Question

what is the largest acceleration a car can have if Uk= 0.38 and Us= 0.65 ?

Answer 1

Using Newton's 2nd Law of Motion,

F = ma

where

F = force acting on the car

m = mass of the car

a = acceleration

The only force acting on the car is the frictional force which is equal to

F = µN

where

µ = coefficient of friction

N = normal force = mg

m = mass (as defined above)

g = acceleration due to gravity = 9.8 m/sec^2

Substituting values,

µmg = ma

and since "m" appears on both sides of the equation, it will simply cancel out hence the above becomes,

µg = a

Now, µ_s>µ_k, so µ_s will give maximum acceleration

and solving for "a"

a = 0.65*9.8

a = 6.37 m/sec^2