Question
The student says that a ball dropped from a height of 3.0 meters would have less than 96 joules of kinetic energy when it hits the ground. Is she correct and why?
Answers
GPT 3.5
To determine if the student is correct, we can use the formula for gravitational potential energy:
Potential energy (PE) = mass (m) * gravity (g) * height (h)
Since the student mentioned that the ball was dropped, we can assume that it has negligible initial velocity, thus the initial kinetic energy is 0 joules. The potential energy at the height of 3.0 meters would be:
PE = m * g * h
Given that the mass and gravity are constant, we can disregard them for this comparison. Therefore, the potential energy is directly proportional to the height:
PE ∝ h
Since kinetic energy is equal to potential energy when the object is in free fall, we can conclude that the kinetic energy is also directly proportional to the height.
KE ∝ h
Therefore, if the height is reduced, the kinetic energy will also be reduced. In this case, if the ball is dropped from a height of 3.0 meters, the kinetic energy would be less than 96 joules, as stated by the student. Hence, the student's statement is correct.
Potential energy (PE) = mass (m) * gravity (g) * height (h)
Since the student mentioned that the ball was dropped, we can assume that it has negligible initial velocity, thus the initial kinetic energy is 0 joules. The potential energy at the height of 3.0 meters would be:
PE = m * g * h
Given that the mass and gravity are constant, we can disregard them for this comparison. Therefore, the potential energy is directly proportional to the height:
PE ∝ h
Since kinetic energy is equal to potential energy when the object is in free fall, we can conclude that the kinetic energy is also directly proportional to the height.
KE ∝ h
Therefore, if the height is reduced, the kinetic energy will also be reduced. In this case, if the ball is dropped from a height of 3.0 meters, the kinetic energy would be less than 96 joules, as stated by the student. Hence, the student's statement is correct.