The electric motor of a model train accelerates the train from rest to 0.700 m/s in 17.0 ms. The total mass of the train is 670 g. Find the average power delivered to the train during its acceleration.
To find the average power delivered to the train during its acceleration, we can use the formula:
Power = (work done) / (time)
The work done on an object can be calculated using the formula:
Work = force × distance
In this case, the force can be calculated using Newton's second law:
Force = mass × acceleration
Given information:
Initial velocity (u) = 0 m/s
Final velocity (v) = 0.700 m/s
Time (t) = 17.0 ms = 0.017 s
Mass (m) = 670 g = 0.670 kg
Step 1: Calculate the acceleration of the train.
Acceleration (a) = (v - u) / t
= (0.700 m/s - 0 m/s) / 0.017 s
Step 2: Calculate the force exerted by the motor.
Force = mass × acceleration
Step 3: Calculate the work done.
Work = force × distance
Since the train starts from rest, the initial distance is 0. As the train moves in a straight line, the work done is equal to the kinetic energy gained by the train.
Kinetic energy = (1/2) × mass × (final velocity)^2
Step 4: Calculate the power.
Power = work / time
Let's calculate step by step:
Step 1: Calculate the acceleration (a):
a = (0.700 m/s - 0 m/s) / 0.017 s
Step 2: Calculate the force (F):
F = mass × acceleration
Step 3: Calculate the work done (W) or kinetic energy gained:
Kinetic energy = (1/2) × mass × (final velocity)^2
Step 4: Calculate the power (P):
Power = work / time
Plugging in the given values, we get:
Step 1: Calculate the acceleration (a):
a = (0.700 m/s - 0 m/s) / 0.017 s
Step 2: Calculate the force (F):
F = mass × acceleration
Step 3: Calculate the work done (W) or kinetic energy gained:
Kinetic energy = (1/2) × mass × (final velocity)^2
Step 4: Calculate the power (P):
Power = work / time
Let's calculate step by step:
Step 1: Calculate the acceleration (a):
a = (0.700 m/s - 0 m/s) / 0.017 s
= 41.176 m/s^2
Step 2: Calculate the force (F):
F = mass × acceleration
= 0.670 kg × 41.176 m/s^2
Step 3: Calculate the work done (W) or kinetic energy gained:
Kinetic energy = (1/2) × mass × (final velocity)^2
= (1/2) × 0.670 kg × (0.700 m/s)^2
Step 4: Calculate the power (P):
Power = work / time
= kinetic energy / time
Plugging in the calculated values, we get:
Power = [(1/2) × 0.670 kg × (0.700 m/s)^2] / 0.017 s
Now you can calculate the final answer.