What is the maximum speed of this car?

[RustyComputer]

Centripetal Force Question

Homework Statement

The question, straight from the book:
What is the maximum speed with which a 1050-kg car can round a turn of radius 70 m on a flat road if the coefficient of friction between tires and the road is 0.80? Is this result independent of the mass of the car?

What I know:
Mass(m): 1050-kg
Radius(r): 70 m
Coefficient of friction: 0.80

Homework Equations

$$a_c$$ = v^2/r
$$F_c$$ = mv^2/r
$$F_n$$ = mg
$$F_f$$ = MF_n

The Attempt at a Solution

First, I drew out the free-body diagram,with a circle and a box, which is supposed to be the car. I put $$a_c$$ on an arrow pointing to the middle, and V tangent to where the box is. I found out the normal force,

$$F_n = mg$$
$$F_n = (1050)(9.8)$$
$$F_n =10290$$

And after that, I have no idea what to do to find the velocity...

 

[PhanthomJay]

What force provides the centripetal acceleration?

What results do you get if you assign the letter 'm' to the mass of the car instead of using a numerical value for the mass?

 

[RustyComputer]

What force provides the centripetal acceleration?

What results do you get if you assign the letter 'm' to the mass of the car instead of using a numerical value for the mass?

I'm not sure what you mean by the first question, but with what I think you're saying, centripetal force provides for centripetal acceleration. What I think is probably wrong, though.

For the second question, I'm not sure, but what equation do you want me to apply the method to?

 

[PhanthomJay]

Draw a free body diagram of the forces acting on the car. There are 3 of them. Which force acts in the direction of the centripetal acceleration a_c? That force is called the centripetal (center-seeking) force. Then apply Newton 2 in that direction. You already have listed all the correct equations.

 

[RustyComputer]

So the three forces are a_c, to the center of the circle, the one that goes tangent to the circle, and perpendicular to a_c, and normal force?

As to the second part of your post... I still don't fully understand...

 

[PhanthomJay]

So the three forces are a_c, to the center of the circle, the one that goes tangent to the circle, and perpendicular to a_c, and normal force?

As to the second part of your post... I still don't fully understand...

$$a_c$$ is not a force, it is an acceleration. Force and acceleration are related by Newton's 2nd law. Basically, in the study of the Introductory mechanics branch of Physics, gravity (weight) is one of the forces always acting. It is a non-contact force. All other forces are contact forces, like the Normal force, which acts perpendicular to the object, and the friction force, which acts opposite to the direction of relative or pending motion between the surfaces. Now which of these forces, weight, the normal force, or the friction force, acts in the centripetal direction toward the center? Don't confuse the problem by looking at forces in the tangential direction into the plane of the page. Keep it in 2 dimensions, vertical and horizontal.