Questions: A roller coaster is at the top of a 72 m hill and weighs 966 N. At the top of the hill the coaster car has energy. Calculate it.

Transcript text: 13. A roller coaster is at the top of a 72 m hill and weighs 966 N . At the top of the hill the coaster car has $\qquad$ energy. Calculate it.

Solution

Solution Steps

Step 1: Identify the Type of Energy at the Top of the Hill

At the top of the hill, the roller coaster primarily has gravitational potential energy (GPE) due to its height above the ground. The formula for gravitational potential energy is:

\[ \text{GPE} = mgh \]

where:

$ m $ is the mass of the roller coaster,
$ g $ is the acceleration due to gravity (approximately $ 9.81 \, \text{m/s}^2 $),
$ h $ is the height of the hill.

Step 2: Calculate the Mass of the Roller Coaster

The weight of the roller coaster is given as 966 N. Weight is the force due to gravity and is calculated as:

\[ W = mg \]

where $ W $ is the weight. We can rearrange this formula to solve for mass $ m $:

\[ m = \frac{W}{g} = \frac{966 \, \text{N}}{9.81 \, \text{m/s}^2} \]

Step 3: Calculate the Gravitational Potential Energy

Substitute the values of $ m $, $ g $, and $ h $ into the GPE formula:

Calculate the mass: \[ m = \frac{966}{9.81} \approx 98.47 \, \text{kg} \]
Calculate the GPE: \[ \text{GPE} = 98.47 \times 9.81 \times 72 \]

\[ \text{GPE} \approx 69888.38 \, \text{J} \]