College

What is the potential energy of a 25 kg bicycle resting at the top of a hill 3 m high? (Formula: [tex]PE = mgh[/tex])

A. 75 J
B. 735 J
C. 245 J
D. 37.8 J

Answer :

To find the potential energy of a 25 kg bicycle at the top of a hill 3 meters high, you use the formula for potential energy:

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

where:
- [tex]\( PE \)[/tex] is the potential energy,
- [tex]\( m \)[/tex] is the mass of the object,
- [tex]\( g \)[/tex] is the acceleration due to gravity,
- [tex]\( h \)[/tex] is the height above the ground.

In the problem:
- The mass [tex]\( m \)[/tex] is 25 kg,
- The acceleration due to gravity [tex]\( g \)[/tex] is approximately 9.8 m/s²,
- The height [tex]\( h \)[/tex] is 3 m.

Now, plug in the given values:

[tex]\[ PE = 25 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times 3 \, \text{m} \][/tex]

When you multiply these numbers together:

[tex]\[ PE = 25 \times 9.8 \times 3 \][/tex]

[tex]\[ PE = 735 \, \text{Joules} \][/tex]

Therefore, the potential energy of the bicycle is 735 Joules, which matches the second option [tex]\( \text{735 J} \)[/tex].