You are riding on a roller coaster at your favorite amusement park. At the top of the first hill, your cart pauses momentarily. Determine the energy type that exists at that moment, is it potential or kinetic energy? The mass of the cart with everyone in it is 12.5 kg, at its maximum speed it travels 16.3 m/s and the height of the hill is 13.5 m. Calculate the energy the cart has at that moment.
At the top of the first hill, the roller coaster cart momentarily comes to a stop before descending. At this moment, the only energy type that exists is potential energy.
To calculate the potential energy of the cart at the top of the hill, we can use the formula:
Potential energy (PE) = mass (m) * gravitational acceleration (g) * height (h)
Given:
Mass of cart (m) = 12.5 kg
Height of the hill (h) = 13.5 m
Gravitational acceleration (g) = 9.8 m/s^2
PE = 12.5 kg * 9.8 m/s^2 * 13.5 m
Calculating this, we get:
PE = 1661.25 Joules
Therefore, at the top of the first hill, the roller coaster cart has 1661.25 Joules of potential energy.