Question
A roller coaster is at the top of a 72 m hill and weighs 966 N. The coaster (at this moment) has ____________ energy. Calculate it.
Answers
GPT-4o mini
To determine the energy of the roller coaster at the top of a 72 m hill, we can calculate its gravitational potential energy (PE). The formula for gravitational potential energy is:
\[
PE = mgh
\]
where:
- \(PE\) is the potential energy,
- \(m\) is the mass of the object,
- \(g\) is the acceleration due to gravity (approximately \(9.81 \, \text{m/s}^2\)),
- \(h\) is the height above the reference point (in meters).
However, we are given the weight of the roller coaster directly, which is \(966 \, \text{N}\). Weight (W) is related to mass (m) and gravity (g) by the formula:
\[
W = mg
\]
Since we need to find the potential energy at the height of 72 m, we can replace \(m \times g\) with the weight \(W\):
\[
PE = W \times h
\]
Substituting the given values:
\[
PE = 966 \, \text{N} \times 72 \, \text{m}
\]
Calculating that:
\[
PE = 69672 \, \text{J}
\]
Thus, the roller coaster at the top of a 72 m hill has **69,672 joules (J)** of gravitational potential energy.
\[
PE = mgh
\]
where:
- \(PE\) is the potential energy,
- \(m\) is the mass of the object,
- \(g\) is the acceleration due to gravity (approximately \(9.81 \, \text{m/s}^2\)),
- \(h\) is the height above the reference point (in meters).
However, we are given the weight of the roller coaster directly, which is \(966 \, \text{N}\). Weight (W) is related to mass (m) and gravity (g) by the formula:
\[
W = mg
\]
Since we need to find the potential energy at the height of 72 m, we can replace \(m \times g\) with the weight \(W\):
\[
PE = W \times h
\]
Substituting the given values:
\[
PE = 966 \, \text{N} \times 72 \, \text{m}
\]
Calculating that:
\[
PE = 69672 \, \text{J}
\]
Thus, the roller coaster at the top of a 72 m hill has **69,672 joules (J)** of gravitational potential energy.