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Answer :
To find the potential energy of a 25 kg bicycle resting at the top of a hill that is 3 meters high, we can use the formula for potential energy:
[tex]\[ PE = m \cdot g \cdot h \][/tex]
where:
- [tex]\( PE \)[/tex] is the potential energy,
- [tex]\( m \)[/tex] is the mass of the object (25 kg in this case),
- [tex]\( g \)[/tex] is the acceleration due to gravity (approximately 9.8 m/s² on Earth),
- [tex]\( h \)[/tex] is the height above the ground (3 meters).
Step-by-step solution:
1. Identify the given values:
- Mass ([tex]\( m \)[/tex]) = 25 kg
- Height ([tex]\( h \)[/tex]) = 3 m
- Gravitational acceleration ([tex]\( g \)[/tex]) = 9.8 m/s²
2. Substitute the values into the potential energy formula:
[tex]\[ PE = 25 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times 3 \, \text{m} \][/tex]
3. Multiply the values together:
[tex]\[ PE = 25 \times 9.8 \times 3 = 735 \, \text{J} \][/tex]
Therefore, the potential energy of the bicycle at the top of the hill is 735 J (joules).
So, the answer is 735 J.
[tex]\[ PE = m \cdot g \cdot h \][/tex]
where:
- [tex]\( PE \)[/tex] is the potential energy,
- [tex]\( m \)[/tex] is the mass of the object (25 kg in this case),
- [tex]\( g \)[/tex] is the acceleration due to gravity (approximately 9.8 m/s² on Earth),
- [tex]\( h \)[/tex] is the height above the ground (3 meters).
Step-by-step solution:
1. Identify the given values:
- Mass ([tex]\( m \)[/tex]) = 25 kg
- Height ([tex]\( h \)[/tex]) = 3 m
- Gravitational acceleration ([tex]\( g \)[/tex]) = 9.8 m/s²
2. Substitute the values into the potential energy formula:
[tex]\[ PE = 25 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times 3 \, \text{m} \][/tex]
3. Multiply the values together:
[tex]\[ PE = 25 \times 9.8 \times 3 = 735 \, \text{J} \][/tex]
Therefore, the potential energy of the bicycle at the top of the hill is 735 J (joules).
So, the answer is 735 J.
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