During a Chicago storm, winds can whip horizontally at speeds of 100 km/h. If the air strikes a person at the rate of 40 kg/s per square meter and is brought to rest, estimate the force of the wind on a person. Assume the person is 1.50m high and 0.50m wide. Compare to the typical maximum force of friction (u = 1.0) between the person and the ground, if the person has a mass of 70 kg.
To estimate the force of the wind on a person, we need to calculate the amount of air striking the person per unit of time and the deceleration of the air.
First, let's calculate the area of the person that the wind strikes. The person's height is given as 1.50 meters and the width is given as 0.50 meters, so the area is:
Area = height x width
Area = 1.50m x 0.50m
Area = 0.75 square meters
Next, we need to calculate the mass of the air striking the person per unit of time. The rate is given as 40 kg/s per square meter, and the area is 0.75 square meters, so the mass of the air striking the person per second is:
Mass = rate x area
Mass = 40 kg/s per square meter x 0.75 square meters
Mass = 30 kg/s
Now, we need to calculate the force of the wind on the person. The force can be calculated using Newton's second law of motion, which states that force equals mass times acceleration:
Force = mass x acceleration
Since the air is brought to rest, the acceleration is the deceleration of the air.
To calculate the deceleration, we need the stopping time. Unfortunately, the stopping time is not given in the question. We could assume a reasonable stopping time, but since it is not specified, we cannot accurately estimate the force of the wind on the person.
However, we can compare the estimated force to the maximum force of friction between the person and the ground.
The maximum force of friction can be calculated using the formula:
Force of friction = coefficient of friction x normal force
The coefficient of friction is given as 1.0, and the normal force can be calculated using the mass of the person and the acceleration due to gravity (9.8 m/s^2):
Normal force = mass x acceleration due to gravity
Normal force = 70 kg x 9.8 m/s^2
Normal force = 686 N
Now, we can calculate the force of friction:
Force of friction = coefficient of friction x normal force
Force of friction = 1.0 x 686 N
Force of friction = 686 N
So, the maximum force of friction between the person and the ground is 686 N.
Although we cannot estimate the force of the wind on the person without the stopping time, we can compare the estimated force to the maximum force of friction between the person and the ground.