Acar travels along a horizontal road which is an
arc of a circle of radius 125m. the greatest speed.
at which the car can travel without slipping is
42km/hr. Find the coefficient of friction between
the tyres of the car and the road surface.(A)0.11
To find the coefficient of friction, we can use the formula:
v = √(rg)
Where:
v = velocity of the car (converted to m/s)
r = radius of the circle (125m)
g = acceleration due to gravity (9.8 m/s^2)
First, let's convert the velocity from km/hr to m/s:
42 km/hr * (1000 m/1 km) * (1 hr/3600 s) = 11.67 m/s
Now let's plug in the values into the formula:
11.67 m/s = √(125m * 9.8m/s^2 * μ)
Simplifying:
11.67 m/s = √(1225m^2/s^2 * μ)
Square both sides:
(11.67 m/s)^2 = 1225m^2/s^2 * μ
Solving for μ:
μ = (11.67 m/s)^2 / (1225m^2/s^2)
μ = 0.1113
Rounding to two decimal places, the coefficient of friction is approximately 0.11. Therefore, the correct answer is (A) 0.11.
To find the coefficient of friction between the tires of the car and the road surface, we need to use the maximum speed of the car without slipping and the radius of the road.
Step 1: Convert the maximum speed from km/hr to m/s.
42 km/hr * (1000 m / 1 km) * (1 hr / 3600 s) = 11.67 m/s
Step 2: Calculate the acceleration of the car using the centripetal acceleration formula.
Centripetal acceleration (a) = v^2 / r
where v is the velocity and r is the radius.
So, a = (11.67 m/s)^2 / 125 m = 1.082 m/s^2
Step 3: Calculate the gravitational force acting on the car.
The gravitational force (Fg) is equal to the weight of the car (mass x gravity).
Assuming the mass of the car is m kg and the acceleration due to gravity is g = 9.8 m/s^2, we have Fg = m * g.
Step 4: Calculate the maximum frictional force (Ff) that can prevent slipping.
The maximum frictional force (Ff) is equal to the product of the coefficient of friction (μ) and the normal force (Fn) acting on the car. Since the car is on a flat horizontal surface, the normal force is equal to the gravitational force (Fn = Fg). Therefore, Ff = μ * Fg.
Step 5: Equate the centripetal acceleration and the maximum frictional force.
Since the centripetal acceleration is caused by the frictional force, we have a = Ff / m.
By combining steps 4 and 5, we can write:
μ * Fg / m = a
Step 6: Substitute the expressions for Fg and a.
μ * (m * g) / m = a
μ * g = a
Step 7: Solve for the coefficient of friction (μ).
μ = a / g = 1.082 m/s^2 / 9.8 m/s^2 ≈ 0.11
Therefore, the coefficient of friction between the tires of the car and the road surface is approximately 0.11.