The electric motor of a model train accelerates the train from rest to 0.780 m/s in 33.0 ms. The total mass of the train is 510 g. Find the average power delivered to the train during its acceleration.
a = (Vf - Vo) / t,
a = (0.78 - 0) / 0.033s = 23.64m/s^2.
Fn = ma = 0.51 * 23.64 = 12.06N. = Net
force.
W = F*d / t = 12.06 * 0.01287 / 0.033 =
4.7J.
Correction: Po = F*d/t = 4.7Watts.
where did you get the value .01287 for d when calculating for work in the last step of the problem
To find the average power delivered to the train during its acceleration, we can use the formula:
Average Power = Work / Time
First, let's find the work done on the train.
Work is given by the formula:
Work = force * distance
The force on the train can be calculated using Newton's second law:
Force = mass * acceleration
The mass of the train is given as 510 g, which is equal to 0.510 kg.
The acceleration of the train can be calculated using the formula:
Acceleration = (Final Velocity - Initial Velocity) / Time
Given that the initial velocity is 0 and the final velocity is 0.780 m/s, and the time taken is 33.0 ms which is equal to 0.033 s, we can substitute these values into the formula:
Acceleration = (0.780 m/s - 0 m/s) / 0.033 s = 23.636 m/s^2
Now, we can calculate the force:
Force = mass * acceleration = 0.510 kg * 23.636 m/s^2 ≈ 12.055 N
Next, we can calculate the work done:
Work = force * distance
Since the train starts from rest, the distance traveled is given by:
Distance = (1/2) * acceleration * time^2
Substituting the given values, we get:
Distance = (1/2) * 23.636 m/s^2 * (0.033 s)^2 ≈ 0.020 m
Therefore:
Work = force * distance = 12.055 N * 0.020 m ≈ 0.241 J
Finally, we can calculate the average power:
Average Power = Work / Time = 0.241 J / 0.033 s ≈ 7.303 W
Therefore, the average power delivered to the train during its acceleration is approximately 7.303 Watts.