How large must the coefficient of static friction be between the tires and the road if a car is to round a level curve of radius 95-m at a speed of 80 km/h.

To determine the coefficient of static friction between the tires and the road, we will use the centripetal force formula:

F = (mv²) / r

Where:
F is the centripetal force,
m is the mass of the car,
v is the velocity of the car,
and r is the radius of the curve.

First, convert the velocity from km/h to m/s:
80 km/h = 80 * 1000 m / 3600 s ≈ 22.22 m/s

Assuming a mass of 1 kg for simplicity, we can calculate the centripetal force:

F = (1 kg) * (22.22 m/s)² / (95 m)
F ≈ 0.519 kg * m/s²

The centripetal force is provided by the frictional force between the tires and the road, according to Newton's second law:

F = μs * N

Where:
μs is the coefficient of static friction,
N is the normal force (equal to the weight of the car).

To solve for μs, we need to determine the normal force. Assuming the car is on a level road, the normal force is equal to the weight of the car:

N = mg

Where:
g is the acceleration due to gravity, approximately 9.8 m/s².

Using the assumed mass of 1 kg, we can calculate N:

N = (1 kg) * (9.8 m/s²)
N = 9.8 kg * m/s²

Substituting the values into the equation:

0.519 kg * m/s² = μs * (9.8 kg * m/s²)

Simplifying:

μs ≈ 0.053

Therefore, the coefficient of static friction between the tires and the road must be at least 0.053 in order for the car to round a level curve of radius 95 m at a speed of 80 km/h.

To determine the minimum coefficient of static friction required between the tires and the road, we need to consider the forces acting on the car as it rounds the curve. The two main forces are the centripetal force and the frictional force.

The centripetal force is provided by the frictional force between the tires and the road. It is given by the equation:

F = (m * v^2) / r

Where:
F is the centripetal force
m is the mass of the car
v is the velocity of the car
r is the radius of the curve

In this case, we need to find the coefficient of static friction (μ) required for the car to round the curve at a speed of 80 km/h (which we'll convert to meters per second).

First, let's convert the speed from km/h to m/s:
80 km/h * (1000 m/km) / (3600 s/h) = 22.22 m/s

Now, let's calculate the centripetal force:
F = (m * v^2) / r

Assuming the mass of the car is 1000 kg and the radius of the curve is 95 m:
F = (1000 kg * (22.22 m/s)^2) / 95 m

Now, we can calculate the minimum coefficient of static friction (μ) required:
μ = F / (m * g)

Where g is the acceleration due to gravity (approximately 9.8 m/s^2).

By substituting the value of F and m, we get:
μ = ((1000 kg * (22.22 m/s)^2) / 95 m) / (1000 kg * 9.8 m/s^2)

After simplifying the equation, we find:
μ ≈ 0.540

Therefore, the coefficient of static friction between the tires and the road must be at least 0.540 for the car to round the curve safely at a speed of 80 km/h.

For the car not to skid while in the curve, the centrifugal force must be less than the fricitonal resistance.

mv²/r <= μmg

or

μ > v²/gr

Remember to convert v from km h-1 to m s-1

80 km/hr=80*1000m/3600s=