A car is moving up the plane. Angle of inclination is theta and coeffcient of friction is mu (a)What is the condition in which car can be acceleration? If this condition is satisfied then find (b) maximum acceleration of the car. (c) maximum retardation of the car. (d) maximum retardation of the car.
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(a) mgsinθ in all condition is downwards but direction of friction may be upwards or downwards.
The accelerator needs to be pressed for an upward friction and brakes for downwards friction. To accelerate the car friction should be upwards .
Therefore car can be accelerated if maximum upwards friction >mgsinθ
or μmgcosθ>mgsinθ or μ>tanθ
(b) Maximum acceleration = maximum upward force / mass
= μmgcosθ − mgsinθ / m
= ( μgcosθ − mgsinθ )
(c) Minimum retardation wil be zero , when upward friction is mgsinθ
(d) Maximum retardation = Maximum upwards force / m
= mgsinθ + μmgcosθ/m
= (gsinθ+μgcosθ)
Here,the maximum friction force acts in downward direction
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