A locomotive train is experiencing a frictional resistance when traveling at 20m/s and the resistance is 1500N. The power development by its engine is 200kW
Calculate
a) The output power of the train
b) the efficiency of the train
a) To calculate the output power of the train, we first need to determine the total resistance the train is facing at 20m/s. This can be done using the formula:
Total resistance = Frictional resistance + Air resistance
Given that the frictional resistance is 1500N and the air resistance is not provided, we will assume the air resistance to be negligible for the calculation.
Total resistance = 1500N
Next, we can calculate the output power of the train using the formula:
Output power = Force x Velocity
Output power = Total resistance x Velocity
Output power = 1500N x 20m/s
Output power = 30000 watts
Convert watts to kilowatts:
Output power = 30000 watts = 30 kW
Therefore, the output power of the train is 30 kW.
b) The efficiency of the train can be calculated using the formula:
Efficiency = (Output power / Input power) x 100%
Given that the input power is 200 kW, we can substitute the values into the formula:
Efficiency = (30 kW / 200 kW) x 100%
Efficiency = 0.15 x 100%
Efficiency = 15%
Therefore, the efficiency of the train is 15%.