A 5 kg ball is initially at rest at the top of a hill 10m high. If it rolls down the hill (converting all of its potential energy to kinetic energy,) what is the maximum kinetic energy it could have at the bottom of the hill?
-I am not sure what formula to use?
wait just figured it out pe=mgh
the KE will equal to the initial PE, mgh
To find the maximum kinetic energy of the 5 kg ball at the bottom of the hill, you need to use the principle of conservation of energy. According to this principle, the total mechanical energy of a system remains constant if no external forces are acting on it.
In this case, the ball is only subjected to the force of gravity, which is a conservative force. Therefore, the total mechanical energy, which is the sum of potential energy and kinetic energy, remains constant throughout the motion.
At the top of the hill, the ball has potential energy equal to its mass (m = 5 kg) multiplied by the acceleration due to gravity (g = 9.8 m/s^2) multiplied by the height of the hill (h = 10 m). Therefore, its initial potential energy can be calculated as:
Potential energy = m * g * h = 5 kg * 9.8 m/s^2 * 10 m = 490 J.
Since the ball starts from rest at the top of the hill, it has zero kinetic energy initially. As it rolls down, its potential energy is converted into kinetic energy. At the bottom of the hill, the potential energy is entirely converted into kinetic energy, so the maximum kinetic energy of the ball can be calculated as:
Maximum kinetic energy = Potential energy = 490 J.
Therefore, the maximum kinetic energy of the 5 kg ball at the bottom of the hill is 490 Joules.