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A roller coaster with a potential energy of [tex]$235,200 J$[/tex] sits at the top of a 30 m high hill. What is the mass of the roller coaster?

Use the formula: [tex]$PE = mgh$[/tex].

A. 800 kg
B. 7.840 kg
C. 8,000 kg
D. 78,400 kg

Answer :

To find the mass of the roller coaster, we can use the formula for potential energy, which is given by:

[tex]\[ PE = m \cdot g \cdot h \][/tex]

where:
- [tex]\( PE \)[/tex] is the potential energy,
- [tex]\( m \)[/tex] is the mass,
- [tex]\( g \)[/tex] is the acceleration due to gravity, which is approximately [tex]\( 9.81 \, \text{m/s}^2 \)[/tex],
- [tex]\( h \)[/tex] is the height.

We know the potential energy (PE) is [tex]\( 235,200 \, \text{J} \)[/tex] and the height (h) is 30 meters.

We need to solve for the mass (m). Rearrange the formula to find [tex]\( m \)[/tex]:

[tex]\[ m = \frac{PE}{g \cdot h} \][/tex]

Now, substitute the known values into the equation:

[tex]\[ m = \frac{235,200}{9.81 \cdot 30} \][/tex]

When you calculate this, you will find the mass to be approximately [tex]\( 800 \, \text{kg} \)[/tex].

Therefore, the mass of the roller coaster is about [tex]\( 800 \, \text{kg} \)[/tex].

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