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

[tdusffx]

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...

 

[tdusffx]

grr..haha help please

 

[ogb p]

I would approach this problem by first understanding the concept of Newton's Laws of Motion. The first law states that an object will remain at rest or in uniform motion in a straight line unless acted upon by an external force. The second law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The third law states that for every action, there is an equal and opposite reaction.

Based on these laws, we can break down the forces acting on the driver of the race car. The driver experiences two main forces: the normal force (Fn) from the track pushing up on the car and the force of gravity (mg) pulling down on the car. In this scenario, the normal force is acting at an angle of 45 degrees with the horizontal, so we can use trigonometry to find its components in the x and y directions.

Fx: Fx = Fn*sin(45) - mg*sin(45) = 0
Since the car is not accelerating in the x direction, the net force in the x direction is equal to 0.

Fy: Fy = Fn*cos(45) - mg*cos(45) = mac
We know that the car is traveling at a constant speed of 44m/s, so the acceleration in the y direction is equal to 0. Therefore, we can solve for the normal force:
Fn = mg*cos(45) = (80kg)(9.8m/s^2)*cos(45) = 549.84N

Now, we can use the equation Fc = mac to find the centripetal force acting on the driver:
Fc = mac = (80kg)(44m/s)^2/200m = 704N

Therefore, the magnitude of the resultant force on the driver is equal to the sum of the normal force and the centripetal force:
Fresultant = Fn + Fc = 549.84N + 704N = 1253.84N

In conclusion, the magnitude of the resultant force on the 80kg driver of the race car is 1253.84N. This force is a combination of the normal force from the track and the centripetal force needed to keep the car moving in a circular path. By applying Newton's laws, we can better understand the forces at play in this scenario and accurately calculate the resultant force on the