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.