Calculating Forces on a Banked Curve

[taskev21]

Homework Statement

A curve of radius 152 m is banked at an angle of 12°. An 738-kg car negotiates the curve at 93 km/h without skidding. Neglect the effects of air drag and rolling friction. Find the following.
(a) the normal force exerted by the pavement on the tires


(b) the frictional force exerted by the pavement on the tires


(c) the minimum coefficient of static friction between the pavement and the tires

Homework Equations

F=ma
F= mv^2 /r

The Attempt at a Solution

I got parts A, and C, but I can't seem to get the force of friction.
I have the centripital force = 3240.21, so the incline component is 3240.21/cos(12) = 3312.598. Then I add that to the incline component of the car's weight which is 738*9.81*sin(12) = 1505.234. 1505.234 + 3312.598 = 4871.8329 N. so in kiloNewtons it should be 4.871 kN...what is the problem here?

 

[ehild]

The centripetal force is a resultant force, the vector sum of gravity, normal force and friction.

The incline component of the centripetal force is equal to the incline component of gravity + (or -) friction. So the magnitude of friction is equal to the absolute value of the difference between the components of Fcp and of G.

Fr= 3312.598-1505.234 =1807 N

ehild

 

[kerimek]

I would like to clarify a few points in your solution. Firstly, the value of 3240.21 N that you have calculated is not the centripetal force, but rather the total force acting on the car in the horizontal direction. The centripetal force is a component of this total force, and can be calculated using the formula F=mv^2/r. In this case, the centripetal force would be 3240.21 N.

In order to calculate the frictional force, we need to consider the forces acting on the car in the vertical direction. The normal force, which is equal to the weight of the car in this case, will have a component acting in the downward direction due to the angle of the banked curve. This component can be calculated using the formula F=mg*sin(12°). This force will be balanced by the upward component of the car's weight, which can be calculated using the formula F=mg*cos(12°). The difference between these two forces will give us the normal force exerted by the pavement on the tires.

Once we have calculated the normal force, we can use the formula F=μN to calculate the frictional force, where μ is the coefficient of static friction and N is the normal force. This will give us the answer for part (b).

I hope this explanation helps you understand the problem better and come up with the correct solution. Remember to always consider all the forces acting on an object in order to accurately calculate its motion.