A motor lifts a 70.0 kg box off the ground, starting from rest. In 8.00 seconds it lifts the box to a height of 20.0 m. At that time, the box is moving upward with a velocity of 5.00 m/s. What is the average power of the motor during this time interval?
1820w
P =W/t = ΔE/t = (m•g•h +m•v²/2)/t
P =W/t = ΔE/t = (m•g•h +m•v²/2)/t
To find the average power of the motor, we can use the formula:
Power = Work / Time
First, let's calculate the work done on the box by the motor. The work done is equal to the change in potential energy of the box, which can be calculated using the formula:
Work = Force × Distance
The force can be determined using Newton's second law:
Force = mass × acceleration
Since the box is moving vertically, the only force acting on it is its weight, which can be calculated as:
Weight = mass × gravitational acceleration
Let's calculate the force and then the work done:
Weight = mass × gravitational acceleration
Weight = 70.0 kg × 9.8 m/s^2 (gravitational acceleration)
Weight = 686 N
Now, we can calculate the work done:
Work = Force × Distance
Work = 686 N × 20.0 m (distance)
Work = 13720 J (Joules)
Next, we need to calculate the time:
Time = 8.00 seconds
Finally, we can calculate the average power:
Power = Work / Time
Power = 13720 J / 8.00 s
Power = 1715 W (Watts)
Therefore, the average power of the motor during this time interval is 1715 Watts.