A car is travelling on a banked circular racetrack, Given that the track is banked at an angle of 16degree to the horizontal and the radius of the track is 50 metres and there are no friction forces present

a) draw a free body diagram of the car
b)calculate the linear velocity of the car
c) Describe what will happen to a car that is travelling on the same track but with a higher linear velocity

a) To draw a free body diagram of the car, we need to represent all the forces acting on it. In this case, the forces involved are the gravitational force acting downwards and the normal force acting perpendicular to the track.

First, draw a circle to represent the car. Then, draw an arrow pointing vertically downward from the center of the circle to represent the gravitational force. Label it as "mg" (mass of the car multiplied by the acceleration due to gravity). Next, draw an arrow pointing radially inward and perpendicular to the track starting from the center of the circle. Label this arrow as "N" (normal force).

b) To calculate the linear velocity of the car, we can use the relationship between the gravitational force and the normal force.

The vertical component of the gravitational force (mg) is balanced by the vertical component of the normal force. This can be represented by the equation: mg = N * cosθ (where θ is the angle of inclination).

In this case, the angle of inclination (θ) is given as 16 degrees.

Now, rewrite the equation as: N = mg / cosθ

Next, since there are no friction forces present, the horizontal component of the normal force provides the centripetal force required to keep the car moving in a circular path. This can be represented by the equation: N * sinθ = (mv^2) / r (where m is the mass of the car, v is the linear velocity, and r is the radius of the track).

Substituting the value of N from the previous equation into this equation, we get: (mg / cosθ) * sinθ = (mv^2) / r

Simplifying further, we get: g * tanθ = (v^2) / r

Now, substitute the given values: g = 9.8 m/s^2, θ = 16 degrees, and r = 50 meters.

Using a calculator, you can solve for v by rearranging the equation: v = sqrt(g * r * tanθ).

c) If a car is traveling on the same track but with a higher linear velocity, it means that the car is moving faster. In this scenario, the force required to keep the car in a circular path will also increase.

As the linear velocity increases, the force of inertia (the tendency of the car to move in a straight line) will also increase. Without enough centripetal force provided by the normal force, the car will lose contact with the track and slide off.

To prevent this from happening, the banking angle of the track can be increased, or additional friction forces (such as banking it at a smaller angle or introducing friction coefficients) can be introduced to help keep the car on the track.