How Does Newton's Law Apply to a Race Car on a Banked Track?

AI Thread Summary
To determine the resultant force on an 80 kg driver in a race car traveling at 44 m/s on a banked track with a 45-degree angle and a radius of 200 m, it's essential to analyze the forces acting on the driver. The equations of motion must be set up using the components of forces in the x and y directions. The centripetal acceleration can be calculated with the formula Ac = V^2/R, which is crucial for finding the net force. The free body diagram should include the gravitational force, normal force, and the components of these forces based on the bank angle. Properly resolving these forces will lead to the calculation of the resultant force acting on the driver.
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A race car travels 44m/s around a banked (45degree with the horizontal) circular (radius = 200m) track. What is the magnitude of the resultant force in N on the 80 kg driver of this car.

I've having a hard time setting up the free body diagram.

First I broke into Fx and Fy

Fx:

F - mg*sin(tetha) = 0

Fy:


I know I'm going to have to use the Fc = MAc ; Ac=V^2/R
Fn - mg*cos(tetha) - 0

I seriously don't know where I'm going with these equations...
 
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