Question about uniforn circular motion and highway curves

In summary, the maximum speed for a 1050-kg car to round a turn of radius 77m on a flat road with a coefficient of static friction of .80 is determined by solving for the maximum force of friction, which is 8232 N. This force represents the maximum force that can be used to turn the corner without the car sliding. The next step would be to solve for speed using the equation F = mv^2 / r.
  • #1
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Homework Statement


What is the maximum speed with which a 1050-kg car can round a turn of radius 77m on a flat road if the coefficient of static friction between tires and the road is .80?

Homework Equations


F = mv^2 / r
a = v2 / r
Ffr = mustatic x mg

The Attempt at a Solution



I found the force of friction to be 8232 N: .80 x 1050 x 9.8 = 8232 N
If someone could just tell me the next step that would help me out a lot; i don't know where to go from here. Thanks.
 
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  • #2
Well that is the max force you can use before static friction gives upand the car slides. Therefore that is the max force you can use to turn the corner. All you need to do is solve for speed.
 
  • #3


To find the maximum speed, we can use the equation F = mv^2 / r, where F is the centripetal force, m is the mass of the car, v is the velocity, and r is the radius of the turn.

We already have the value for F (8232 N) and m (1050 kg), so we can rearrange the equation to solve for v: v = √(F x r / m).

Plugging in the values, we get v = √(8232 x 77 / 1050) = 23.8 m/s. This is the maximum speed at which the car can round the turn without slipping, assuming the coefficient of static friction remains constant.
 

What is uniform circular motion?

Uniform circular motion is a type of motion in which an object moves along a circular path at a constant speed. This means that the object covers equal distances in equal amounts of time.

How does uniform circular motion differ from other types of motion?

Uniform circular motion is different from other types of motion because the speed of the object is constant, but its velocity is constantly changing. This is because the direction of motion is constantly changing, even though the speed remains the same.

What is the role of centripetal force in uniform circular motion?

Centripetal force is the force that keeps an object moving in a circular path. In uniform circular motion, this force is directed towards the center of the circle and is responsible for constantly changing the direction of the object's velocity.

How do highway curves affect vehicles in terms of uniform circular motion?

Highway curves can affect vehicles in terms of uniform circular motion by requiring them to constantly change their direction and velocity in order to stay on the curve. This can be achieved through the use of centripetal force, such as friction between the tires and the road.

What factors can impact the uniform circular motion of a vehicle on a highway curve?

The factors that can impact uniform circular motion on a highway curve include the speed of the vehicle, the radius of the curve, and the coefficient of friction between the tires and the road. All of these factors can affect the amount of centripetal force required to keep the vehicle on the curve.

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