High School

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 resting at the top of a hill 3 meters high, we use the formula for potential energy:

[tex]\[ \text{Potential Energy (PE)} = m \times g \times h \][/tex]

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

Let's use these values in the formula:

1. Identify the mass (m): The mass of the bicycle is 25 kg.

2. Identify the acceleration due to gravity (g): The standard value is [tex]\( 9.8 \, \text{m/s}^2 \)[/tex].

3. Identify the height (h): The height of the hill is 3 m.

Now, substitute these values into the formula:

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

4. Calculate the potential energy:
- First, multiply the mass by the acceleration due to gravity:
[tex]\[ 25 \times 9.8 = 245 \][/tex]
- Next, multiply the result by the height:
[tex]\[ 245 \times 3 = 735 \][/tex]

Therefore, the potential energy of the bicycle at the top of the hill is [tex]\( 735 \, \text{Joules (J)} \)[/tex].

So, the correct answer is 735 J.