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Answer :
Certainly! Let's solve the problem step-by-step to find the mass of the roller coaster.
Problem Statement:
A roller coaster with a potential energy of 235,200 J is at the top of a 30 m high hill. We are trying to find the mass of the roller coaster.
Formula:
The formula for potential energy (PE) is given by:
[tex]\[ PE = m \times g \times h \][/tex]
where:
- [tex]\( PE \)[/tex] is the potential energy in joules (J),
- [tex]\( m \)[/tex] is the mass in kilograms (kg),
- [tex]\( g \)[/tex] is the acceleration due to gravity, approximately [tex]\( 9.81 \, \text{m/s}^2 \)[/tex],
- [tex]\( h \)[/tex] is the height in meters (m).
Given Values:
- Potential energy (PE) = 235,200 J
- Height (h) = 30 m
- Gravity (g) = 9.81 m/s²
To Find:
- Mass (m) of the roller coaster.
Steps to Solve:
1. Rearrange the formula to solve for mass (m):
[tex]\[ m = \frac{PE}{g \times h} \][/tex]
2. Substitute the known values into the formula:
[tex]\[ m = \frac{235,200}{9.81 \times 30} \][/tex]
3. Perform the calculation:
- First, calculate the denominator: [tex]\( 9.81 \times 30 = 294.3 \)[/tex]
- Next, divide the potential energy by this value: [tex]\( \frac{235,200}{294.3} \approx 799.18 \)[/tex]
Therefore, the mass of the roller coaster is approximately 800 kg.
Among the given options, 800 kg is the closest to our calculated value.
Problem Statement:
A roller coaster with a potential energy of 235,200 J is at the top of a 30 m high hill. We are trying to find the mass of the roller coaster.
Formula:
The formula for potential energy (PE) is given by:
[tex]\[ PE = m \times g \times h \][/tex]
where:
- [tex]\( PE \)[/tex] is the potential energy in joules (J),
- [tex]\( m \)[/tex] is the mass in kilograms (kg),
- [tex]\( g \)[/tex] is the acceleration due to gravity, approximately [tex]\( 9.81 \, \text{m/s}^2 \)[/tex],
- [tex]\( h \)[/tex] is the height in meters (m).
Given Values:
- Potential energy (PE) = 235,200 J
- Height (h) = 30 m
- Gravity (g) = 9.81 m/s²
To Find:
- Mass (m) of the roller coaster.
Steps to Solve:
1. Rearrange the formula to solve for mass (m):
[tex]\[ m = \frac{PE}{g \times h} \][/tex]
2. Substitute the known values into the formula:
[tex]\[ m = \frac{235,200}{9.81 \times 30} \][/tex]
3. Perform the calculation:
- First, calculate the denominator: [tex]\( 9.81 \times 30 = 294.3 \)[/tex]
- Next, divide the potential energy by this value: [tex]\( \frac{235,200}{294.3} \approx 799.18 \)[/tex]
Therefore, the mass of the roller coaster is approximately 800 kg.
Among the given options, 800 kg is the closest to our calculated value.
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