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 =
To find the average force of air resistance, we need to use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
In this case, we know the mass of the purse is 7 kg, and we need to find the acceleration due to air resistance. We can calculate the acceleration using the equation for acceleration:
a = (v_f - v_i) / t
where:
- a is the acceleration,
- v_f is the final velocity (17 m/s in this case),
- v_i is the initial velocity (0 m/s if the purse is dropped from rest), and
- t is the time it took for the purse to fall.
Since we are not given the time, we need to calculate it using the equation for falling distance:
d = (1/2) * g * t^2
where:
- d is the distance fallen (53 m in this case),
- g is the acceleration due to gravity (9.8 m/s^2), and
- t is the time it took for the purse to fall.
Rearranging the equation for time, we have:
t = sqrt(2d / g)
Substituting the given values into the equation, we can find the time it took for the purse to fall:
t = sqrt(2 * 53 / 9.8) ≈ 3.25 s
Now that we have the time, we can calculate the acceleration:
a = (17 - 0) / 3.25 ≈ 5.23 m/s^2
Finally, we can find the average force of air resistance using Newton's second law:
F = m * a = 7 * 5.23 ≈ 36.6 N
Therefore, the average force of air resistance is approximately 36.6 Newtons.