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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.
[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.
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