We are given the potential energy PE = 235200 J and height h = 30 m .
We use the formula PE = m g h to relate potential energy, mass, gravity, and height.
Rearrange the formula to solve for mass: m = g h PE .
Substitute the given values and calculate: m = 9.8 × 30 235200 = 800 k g . The mass of the roller coaster is 800 k g .
Explanation
Problem Analysis We are given the potential energy (PE) of a roller coaster, its height (h), and the formula relating these quantities to the mass (m) and the acceleration due to gravity (g). Our goal is to find the mass of the roller coaster.
Formula The formula for potential energy is given by: PE = m g h where:
PE is the potential energy in Joules (J)
m is the mass in kilograms (kg)
g is the acceleration due to gravity, approximately 9.8 m / s 2
h is the height in meters (m)
Rearrange the Formula We need to rearrange the formula to solve for the mass m :
m = g h PE
Substitute the Values Now, we substitute the given values into the formula: m = 9.8 m / s 2 × 30 m 235200 J m = 294 235200 k g m = 800 k g
Final Answer Therefore, the mass of the roller coaster is 800 kg.
Examples
Understanding potential energy is crucial in designing roller coasters. Engineers use the principle PE = m g h to calculate how much energy a roller coaster has at its highest point. This energy is then converted into kinetic energy (motion) as the coaster descends, providing the thrilling ride. Knowing the mass and height allows them to predict the speed and forces experienced during the ride, ensuring safety and excitement.