Question

A roller coaster car with a mass of 500 kg at the top of a hill that is 30 m high. Without friction, what would its kinetic energy be as it reached the bottom of the hill?

Answer 1

147150 Joules

Explanation:

Assuming no friction between the roller coaster car and the hill, and neglecting air resistance, the kinetic energy the roller coaster car would have at the bottom of the hill would be equal to its gravitational potential energy at the top of the hill, by conservation of energy.

At the top of the hill, the roller coaster car only contains potential energy as it is perfectly still, so its total mechanical energy at the top of the hill would be in the form of only potential energy.

At the bottom of the hill, this potential energy would have converted all into kinetic energy, because there are, in this highly ideal situation, no energy losses due to friction.

The law of conservation of mechanical energy states that the total mechanical energy in a system is always conserved.

Let `KE` denote Kinetic Energy

As an equation, the relationship would be:

`mgh = 1/2 mv^2`

OR

`KE = mgh`

Assuming the acceleration due to gravity near the earth's surface is `9.81 m/s`, our equation becomes:

`KE = 500kg * 9.81m/s * 30m`
`KE = 147150` Joules

Therefore, as the cart approaches the bottom of the hill where its gravitational potential energy is converted into kinetic energy, the amount of kinetic energy it would have would be equal to its potential energy at the start.

The cart would have 147150 Joules of Kinetic Energy at the bottom of the hill.