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 gravitational potential energy, we use the formula

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

where
- [tex]$m$[/tex] is the mass,
- [tex]$g$[/tex] is the acceleration due to gravity,
- [tex]$h$[/tex] is the height.

Given:
- [tex]$m = 25 \text{ kg}$[/tex],
- [tex]$g = 9.8 \text{ m/s}^2$[/tex],
- [tex]$h = 3 \text{ m}$[/tex].

Step 1: Calculate the weight (force) acting on the bicycle:

[tex]$$
\text{Weight} = m \cdot g = 25 \times 9.8 = 245 \text{ N}.
$$[/tex]

Step 2: Compute the potential energy by multiplying the weight by the height:

[tex]$$
PE = m \cdot g \cdot h = 25 \times 9.8 \times 3 = 735 \text{ Joules}.
$$[/tex]

Thus, the potential energy of the bicycle is [tex]$\boxed{735 \text{ J}}$[/tex].