Physics for Scientists and Engineers: Foundations and Connections
Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN: 9781133939146
Author: Katz, Debora M.
Publisher: Cengage Learning
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Chapter 6, Problem 40PQ

(a)

To determine

Give estimation on weight and area of a typical car.

(a)

Expert Solution
Check Mark

Answer to Problem 40PQ

A typical car can have weight around 906kg and area 2m2.

Explanation of Solution

The average of weight of car can be taken as two thousand pounds. Express two thousand pounds in kilogram.

    2000pounds(0.453kg1pound)=906kg

Normally a car can have 6feet width and 3feet height. Express area in square meter.

    (6feet×3feet)(0.0929m21foot)2m2

Conclusion:

Therefore, a typical car can have weight around 906kg and area 2m2.

(b)

To determine

Draw the graph of v2 against FD and check whether the shape of graph conveys sensible data.

(b)

Expert Solution
Check Mark

Answer to Problem 40PQ

Graph of v2 against FD is drawn and the conveying result is consistent with equation for drag force.

Explanation of Solution

The graph of v2 with FD is drawn below.

    Physics for Scientists and Engineers: Foundations and Connections, Chapter 6, Problem 40PQ

Write the equation for drag force.

    FD=12CρAv2

Here, FD is the drag force, C is the drag coefficient, ρ is the density of air, and v is the speed of air.

Substitute 0.4 for C, 1.3kg/m3 for ρ, and 2m2 for A in the above equation.

    FD=12(0.4)(1.3kg/m3)(2m2)v20.5v2                                                             (I)

The equation tells that the drag force is varying with the square of speed of car. It can be seen that the graph is also conveying the same result. Graph shows that FD is directly proportional to v2.

Conclusion:

Therefore, the graph of v2 against FD is drawn and the conveying result is consistent with equation for drag force.

(c)

To determine

The value of Rolling frictional force of car and add the estimate to graph.

(c)

Expert Solution
Check Mark

Answer to Problem 40PQ

Rolling frictional force is 180N and it appears as a straight line in the graph.

Explanation of Solution

Write the equation to find the rolling friction.

    Fr=μr(mg)

Here, Fr is the rolling frictional force, μr is the coefficient of friction, m is the mass of car, and  g is the gravitational acceleration.

Conclusion:

Substitute 0.02 for μr, 900kg for m, and 9.8m/s2 for g in the above equation to find Fr.

    Fr=(0.02)(900kg)(9.8m/s2)=180N                                                                 (II)

It can be seen that Fr is independent of v. So, it appears as a straight line in the graph.

Therefore, the rolling frictional force is 180N and it appears as a straight line in the graph.

(d)

To determine

The speed at which drag force equals rolling frictional force and the range of speed which the drag force can be neglected.

(d)

Expert Solution
Check Mark

Answer to Problem 40PQ

The speed at which drag force equals rolling frictional force is 19m/s and the drag force can be neglected for speed less than around 10m/s.

Explanation of Solution

Equate the right hand sides of equations (1) and (II).

    0.5v2=180Nv2=360N

Rewrite the above expression in terms of v.

    v=19m/s

It can be seen that lower speeds, drag force will be lesser than rolling frictional force. So drag force can be neglected at lower speed. It is better to limit the speed within 10m/s. Note that this value is not a result of exact calculation.

Conclusion:

Therefore, the speed at which drag force equals rolling frictional force is 19m/s and the drag force can be neglected for speed less than around 10m/s.

(e)

To determine

The change in answer on the assumption that Fd is proportional to v instead of v2.

(e)

Expert Solution
Check Mark

Answer to Problem 40PQ

Fd would decrease more if is proportional to v instead of v2.

Explanation of Solution

Fd is directly proportional to v. On comparing the value of Fd for same value of speed in v and v2. Lower value of Fd is obtained while the variation is proportional to v. In other words, it tells that it would be more safe to ignore the frictional force too at the lower speeds.

Therefore, the Fd would decrease more if is proportional to v instead of v2.

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Chapter 6 Solutions

Physics for Scientists and Engineers: Foundations and Connections

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