What Is the Maximum Speed a Car Can Maintain in a Curve Without Skidding?

[datajd]

A car rounds a corner of radius r= 45 m. If the coefficient of static friction between the car and the road is= 0.82, what is the greatest speed the car can have in the corner without skidding?

am i in the right direction with v^2=.82*9.8*45m? then square root both sides for the answer?

 

[kuruman]

You are on the right rack.

 

[kerimek]

Yes, you are on the right track with your equation. The centripetal acceleration is given by the formula a = v^2 / r, where v is the velocity and r is the radius of the curve. In this case, the maximum velocity that the car can have without skidding can be found by setting the centripetal acceleration equal to the maximum static friction force (which is equal to μs * mg, where μs is the coefficient of static friction and mg is the weight of the car). So, your equation is correct: v^2 = μs * g * r. To find the maximum velocity, you would then take the square root of both sides of the equation. The final answer would depend on the value of g, which is approximately 9.8 m/s^2 on Earth. So, the greatest speed the car can have in the corner without skidding would be approximately 19.2 m/s (or 43 mph).