College Physics, Volume 1
College Physics, Volume 1
2nd Edition
ISBN: 9781133710271
Author: Giordano
Publisher: Cengage
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Chapter 4, Problem 45P
To determine

The stopping distance of the car measured along the incline.

Expert Solution & Answer
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Answer to Problem 45P

The stopping distance of the car measured along the incline is 25m_.

Explanation of Solution

Figure 1 represents the free body diagram of car on level ground.

College Physics, Volume 1, Chapter 4, Problem 45P , additional homework tip  1

Figure 1 represents the free body diagram of car on the incline .

College Physics, Volume 1, Chapter 4, Problem 45P , additional homework tip  2

Write the kinematic equation.

    v2=v02+2ax        (I)

Here, v is the final velocity, v0 is the initial velocity, a is the acceleration, and x is the initial distance of the car.

Write the expression for net force acting on the car.

F=ma        (II)

Here, m is the mass of the car, and a is the acceleration of the car.

Write the expression for kinetic friction force.

    Ffriction=μkN

Here, Ffriction is the friction force, μk is the coefficient of friction force, and N is the normal force.

The above equation can be written as

    Ffriction=μkmg        (III)

The net force acting on the level car is opposite to the friction force.

    malevelcar=μkmg

Rearrange the above equation.

    malevelcar=μkmgμk=alevelcarg        (IV)

Since the car on the level ground is at rest, equation (I) is written as

    v2=v02+2alevel carxlevel caralevel car =v022xlevel car 

Use the above equation in equation (IV).

    μk=(v022xlevel car )g=v022gxlevel car         (V)

Write the acceleration of the object down an incline from equation.

    aincline=g(sinθμkcosθ)

Here, aincline is the acceleration of the incline, g is acceleration due to gravity, μk is the coefficient of kinetic friction, and θ is the angle of inclination.

Use the above equation in equation (V).

    aincline=g(sinθ(v022gxlevel car )cosθ)        (VI)

Write the kinematic equation of the car in inclined motion.

    v2=v02+2ainclinexincline 

Here, v is the final velocity of the car in inclined motion, vo is the initial velocity of the car in inclined motion, aincline is the acceleration of the car in incline plane, and xincline  is the stopping distance of the car.

Since the final velocity of the car in inclined motion is zero, the above equation is written as

    0=v02+2ainclinexincline v02=2ainclinexincline xincline =v022aincline        (VII)

Conclusion:

Substitute 9.8m/s2 for g, 8.0° for θ, 25m/s for v0, 22m for vlevel car  in equation (VI), to find aincline .

    aincline=(9.8m/s2)[sin8.0°((25m/s)22(9.8m/s2)22m)cos8.0°]=12m/s2

Substitute 9.8m/s2 for g, 25m/s for v0, 12.7m/s2 for aincline car in equation (VII), to find xincline .

    xincline =(25m/s)22(12.7m/s2)=25m

Therefore, the stopping distance of the car measured along the incline is 25m_.

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Chapter 4 Solutions

College Physics, Volume 1

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