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Answer :
Sure! Let's solve the problem of finding the mass of the roller coaster using the given formula for potential energy:
1. Understand the Formula:
The formula for potential energy (PE) is given by:
[tex]\[
PE = m \cdot g \cdot h
\][/tex]
where [tex]\( PE \)[/tex] is potential energy, [tex]\( m \)[/tex] is mass, [tex]\( g \)[/tex] is the acceleration due to gravity (approximately [tex]\( 9.8 \, \text{m/s}^2 \)[/tex]), and [tex]\( h \)[/tex] is height.
2. Identify Given Values:
From the problem, we know:
- [tex]\( PE = 235,200 \, \text{Joules} \)[/tex]
- [tex]\( h = 30 \, \text{meters} \)[/tex]
- [tex]\( g = 9.8 \, \text{m/s}^2 \)[/tex]
3. Rearrange the Formula:
To find the mass [tex]\( m \)[/tex], we can rearrange the formula to solve for [tex]\( m \)[/tex]:
[tex]\[
m = \frac{PE}{g \cdot h}
\][/tex]
4. Substitute the Known Values into the Formula:
[tex]\[
m = \frac{235,200}{9.8 \times 30}
\][/tex]
5. Calculate the Mass:
[tex]\[
m = \frac{235,200}{294} = 800
\][/tex]
Therefore, the mass of the roller coaster is 800 kg.
1. Understand the Formula:
The formula for potential energy (PE) is given by:
[tex]\[
PE = m \cdot g \cdot h
\][/tex]
where [tex]\( PE \)[/tex] is potential energy, [tex]\( m \)[/tex] is mass, [tex]\( g \)[/tex] is the acceleration due to gravity (approximately [tex]\( 9.8 \, \text{m/s}^2 \)[/tex]), and [tex]\( h \)[/tex] is height.
2. Identify Given Values:
From the problem, we know:
- [tex]\( PE = 235,200 \, \text{Joules} \)[/tex]
- [tex]\( h = 30 \, \text{meters} \)[/tex]
- [tex]\( g = 9.8 \, \text{m/s}^2 \)[/tex]
3. Rearrange the Formula:
To find the mass [tex]\( m \)[/tex], we can rearrange the formula to solve for [tex]\( m \)[/tex]:
[tex]\[
m = \frac{PE}{g \cdot h}
\][/tex]
4. Substitute the Known Values into the Formula:
[tex]\[
m = \frac{235,200}{9.8 \times 30}
\][/tex]
5. Calculate the Mass:
[tex]\[
m = \frac{235,200}{294} = 800
\][/tex]
Therefore, the mass of the roller coaster is 800 kg.
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