To determine whether the student is correct in claiming that a ball dropped from a height of 3.0 meters would have fewer than 96 joules of kinetic energy upon hitting the ground, we can use the concept of gravitational potential energy.
The potential energy (PE) at the height is given by the formula:
\[ PE = mgh \]
where:
- \(m\) = mass of the ball (in kilograms)
- \(g\) = acceleration due to gravity (approximately \(9.81 , \text{m/s}^2\))
- \(h\) = height (3.0 meters in this case)
This potential energy is converted entirely into kinetic energy (KE) just before the ball hits the ground if we neglect air resistance. Thus, at the moment just before impact, the kinetic energy will equal the potential energy at the height from which it was dropped.
Using this formula, we can set it equal to 96 joules to find the maximum mass the ball could have:
\[ 96 = m \cdot 9.81 \cdot 3.0 \]
Solving for \(m\):
\[ 96 = m \cdot 29.43 \] \[ m = \frac{96}{29.43} \approx 3.26 , \text{kg} \]
This indicates that a ball with a mass of approximately 3.26 kg dropped from 3.0 meters would have 96 joules of kinetic energy upon hitting the ground.
If the mass of the ball is less than 3.26 kg, it will indeed have less than 96 joules of kinetic energy upon impact. However, if the mass is greater than 3.26 kg, it will have more than 96 joules.
So the correct response to the student's claim would depend on the mass of the ball. However, since we know that there are balls with varying health constraints that would reach the energy thresholds when dropped, we can conclude that:
The student is wrong. The higher the drop, the more kinetic energy the ball will have upon hitting the ground.
1 answer