A helicopter, starting from rest, accelerates straight up from the roof of a hospital. The lifting force does work in raising the helicopter. An 740-kg helicopter rises from rest to a speed of 7.6 m/s in a time of 3.1 s. During this time it climbs to a height of 8.6 m. What is the average power generated by the lifting force?
power=work/time=mgh/time +finalKE/time
To find the average power generated by the lifting force, we need to calculate the work done by the lifting force and divide it by the time interval.
First, let's calculate the work done by the lifting force. The work done to raise an object against gravity is given by the formula:
Work = Force × Distance × cos(θ), where θ is the angle between the force and the displacement.
In this case, the lifting force is acting in the opposite direction to the displacement, so cos(θ) = -1. Therefore, the formula for work becomes:
Work = -Force × Distance
The distance traveled by the helicopter is given as 8.6 m. The lifting force is equal to the weight of the helicopter, which can be calculated using the formula:
Force = mass × acceleration due to gravity
Given that the mass of the helicopter is 740 kg and acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the lifting force.
Force = 740 kg × 9.8 m/s^2
Now, we can calculate the work done by the lifting force.
Work = -(740 kg × 9.8 m/s^2) × 8.6 m
Next, we can calculate the time interval. Given that the helicopter reaches a speed of 7.6 m/s in a time of 3.1 s, we can use this information to find the average velocity during this time.
Average velocity = Change in displacement / Time interval
The change in displacement is equal to the height climbed, which is 8.6 m. Rearranging the formula, we get:
Time interval = Change in displacement / Average velocity
Time interval = 8.6 m / 7.6 m/s
Finally, we can calculate the average power generated by the lifting force.
Average power = Work / Time interval
Substituting the values we calculated earlier, we can find the answer.