find the power of an engine in kilowatts which pulls a train of mass 600 tonnes up an incline of 1 in 100 at the rate of 60 km per hour. the weight of the engine is 200 tonnes and the resistance due to friction is 50 newton per tonne
It is important for board exam
To find the power of the engine in kilowatts, we need to consider several factors: the mass of the train, the incline, the velocity, the weight of the engine, and the resistance due to friction.
First, let's convert the given values to SI units for consistency:
Mass of the train = 600 tonnes = 600,000 kg
Incline = 1 in 100 = 1/100
Velocity = 60 km/h = (60,000 m) / (3600 s) = 16.67 m/s
Weight of the engine = 200 tonnes = 200,000 kg
Resistance due to friction = 50 N/tonne
Next, we need to calculate the force required to pull the train up the incline, taking into account gravity and friction. The force equation is as follows:
Force = (Mass × Acceleration) + Resistance
Since the train is moving up an incline, acceleration is the product of the gravitational acceleration (9.8 m/s^2) and the sine of the angle of the incline:
Acceleration = 9.8 m/s^2 × (1/100)
Now let's calculate the force:
Force = (600,000 kg × 9.8 m/s^2 × (1/100)) + (200,000 kg × 9.8 m/s^2) + (50 N/tonne × 600 tonnes)
Next, we need to calculate the work done to move the train up the incline. The work equation is as follows:
Work = Force × Distance
In this case, the distance is the rate of velocity multiplied by time:
Distance = Velocity × Time
Given that the distance is 1 unit (1 in 100) and velocity is 16.67 m/s, we can calculate the time required to cover the distance:
Time = Distance / Velocity
Now we can calculate the work:
Work = Force × Distance = Force × (Velocity × Time)
Finally, to find the power, we divide the work done by the time:
Power = Work / Time
Now, let's plug in the values and calculate the power.
Power = (Force × (Velocity × Time)) / Time
Please provide the time it takes to cover the distance, or if you want to calculate the power over a given time interval.