The electric motor of a model train accelerates the train from rest to 0.580 m/s in 33.0 ms. The total mass of the train is 565 g. Find the average power delivered to the train during its acceleration.
power= work/time=changeKE/time= 1/2 mass(.580)^2 /.033 watts mass has to be in kg.
To find the average power delivered to the train during its acceleration, we can use the formula:
Average Power = Work / Time
First, let's calculate the work done on the train during its acceleration. The work done is equal to the change in kinetic energy.
The formula for kinetic energy is:
Kinetic Energy = (1/2) * mass * velocity^2
Since the train starts from rest, its initial kinetic energy is zero. So, the change in kinetic energy is equal to the final kinetic energy.
Final Kinetic Energy = (1/2) * mass * velocity^2
Plugging in the given values:
Mass = 565 g = 0.565 kg
Velocity = 0.580 m/s
Final Kinetic Energy = (1/2) * 0.565 kg * (0.580 m/s)^2
Now, let's calculate the time taken for the acceleration. The given time is 33.0 ms, which is equal to 0.033 s.
Now, we can substitute the values into the formula for average power:
Average Power = (Final Kinetic Energy - Initial Kinetic Energy) / Time
Since the initial kinetic energy is zero, the formula simplifies to:
Average Power = Final Kinetic Energy / Time
Average Power = [(1/2) * 0.565 kg * (0.580 m/s)^2] / 0.033 s
Calculating this expression will give us the average power delivered to the train during its acceleration.