2. How much energy would a body of mass 50kg need to provide for the following:
a. Climbing a hill 500m high.
b. Walking up steps 10m tall.
c. Jumping 10cm up.
Work done (energy required) = mgh
m=50 kg
g=9.8 m/s²
h=difference in elevation in metres.
Energy/work in joules.
To calculate the energy required for each scenario, we need to use the formula for gravitational potential energy:
Potential Energy = Mass x Gravity x Height
Where:
- Mass is the mass of the body in kilograms (kg)
- Gravity is the acceleration due to gravity, which is approximately 9.8 meters per second squared (m/s²)
- Height is the vertical distance in meters (m)
Let's calculate the energy required for each scenario:
a. Climbing a hill 500m high:
Potential Energy = Mass x Gravity x Height
Potential Energy = 50 kg x 9.8 m/s² x 500 m
Potential Energy = 245,000 Joules (J)
So, the body would need to provide 245,000 Joules of energy to climb a hill 500m high.
b. Walking up steps 10m tall:
Potential Energy = Mass x Gravity x Height
Potential Energy = 50 kg x 9.8 m/s² x 10 m
Potential Energy = 4,900 Joules (J)
Therefore, the body would need to provide 4,900 Joules of energy to walk up steps 10m tall.
c. Jumping 10cm up:
Potential Energy = Mass x Gravity x Height
Before we proceed, we need to convert 10cm to meters. There are 100 centimeters in 1 meter, so 10cm is equivalent to 0.1 meters.
Potential Energy = 50 kg x 9.8 m/s² x 0.1 m
Potential Energy = 49 Joules (J)
Hence, the body would need to provide 49 Joules of energy to jump 10cm up.