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Answer :
To find the potential energy of a 25 kg bicycle resting at the top of a hill 3 meters high, we can use the formula for gravitational potential energy:
[tex]\[ PE = mgh \][/tex]
where:
- [tex]\( PE \)[/tex] is the potential energy,
- [tex]\( m \)[/tex] is the mass in kilograms,
- [tex]\( g \)[/tex] is the acceleration due to gravity (approximately 9.8 m/s[tex]\(^2\)[/tex]),
- [tex]\( h \)[/tex] is the height in meters.
Here's how to calculate it step-by-step:
1. Identify the mass ([tex]\( m \)[/tex]): The mass of the bicycle is given as 25 kg.
2. Identify the gravitational acceleration ([tex]\( g \)[/tex]): Use the standard acceleration due to gravity, which is approximately 9.8 m/s[tex]\(^2\)[/tex].
3. Identify the height ([tex]\( h \)[/tex]): The height of the hill is given as 3 meters.
4. Substitute these values into the formula:
[tex]\[
PE = 25 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times 3 \, \text{m}
\][/tex]
5. Calculate the potential energy:
[tex]\[
PE = 735 \, \text{Joules}
\][/tex]
So, the potential energy of the bicycle at the top of the hill is 735 Joules.
[tex]\[ PE = mgh \][/tex]
where:
- [tex]\( PE \)[/tex] is the potential energy,
- [tex]\( m \)[/tex] is the mass in kilograms,
- [tex]\( g \)[/tex] is the acceleration due to gravity (approximately 9.8 m/s[tex]\(^2\)[/tex]),
- [tex]\( h \)[/tex] is the height in meters.
Here's how to calculate it step-by-step:
1. Identify the mass ([tex]\( m \)[/tex]): The mass of the bicycle is given as 25 kg.
2. Identify the gravitational acceleration ([tex]\( g \)[/tex]): Use the standard acceleration due to gravity, which is approximately 9.8 m/s[tex]\(^2\)[/tex].
3. Identify the height ([tex]\( h \)[/tex]): The height of the hill is given as 3 meters.
4. Substitute these values into the formula:
[tex]\[
PE = 25 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times 3 \, \text{m}
\][/tex]
5. Calculate the potential energy:
[tex]\[
PE = 735 \, \text{Joules}
\][/tex]
So, the potential energy of the bicycle at the top of the hill is 735 Joules.
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