.6 J) and the rebound potential energy (9.8 J), resulting in 9.8 joules of energy being dissipated as heat.
Step-by-step explanation:
The student has asked to calculate the amount of energy converted to heat when a 1-kg ball dropped from 2 m rebounds to a height of only 1.0 m after hitting the ground. To solve this problem, we use the principle of conservation of energy. The potential energy lost by the ball when it drops from the initial height is partly converted to kinetic energy as it hits the ground and partly dissipated as heat. Since the ball does not return to its original height, not all of its initial potential energy is converted back into gravitational potential energy upon rebound.
The initial potential energy (PE) of the ball when dropped is given by PE = m * g * h, where m is the mass, g is the acceleration due to gravity (9.8 m/s2), and h is the height. Here it is PE_initial = 1 kg * 9.8 m/s2 * 2 m = 19.6 J.
The potential energy of the ball at the rebound height is PE_rebound = 1 kg * 9.8 m/s2 * 1 m = 9.8 J. The difference between the initial potential energy and the rebound potential energy gives the amount of energy converted to heat, which is 19.6 J - 9.8 J = 9.8 J.
Therefore, 9.8 joules of energy are converted to heat during the ball's collision with the ground.