A 7 kg purse is dropped from the top of the Leaning Tower of Pisa and falls 53 m before reaching the ground with a speed of 17 m/s. What was the average force of air resistance?
F_{average} =
loss of potential energy = m g h
gain of kinetic energy = (1/2)m v^2
difference = work against friction
which = F * 53 neters
To calculate the average force of air resistance, we can use the work-energy theorem. The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy.
In this case, the initial kinetic energy of the purse is zero (since it was dropped from rest), and the final kinetic energy is given by the formula:
Kinetic energy = (1/2) * mass * velocity^2
So, the change in kinetic energy is:
Change in kinetic energy = (1/2) * mass * velocity^2 - 0
Now, work done by air resistance is equal to the change in kinetic energy:
Work done by air resistance = Change in kinetic energy
As the work done is equal to force times distance, we can express it as:
Work done by air resistance = Force * distance
Since we have already provided the distance the purse falls (53 m), we can rearrange the equation to solve for the force of air resistance:
Force = (Change in kinetic energy) / distance
Substituting the given values into the equation, we get:
Force = [(1/2) * mass * velocity^2 - 0] / distance
Force = [(1/2) * 7 kg * (17 m/s)^2] / 53 m
Simplifying the equation:
Force ≈ 142.42 N
Therefore, the average force of air resistance on the purse is approximately 142.42 Newtons.