what is the maximum speed with which a car can round a turn of radius of 80.0m on a flat road if the coefficient of friction between tires and the road is .700?
My teacher said two substitutions and I don't have a mass. Thanks (:
you screwed buddy
To determine the maximum speed at which a car can round a turn on a flat road, we can use the concept of centripetal force. The maximum speed occurs when the centripetal force is equal to the maximum frictional force between the tires and the road.
Here's how you can find the answer using two substitutions:
1. Start by recalling the formula for centripetal force: Fc = (mv^2) / r, where Fc is the centripetal force, m is the mass of the car, v is the velocity, and r is the radius of the turn.
2. Since you don't have the mass of the car, you need to eliminate it from the equation. You can do this by substituting the weight of the car (mg) with the normal force (N) between the car and the road. This substitution is valid because the normal force is equal to the weight when the car is on a flat surface.
3. In this case, the maximum static frictional force can be expressed as the coefficient of friction (µ) multiplied by the normal force: Fs = µN.
4. The normal force (N) is equal to the weight (mg), where g is the acceleration due to gravity (approximately 9.8 m/s^2).
5. Now you can substitute the formula for the centripetal force (Fc) with the maximum frictional force (Fs): Fs = (mv^2) / r.
6. Substitute Fs with µN and N with mg: µmg = (mv^2) / r.
7. Simplify the equation by canceling out the mass (m) on both sides: µg = (v^2) / r.
8. Solve for the maximum velocity (v): v^2 = µgr.
9. Finally, take the square root of both sides to find the maximum speed: v = √(µgr).
10. Substitute the given values: µ = 0.700 and r = 80.0 m into the equation to find the maximum speed of the car while rounding the turn.
By following these steps and using the given values, you can calculate the maximum speed at which the car can round the turn.