A sports car is accelerating up a hill that rises 18.0∘ above the horizontal. The coefficient of static friction between the wheels and the road is μs=0.77.It is the static frictional force that propels the car forward. (a) What is the magnitude of the maximumacceleration that the car can have? (b) What is the magnitude of the maximum acceleration if the car isbeing driven down the hill?

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A sports car is accelerating up a hill that rises 18.0∘ above the horizontal. The coefficient of static friction between the wheels and the road is μs=0.77.It is the static frictional force that propels the car forward.  (a) What is the magnitude of the maximumacceleration that the car can have?  (b) What is the magnitude of the maximum acceleration if the car isbeing driven down the hill?

au4gsf · Accepted Answer

First we have draw the free body diagram    The angle between horizontal and inclined plane is θ=18∘  a) From the diagram we can write  mgsin⁡θ+fs=ma  mgsin⁡θ+μsmgcos⁡θ=ma  Therefore the magnitude od acceleration  a=g(sin⁡θ+μsmgcos⁡θ=ma  b) For this in the diagram the direction offriction reversed.  Therefore we can write  mgsin⁡θ−μsmgcos⁡θ=ma  Therefore the magnitude of acceleration  a=g(sin⁡θ−μscos⁡θ=ma  substitute the given values.

A sports car is accelerating up a hill that rises 18.0^\circ above the horizontal. The coefficient of static friction between the wheels and the road

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