Banked Circular Motion Problem: Calculating Normal and Friction Forces

[petsgomoo13]

Homework Statement

A car travels at a speed of 21 m/s around a
curve of radius 31 m.
The acceleration of gravity is 9.8 m/s2 .
It weighs 2600 kG, and is banked at 23 degrees.
Suppose the friction force is sufficient to keep the car from skidding. Calculate the
magnitude of the normal force exerted on the
car by the road’s surface.
Also, calculate the magnitude of the friction force.

Homework Equations

?

The Attempt at a Solution

F_static*cos 23 = m*v²/r
Would that make F_static 441*2600/(31 cos 23) = 40181.3164?
I have no clue how to find the normal...

 

[alphysicist]

Hi petsgomoo13,

Homework Statement

A car travels at a speed of 21 m/s around a
curve of radius 31 m.
The acceleration of gravity is 9.8 m/s2 .
It weighs 2600 kG, and is banked at 23 degrees.
Suppose the friction force is sufficient to keep the car from skidding. Calculate the
magnitude of the normal force exerted on the
car by the road’s surface.
Also, calculate the magnitude of the friction force.

Homework Equations

?

The Attempt at a Solution

F_static*cos 23 = m*v²/r

I don't think this is right. You have correctly found the horizontal component of the frictional force, which is right because the centripetal acceleration is horizontal. But there is another force present that has a horizontal component. What would that be? Do you see what your equations would then become?

 

[f(x)]

Try drawing a FreeBody Diagram with all the forces ACTING on the body, that'll help