the retarding acceleration of 7.35m/s^2 due to frictional force stops the car of mass 400 kg travelling in a road. the coefficient of friction between the tyre of the car and the road is
force=ma
=7.35*400
=2940N
µsN=2970
µ=0.98
To find the coefficient of friction between the tyre of the car and the road, we can use the equation µsN = f, where µs is the coefficient of friction, N is the normal force, and f is the frictional force.
Given that the car has a mass of 400 kg and is experiencing a retarding acceleration of 7.35 m/s^2, we can calculate the frictional force using the formula f = ma, where m is the mass of the car and a is the acceleration.
f = ma
= 7.35 * 400
= 2940 N
Now, we can substitute the value of the frictional force (2940 N) into the equation µsN = f.
µsN = f
µsN = 2940 N
Since we need to find the coefficient of friction (µs), we can rearrange the equation to solve for it.
µs = f / N
To determine the normal force (N), we need to consider that when the car is on a flat road, the weight of the car is balanced by the normal force.
Hence, the normal force can be calculated as N = mg, where m is the mass of the car and g is the acceleration due to gravity (approximately 9.8 m/s^2).
N = mg
= 400 * 9.8
= 3920 N
Now, substituting the values of f and N into the equation, we can calculate the coefficient of friction (µs).
µs = f / N
= 2940 / 3920
≈ 0.75
Therefore, the coefficient of friction between the tyre of the car and the road is approximately 0.75.
To find the coefficient of friction between the tire of the car and the road, we can use the formula:
µ = F/N
Where:
µ is the coefficient of friction
F is the frictional force
N is the normal force
In this case:
F = 2940 N (as calculated)
N = weight = m*g
The weight (W) is given by the formula:
W = m * g
Where:
m is the mass of the car
g is the acceleration due to gravity (approximately 9.8 m/s^2)
In this case:
m = 400 kg (as given)
g = 9.8 m/s^2 (approximate value)
So:
W = 400 kg * 9.8 m/s^2
W = 3920 N
Now, we can substitute the values into the formula:
µ = F/N
µ = 2940 N / 3920 N
µ ≈ 0.75
Therefore, the coefficient of friction between the tire of the car and the road is approximately 0.75.