Concept explainers
The coefficient of static friction between the car’s tires and the road.
Answer to Problem 77PQ
The coefficient of static friction between the car’s tires and the road is
Explanation of Solution
The force of static friction on the automobile must act forward and then more and more inward on the tires, to produce both tangential acceleration and to maintain the centripetal acceleration.
Write the equation for the tangential force.
Here,
The
Write the equation for the centripetal force.
Here,
Write the equation for
Here,
Write the equation for the angular speed.
Here,
Multiply both numerator and denominator of right hand side of equation (III) and put the above equation in it.
Put the above equation in equation (II).
The centripetal force increases with time as the speed increases and it reaches its maximum value when the automobile has travelled
Write the equation for
Here,
Put the above equation in equation (IV).
The automobile starts from rest so that its initial angular velocity must be zero.
Substitute
Write the equation for the linear acceleration in terms of angular acceleration.
Put the above equation in equation (V).
The force of friction when the car slips is equal to the magnitude of the total force found using the Pythagorean theorem.
Here,
Write the equation for
Here,
The normal force is equal to the weight of the car.
Write the equation for
Here,
Put the above equation in equation (VIII).
Put equations (I), (VI) and (IX) in equation (VII) and rewrite the equation for
Conclusion:
Given that the tangential acceleration is
Substitute
Therefore, the coefficient of static friction between the car’s tires and the road is
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Chapter 12 Solutions
Physics for Scientists and Engineers: Foundations and Connections
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