WTF...Kaplan screw-up on physics question?

[GeorgianCMV]

This is from Kaplan's high yield problem solving guide:

"A car rounds a curve with a constant velocity of 25 m/s. The curve is a circle of radius 40 m. What must the coefficient of static friction between the road and the wheels be to keep the car from slipping?"

First, isn't it true that when a car is going around a curve, there's no way it can have constant velocity because the direction is constantly changing, but it can have constant speed. Right?

Second, they have you draw a free body diagram with the direction of the frictional force pointing towards the center of the circle. I thought that centripetal force pointed in this direction, and that the frictional force and centripetal force are two different forces entirely.

The problem is easy once I set the frictional force equal to m v^2/r. But where did the centripetal force go, and how did they figure out the direction of the frictional force.

---

Members don't see this ad.

 

[Vihsadas]

Maybe asking this question will help you:

Is it possible for a car to travel in a circle if there is no friction?
What would happen to the path of the car if the friction in the system disappeared?

 

[bluemonkey]

This is from Kaplan's high yield problem solving guide:

"A car rounds a curve with a constant velocity of 25 m/s. The curve is a circle of radius 40 m. What must the coefficient of static friction between the road and the wheels be to keep the car from slipping?"

First, isn't it true that when a car is going around a curve, there's no way it can have constant velocity because the direction is constantly changing, but it can have constant speed. Right?

Second, they have you draw a free body diagram with the direction of the frictional force pointing towards the center of the circle. I thought that centripetal force pointed in this direction, and that the frictional force and centripetal force are two different forces entirely.

The problem is easy once I set the frictional force equal to m v^2/r. But where did the centripetal force go, and how did they figure out the direction of the frictional force.

In addition to what Vihsadas said, what exactly is a centripetal force? Is it composed of other forces or is it a force in and of itself?

 

[tncekm]

This is from Kaplan's high yield problem solving guide:

"A car rounds a curve with a constant velocity of 25 m/s. The curve is a circle of radius 40 m. What must the coefficient of static friction between the road and the wheels be to keep the car from slipping?"

First, isn't it true that when a car is going around a curve, there's no way it can have constant velocity because the direction is constantly changing, but it can have constant speed. Right?

Yes, they misused the word velocity and should have used speed. But, that shouldn't stop you from answering the questions

Second, they have you draw a free body diagram with the direction of the frictional force pointing towards the center of the circle. I thought that centripetal force pointed in this direction, and that the frictional force and centripetal force are two different forces entirely.

The problem is easy once I set the frictional force equal to m v^2/r. But where did the centripetal force go, and how did they figure out the direction of the frictional force.

Think of centripetal force for the car example, then for a satellite, then for a rock on a string being whirled in a circle. Like Bluemonkey asked, is there an actual "centripetal force"? (http://en.wikipedia.org/wiki/Centripetal_force)

In this case the frictional force DOES point toward the center of the circle the car is circumscribing. If it didn't the car would continue in a straight line if there were no friction, or if the frictional force pointed away from the circle the car would accelerate in a manner that wouldn't allow for the circumscription of a circle. The frictional force is the only force acting on the car, other than gravity and the normal force (which is a component of the kinetic frictional force).

 

[GeorgianCMV]

Ohhhh. Ok that helped. So essentially, the centripetal force can be any force, and in this case, the centripetal force IS the frictional force? It's "centripetal" in the sense that it is the only force keeping the car moving in a circle?

 

[physics junkie]

Ohhhh. Ok that helped. So essentially, the centripetal force can be any force, and in this case, the centripetal force IS the frictional force? It's "centripetal" in the sense that it is the only force keeping the car moving in a circle?

Yes, the friction is the force keeping the car in a circle. It points towards the center of the circle.

 

[3 little birds]

Velocity is constantly changing direction, but magnitude of velocity stays the same. This is easy to understand when you realize that the car has linear (due to changing direction) but no angular acceleration. It is technically accelerating toward the center of the circle, which makes sense when you consider that without friction the car "wants" to peel out and leave the circle. Friction force points to the center, preventing this and resulting in an acceleration toward the center of the circle, since F(vector) = m*a(vector).

This situation is the same as a satellite in orbit around the earth. Tangential velocity is constant in magnitude but changing direction, force of gravity points in to center of circle, acceleration is in to center, resulting in a circular path with velocity tangential to the circle. Here, gravity plays the same role as friction in the car example.