Concept explainers
The coefficient of kinetic friction between the drag-race tires in contact with an asphalt surface.
Answer to Problem 43P
Solution:
The coefficient of kinetic friction between the drag-race tires and asphalt was found to be 1.4.
Explanation of Solution
During a drag-race, the vehicle exerts a very strong force on the ground. This in turn exerts a very large acceleration on the vehicle. The force of kinetic friction between the tires and the surface provides the acceleration for the vehicle.
Given:
The distance covered by the drag-racer
The time taken to cover the distance
The initial speed of the drag-racer is
Formula used:
According to Newton’s second law of motion:
Second equation of motion is:
Here, the force of kinetic friction is
The weight W of the car acts vertically downwards and due to Newton’s third law, the car experiences an upward force called normal force
Therefore,
The normal force has the same magnitude as that of the weight and it acts opposite to the direction of the weight.
As the magnitude of the normal force is
The force of kinetic friction is related to the normal force as,
Therefore
This force provides accelerationa on the vehicle.
From equations (1) and (2),
The acceleration experienced by the car is given by,
Calculation:
The acceleration of the vehicle can be calculated using the equation of motion,
Since, the vehicle starts from rest,
Therefore,
From equations (3) and (4),
Using the given values of s , g and t in the equation
Conclusion:
The drag-racer would cover a distance of 1 km in 12 s starting from rest if the coefficient of kinetic friction between the tires and the asphalt surface is 1.4.
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