What is the maximum speed with which a 1070 kg car can round a turn of radius 80 m on a flat road if the coefficient of static friction between tires and road is 0.80?
Matching the centrifugal force with the frictional resistance,
μmg = mv²/r
solving for v,
v=√(μgr)
=25 m/s
This is assuming that there is no superelevation built into the bend.
To find the maximum speed at which a car can round a turn, we need to consider the balance of forces acting on the car.
First, we need to calculate the maximum friction force that the tires can provide. The formula for static friction is:
friction force = coefficient of static friction × normal force
The normal force is equal to the weight of the car, which can be calculated as:
weight = mass × acceleration due to gravity
Using the given mass of the car (1070 kg) and assuming the acceleration due to gravity is 9.8 m/s², we find:
weight = 1070 kg × 9.8 m/s²
Next, we can calculate the maximum friction force:
friction force = 0.80 × weight
Now, we need to consider the centripetal force required to keep the car moving in a circle. The centripetal force is given by:
centripetal force = (mass × velocity²) / radius
We can rearrange this equation to solve for the velocity:
velocity = √((centripetal force × radius) / mass)
In this case, the centripetal force is equal to the maximum friction force. Plugging in the known values:
velocity = √((friction force × radius) / mass)
Finally, we can substitute the values we calculated earlier for the friction force, radius, and mass into the equation to find the maximum velocity:
velocity = √((0.8 × weight × radius) / mass)
Solving this equation will give us the maximum speed at which the car can round the turn on a flat road.