Question
Given that the roller coaster cart is 150 kg, calculate the GPE where the cart is located.
Make sure to show your units.
Make sure to show your units.
Answers
GPT-4o mini
To calculate the gravitational potential energy (GPE) of the roller coaster cart, we can use the formula:
\[
\text{GPE} = m \cdot g \cdot h
\]
where:
- \( m \) is the mass of the cart (in kilograms),
- \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \) on the surface of the Earth),
- \( h \) is the height above the reference point (in meters).
### Given:
- Mass of the cart, \( m = 150 \, \text{kg} \)
- Acceleration due to gravity, \( g = 9.81 \, \text{m/s}^2 \)
You need the height \( h \) at which the cart is located to calculate the GPE. Let's say the height \( h \) is given (for example, \( h = 30 \, \text{m} \)).
### Calculation:
Assuming \( h = 30 \, \text{m} \):
\[
\text{GPE} = 150 \, \text{kg} \cdot 9.81 \, \text{m/s}^2 \cdot 30 \, \text{m}
\]
\[
\text{GPE} = 150 \cdot 9.81 \cdot 30
\]
\[
\text{GPE} = 44145 \, \text{J}
\]
### Conclusion:
The gravitational potential energy (GPE) of the roller coaster cart at a height of \( 30 \, \text{m} \) is \( 44145 \, \text{J} \) (Joules).
If you have a specific height \( h \) in mind, please provide it and we can do the calculation with that value.
\[
\text{GPE} = m \cdot g \cdot h
\]
where:
- \( m \) is the mass of the cart (in kilograms),
- \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \) on the surface of the Earth),
- \( h \) is the height above the reference point (in meters).
### Given:
- Mass of the cart, \( m = 150 \, \text{kg} \)
- Acceleration due to gravity, \( g = 9.81 \, \text{m/s}^2 \)
You need the height \( h \) at which the cart is located to calculate the GPE. Let's say the height \( h \) is given (for example, \( h = 30 \, \text{m} \)).
### Calculation:
Assuming \( h = 30 \, \text{m} \):
\[
\text{GPE} = 150 \, \text{kg} \cdot 9.81 \, \text{m/s}^2 \cdot 30 \, \text{m}
\]
\[
\text{GPE} = 150 \cdot 9.81 \cdot 30
\]
\[
\text{GPE} = 44145 \, \text{J}
\]
### Conclusion:
The gravitational potential energy (GPE) of the roller coaster cart at a height of \( 30 \, \text{m} \) is \( 44145 \, \text{J} \) (Joules).
If you have a specific height \( h \) in mind, please provide it and we can do the calculation with that value.