A 250.0 kg motorcycle can roll 45.9 m up a long hill before coming to a stop if the motorcycle approaches the base of the hill 30.0 m/s.
To find the work done by the motorcycle while climbing the hill, we need to calculate the change in its gravitational potential energy. The formula for gravitational potential energy is:
Potential energy (PE) = mass (m) × gravity (g) × height (h)
Given:
Mass of the motorcycle (m) = 250.0 kg
Height of the hill (h) = 45.9 m
Gravity (g) = 9.8 m/s² (approximate value on Earth)
First, we calculate the initial potential energy (PE_initial) of the motorcycle when it approaches the base of the hill. It is given by:
PE_initial = m × g × 0
= 0 (since the height is 0 at the base of the hill)
Next, we calculate the final potential energy (PE_final) of the motorcycle when it comes to a stop at the top of the hill. It is given by:
PE_final = m × g × h
PE_final = 250.0 kg × 9.8 m/s² × 45.9 m
≈ 111,225 J (Joules)
The work done (W) by the motorcycle is the change in potential energy:
W = PE_final - PE_initial
= PE_final - 0
= PE_final
Hence, the work done by the motorcycle in climbing the hill is approximately 111,225 Joules (J).