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 bicycle resting at the top of a hill, we use the formula for gravitational potential energy:

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

Where:
- [tex]\( m \)[/tex] is the mass of the object (in kilograms),
- [tex]\( g \)[/tex] is the acceleration due to gravity (approximately [tex]\( 9.8 \, \text{m/s}^2 \)[/tex] on Earth),
- [tex]\( h \)[/tex] is the height (in meters).

In this case:
- The mass ([tex]\( m \)[/tex]) of the bicycle is 25 kg,
- The height ([tex]\( h \)[/tex]) of the hill is 3 meters.

Now, substitute these values into the formula:

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

Multiply them together step by step:

1. First, calculate the force due to gravity acting on the bike: [tex]\( 25 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 245 \, \text{N} \)[/tex]

2. Then, calculate the potential energy: [tex]\( 245 \, \text{N} \times 3 \, \text{m} = 735 \, \text{Joules} \)[/tex]

So, the potential energy of the bicycle is [tex]\( 735 \, \text{J} \)[/tex].

Therefore, the correct answer is 735 J.