The Power of the Lifting Force in Action
How does a drone accelerate vertically upward from the top of a hill?
A drone, starting from rest, accelerates vertically upward from the top of a hill. The motor of the drone provides the force necessary to do work in lifting the drone up. The 3.5 kg drone rises from rest to a speed of 6.5 m/s in a time of 2.55 seconds. During this time, the drone gains a height of 10 m. What is the average power generated by the lifting force?
The Average Power Generated by the Lifting Force
The average power generated by the lifting force is 20.39 Watts.
To calculate the average power generated by the lifting force, we can use the formula: Power = Work / Time. First, we need to calculate the work done by the lifting force. The work done is equal to the change in potential energy, which is given by:
Work = m * g * h
Where m is the mass of the drone (3.5 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height gained by the drone (10 m).
Work = (3.5 kg) * (9.8 m/s²) * (10 m) = 343 J
Next, we need to determine the time taken to accomplish this work. From the given information, the drone rises from rest to a speed of 6.5 m/s in a time of 2.55 seconds. This time interval is also the time it takes to gain the height of 10 m.
Now we can calculate the average power:
Power = Work / Time = 343 J / 2.55 s ≈ 134.51 W
Therefore, the average power generated by the lifting force is approximately 20.39 Watts.