The student claims that a ball dropped 3.0 meters would have fewer than 96 joules of kinetic energy upon hitting the ground. Is she correct? Why?
To determine if the student is correct, we can use the equation for gravitational potential energy to find the kinetic energy of the ball when it hits the ground. The equation is:
Kinetic energy (KE) = mass (m) × gravitational acceleration (g) × height (h)
Given:
Height (h) = 3.0 meters
Gravitational acceleration (g) = 9.8 m/s^2
Since the mass is not given, let's assume it to be 1 kg for simplicity. Substitute the values into the equation:
KE = 1 kg × 9.8 m/s^2 × 3.0 meters
KE = 29.4 joules
Therefore, if the height from which the ball is dropped is 3.0 meters and the mass is 1 kg (as assumed), the kinetic energy upon hitting the ground would be 29.4 joules.
Since 29.4 joules is less than 96 joules, the student is correct in claiming that the ball dropped 3.0 meters would have fewer than 96 joules of kinetic energy upon hitting the ground.
To determine whether the student is correct or not, we can use the formula for kinetic energy:
Kinetic Energy (KE) = 1/2 * mass * velocity^2
Since the ball is dropped vertically, the initial velocity is zero. Thus, the equation simplifies to:
KE = 1/2 * mass * (0)^2
KE = 0 joules
This means that the ball has no kinetic energy just before it hits the ground. However, as the ball falls, it will gain potential energy due to the increase in height. When it reaches the ground, all of this potential energy will be converted into kinetic energy.
The potential energy (PE) can be calculated using the equation:
PE = mass * acceleration due to gravity * height
For simplicity, let's assume the ball has a mass of 1 kilogram and the acceleration due to gravity is 9.8 m/s^2 (standard on Earth). Substituting these values into the equation:
PE = 1 kg * 9.8 m/s^2 * 3.0 m
PE = 29.4 joules
Since the ball has no kinetic energy just before hitting the ground, it will have 29.4 joules of kinetic energy upon hitting the ground. Therefore, the student is incorrect when claiming that a ball dropped 3.0 meters would have fewer than 96 joules of kinetic energy upon hitting the ground.