Physics of Everyday Phenomena
Physics of Everyday Phenomena
9th Edition
ISBN: 9781259894008
Author: W. Thomas Griffith, Juliet Brosing Professor
Publisher: McGraw-Hill Education
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Chapter 4, Problem 7SP

A skydiver has a weight of 850 N. Suppose that the air-resistive force acting on the diver increases in direct proportion to his velocity such that for every 10 m/s that the diver’s velocity increases, the force of air resistance increases by 100 N.

  1. a. What is the net force acting on the skydiver when his velocity is 30 m/s?
  2. b. What is the acceleration of the diver at this velocity?
  3. c. What is the terminal velocity of the skydiver?
  4. d. What would happen to the velocity of the skydiver if for some reason (perhaps a brief down draft) his velocity exceeded the terminal velocity? Explain.

(a)

Expert Solution
Check Mark
To determine

The net force acting on the skydiver of weight 850N if the air resistive force will increase by 100N for every 10m/s increase in the velocity.

Answer to Problem 7SP

The net force acting on the skydiver of weight 850N if the air resistive force will increases by 100N for every 10m/s increase in the velocity is 550N.

Explanation of Solution

Given info: The weight of the skydiver is 850N and increase in the air resistive force for every 10m/s increase in the velocity is 100N.

If the air resistive force will increases by 100N for every 10m/s increase in the velocity,300N will increase for a 30m/s increase in the velocity.

Write the net force acting on the skydiver.

Fnet=Fupward+Fdownward

Take Fupward as negative since it is acting in the upward direction.

The only force acting downward is the gravitational force and force acting in the upward direction is the air resistive force.

Therefore substitute 850N for Fdownward and 300N for Fupward in the above equation to gjet Fnet.

Fnet=850N300N=550N

Thus the net force is in the downward direction.

Conclusion:

Thus, the net force acting on the skydiver of weight 850N if the air resistive force will increases by 100N for every 10m/s increase in the velocity is 550N.

(b)

Expert Solution
Check Mark
To determine

The acceleration of the diver at the velocity.

Answer to Problem 7SP

The acceleration of the diver at the velocity is 6.34m/s2.

Explanation of Solution

Given info: The mass of the man is 85kg and acceleration of the man is 1.3m/s2.

Write the expression for the mass of the diver.

m=Wg

Here,

m is the mass of the diver

g is the gravitational acceleration

Substitute 850N for Fnet  and 9.8m/s2 for g in the above equation to get m.

m=850N9.8m/s2=86.73kg

Write the expression for the net force on the diver.

Fnet=ma

Here,

Fnet is the net force acting on the diver

a is the acceleration of the diver

Rearrange the above equation to get a.

a=Fnetm

Substitute 86.73kg for m and 550N for Fnet in the above equation to get Fnet.

a=550N86.73kg=6.34m/s2

Conclusion:

Thus, the acceleration of the diver at the velocity is 6.34m/s2.

(c)

Expert Solution
Check Mark
To determine

The terminal velocity of the skydiver.

Answer to Problem 7SP

The terminal velocity of the skydiver is 85m/s.

Explanation of Solution

Given info: increase in the air resistive force for every 10m/s increase in the velocity is 100N.

The diver will attain terminal velocity if the upward force is equal to the weight of the diver.

The weight of the diver is 850N. This force is acting downward. This force can be balanced by the upward force of magnitude equal to 850N.

Since increase in the air resistive force for every 10m/s increase in the velocity is 100N. Therefore he will attain an air resistive force of 850 N only if velocity of the diver reaches 85m/s.

Therefore at this velocity upward force becomes 8.5 times the force for initial 10m/s. Therefore terminal velocity of the skydiver is equal to 85m/s.

Conclusion:

Thus, the terminal velocity of the skydiver is 85m/s.

(d)

Expert Solution
Check Mark
To determine

What would happen to the velocity of the skydiver if for some reason his velocity exceeded the terminal velocity?

Answer to Problem 7SP

This will cause windburn due to increase in the frictional force and sudden change in velocity to the terminal velocity.

Explanation of Solution

Terminal velocity is the uniform velocity of falling body in a viscous medium if the upward force is equal to downward velocity.

If the velocity is exceeded the terminal velocity, it will cause increase in the resistive force and dissipation of energy in the form of heat occurs. This may create wind burn. This resistive for reduce the velocity to terminal velocity.

Conclusion:

Thus, exceeding velocity more than terminal velocity will cause windburn due to increase in the frictional force and sudden change in velocity to the terminal velocity.

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Chapter 4 Solutions

Physics of Everyday Phenomena

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