friction between tires and pavement supplies the centripetal acceleration necessary for a car to turn. Using the coefficients of friction for rubber on concrete calculate the maximum speed at which a car can round a turn of radius 30 m (a) when the road is dry; (b) when the road is wet.
I assume they gave you mu dry and mu wet
Ac = v^2/R = v^2/30
inward force needed = m Ac = m v^2/30
max inward force provided = mu m g
so
v^2 = 30 mu g
Coefficient of friction=F/R=ma/mg=a/g
Coefficient of friction of rubber on dry concrete=0.6>>0.85
So to make it accurate
coefficient=0.75
0.75=a/10
a=7.5m/s^2
Recall that..
v^2=u^2+2as
v^2=0^2+2×7.5×30
v^2=450
v=√450
v=21.2m/s
(b)coefficient of friction of rubber on wet concrete=0.45>>>0.75
coefficient=0.6
0.6=a/10
a=6m/s^2
v^2=u^2+2as
v^2=0+2×6×30
v=√360
v=18.97m/s
To calculate the maximum speed at which a car can round a turn, we can start by considering the forces acting on the car. In this case, the friction between the tires and the pavement provides the centripetal acceleration necessary for the car to turn. The maximum speed occurs when the friction force reaches its maximum value, which is determined by the coefficient of friction between the rubber tires and the concrete pavement.
(a) When the road is dry:
1. Find the coefficient of friction for rubber on concrete: Look up the coefficient of friction between rubber and concrete, typically denoted as "μ." For the sake of example, let's assume the coefficient of friction is μ = 0.8.
2. Calculate the maximum static friction force: The maximum static friction force is given by the formula F(friction) = μ * N, where N is the normal force between the tires and the pavement. In this case, the normal force is equal to the weight of the car (mg), where m is the mass of the car and g is the acceleration due to gravity (approximately 9.8 m/s^2).
3. Calculate the centripetal force: The centripetal force required to keep the car moving in a circular path is given by F(centripetal) = (mv^2) / r, where m is the mass of the car, v is the velocity of the car, and r is the radius of the turn.
4. Set the maximum static friction force equal to the centripetal force: F(friction) = F(centripetal). Solve this equation for v to find the maximum speed.
(b) When the road is wet:
1. Find the coefficient of friction for rubber on wet concrete: The coefficient of friction for rubber on wet concrete is usually lower than on dry surfaces. Look up the coefficient of friction, typically denoted as "μ_wet." For the sake of example, let's assume μ_wet = 0.5.
2. Repeat steps 2-4 above using the new coefficient of friction (μ_wet) to calculate the maximum speed.
Please note that the coefficients of friction provided in this explanation are just for example purposes. Actual coefficients can vary depending on various factors such as tire condition, road conditions, and weather conditions.