What is the maximum speed (in meters/second) with which a 1300 kg car can round a turn of radius 700 m on a flat road, if the coefficent of friction between tires and road is 0.530 ?
centripetal force = max friction
force
M V^2/R = 0.53 M g
M cancels out
Solve for V
V = sqrt(0.53 g R) = 60.3 m/s
To find the maximum speed with which a car can round a turn, we need to consider the centripetal force acting on the car and the maximum frictional force between the tires and the road.
First, we'll calculate the maximum frictional force. The formula for frictional force is:
Frictional force = coefficient of friction × normal force
The normal force acting on the car is equal to the weight of the car, which can be calculated as:
Weight = mass × gravity
where mass is given as 1300 kg and gravity is approximately 9.8 m/s².
Next, we need to calculate the centripetal force. The centripetal force required to keep an object moving in a circle of radius r with a speed v is given by:
Centripetal force = (mass × velocity²) / radius
where the mass is again 1300 kg and the radius is given as 700 m.
Now, we can equate the maximum frictional force to the centripetal force to find the maximum speed:
Coefficient of friction × normal force = (mass × velocity²) / radius
Substituting the values we have:
0.530 × (mass × gravity) = (mass × velocity²) / radius
Rearranging the equation to solve for velocity:
velocity² = (0.530 × mass × radius × gravity) / mass
Canceling out the mass:
velocity² = 0.530 × radius × gravity
Finally, taking the square root of both sides to solve for velocity:
velocity = √(0.530 × radius × gravity)
Plugging in the given values:
velocity = √(0.530 × 700 × 9.8)
Calculating this expression will give us the maximum speed in meters per second.