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 :

Certainly! To find the potential energy of the bicycle at the top of the hill, we use the formula for gravitational 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, which is 25 kg in this case.
- [tex]\( g \)[/tex] is the acceleration due to gravity. On Earth, this is approximately [tex]\( 9.8 \, \text{m/s}^2 \)[/tex].
- [tex]\( h \)[/tex] is the height of the hill, which is 3 meters.

Let's calculate the potential energy step-by-step:

1. Identify the values:
- Mass, [tex]\( m = 25 \, \text{kg} \)[/tex]
- Gravity, [tex]\( g = 9.8 \, \text{m/s}^2 \)[/tex]
- Height, [tex]\( h = 3 \, \text{m} \)[/tex]

2. Plug these values into the formula:
[tex]\[
PE = 25 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times 3 \, \text{m}
\][/tex]

3. Perform the multiplication:
[tex]\[
PE = 25 \times 9.8 \times 3 = 735 \, \text{joules}
\][/tex]

So, the potential energy of the bicycle at the top of the hill is 735 joules.

The correct answer is [tex]\( 735 \, \text{J} \)[/tex].