Physics question?

Question

Physics question involving centripetal force, coefficient of friction, and banking angle.....
A car of mass 1300 kg is moving at a speed of 28 m/s^2 on a 100 m radius curve. Find centripetal force, the coefficient of friction if there is no banking curve, and the banking angle if there is no friction....

I've found the centripetal force to be 10192 N, but i cant find the coefficient of friction or the banking ange....Any help is appreciated

* oops it is m/s not m/s^2, sorry about that....

Answer 1

You have the centripetal force correct. It is 10192 N. The next part is to compute where this force came from. The centripetal force always needs to be supplied by something else. Sometimes it is supplied by gravity (like for planetary orbits) in this case it is supplied by friction. Therefore the force of friction must be 10192 to keep the car from sliding. Given the force of friction the coefficient of friction can be computed using the following equation:

F = uN. where u is the coefficient of friction and N is the normal force. The normal force is equal to m*g (the weight of the car). Therefor N = m*g = 1300*9.81 = 12753. Plugging this in we get:

10192 = u*12753. u = 0.799

Now for the banking. This would be easier if I could draw a picture.

Picture a right triangle.This triangle represents the bank of the turn. Now the normal force is perpendicular to the sloped surface of the bank. This normal force has two components. The vertical component is cancelling the force of gravity on the car. The horizontal component is supplying the centripetal force. Since we have no friction in this part of the problem, solving the rest is straight forward.

If you draw the normal vector, then draw its horizontal and vertical components, you would get a triangle with one leg equal to the horizontal component, which equals the centripetal force, and one leg equal to the vertical component, which is equal to the weight of the car. Using trigonometry, the banking angle is therefore:

tangent(a) = (m*g)/Fc where Fc is the centripetal force.

tangent(a) = 12753/10192

a = arctangent(12753/10192) = 0.8966 = 51.3687 degrees

now if you look at the drawing you would see that this angle that we computed is not the banking angle, but the complement to the banking angle (if only I could draw a picture). Therefore the banking angle is:

90-51.3687 = 38.6313 degrees. It could also have been done by solving
tangent(a) = Fc/(m*g).
Then solving for "a" would directly give you the banking angle.

Answer 2

You mean 28 meters/second, not what you have.

I hope you realize that the idiot above who says the car is not accelerating gives himself away to be an idiot in the first sentence. Of course the car is accelerating. The accelerating force is the centripital force, turning the car on the curve. In the problem, the centripital force is provided either by friction between the car and the road, or by banking in the case where there is no friction.

The formula for centripital force is

F = mv^2/r

so in your case we have

F = 1300 * 28 * 28 / 100

assuming you meant the speed to be 28 meters/second.

The friction providing the sideways force to turn the car is

F = 1300 * coefficient of friction

So we can say

coefficient of friction = 28 * 28 / 100

I don't think you can really have a coefficient of friction as great as that, so with these numbers the car would not be able to turn and would fly off.

Or do you mean that centripital acceleration is 28 meters/second^2?

Answer 3

If the car is not accelerating - there is no force and no friction acting on the car. The centripetal force acts towards the center of the curve - not tangential to the car.

Those who call others idiots (especially those with engineering degrees) should look at themselves - centripetal acceleration is v^2 / r = 7.84 m/s^2. If the car is moving at constant velocity - tangential acceleration is zero and the sum of the forces acting on the car equals 0.

The coefficient of friction is a function of the banking angle - which is not given. I suggest that the asker refer to this link which will answer his questions:
http://www.vast.org/vip/book/BANKEDCU/HOME.HTM

I strongly advise the other poster to redact his comments referring to me as an idiot or I will report you for abuse.