A motorcyclist (with a total mass of 180kg) travels up a hill. When she starts at the bottom of the hill (altitude 32m) her velocity is 43km/h. At the top of the hill (altitude 365m) she has a speed of 115km/h. The hill is 12km long and during the journey she applies a braking force of 694N over a distance of 8m. Calculate the useful work done by the motorcycle engine assuming that resistance to motion is constant and equal to 186N throughout the journey, calculate the useful power supplied by the engine if the whole journey took 9min and calculate the fuel energy required if the engine has an efficiency of 59%. Please guys help me out on this problem
To solve this problem, we need to calculate the useful work done by the motorcycle engine, the useful power supplied by the engine, and the fuel energy required. Let's break it down step by step.
1. Calculate the gravitational potential energy difference:
The work done against gravity can be calculated using the formula:
Work = m * g * h (mass * acceleration due to gravity * height difference)
Where:
m = mass of the motorcyclist (180kg)
g = acceleration due to gravity (9.8 m/s^2)
h = difference in altitude (365m - 32m = 333m)
Work = 180kg * 9.8 m/s^2 * 333m
2. Calculate the work done against resistance to motion:
The work done against resistance to motion can be calculated using the formula:
Work = force * distance
Where:
force = resistance to motion (186N)
distance = total distance traveled (12km = 12,000m)
Work = 186N * 12,000m
3. Calculate the work done against braking force:
The work done against braking force can be calculated using the formula:
Work = force * distance
Where:
force = braking force applied (694N)
distance = distance over which the braking force is applied (8m)
Work = 694N * 8m
4. Calculate the useful work done by the engine:
The useful work done by the engine is the total work done minus the work done against resistance and braking force.
Useful Work = Total Work - Work against Resistance - Work against Braking Force
5. Calculate the useful power supplied by the engine:
Useful power can be calculated using the formula:
Power = Work / Time
Where:
Work = Useful Work done by the engine
Time = Total time taken for the journey (9 minutes = 9 * 60 seconds)
Useful Power = Useful Work / Time
6. Calculate the fuel energy required:
Fuel energy required can be calculated using the formula:
Fuel energy = Useful Work / Engine Efficiency
Where:
Useful Work = Useful Work done by the engine
Engine Efficiency = efficiency of the engine (59% = 0.59)
Fuel Energy = Useful Work / Engine Efficiency
Now, let's calculate the values:
1. Calculate the gravitational potential energy difference:
Work = 180kg * 9.8 m/s^2 * 333m
2. Calculate the work done against resistance to motion:
Work = 186N * 12,000m
3. Calculate the work done against braking force:
Work = 694N * 8m
4. Calculate the useful work done by the engine:
Useful Work = Total Work - Work against Resistance - Work against Braking Force
5. Calculate the useful power supplied by the engine:
Useful Power = Useful Work / Time
6. Calculate the fuel energy required:
Fuel Energy = Useful Work / Engine Efficiency
Using these calculations, you can find the answers to the questions.