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 traveling on a banked circular racetrack, we need to consider the forces acting on the car. The forces involved are the gravitational force, normal force, and the centrifugal force (resulting from the circular motion).

- The gravitational force (mg) acts vertically downward.
- The normal force (N) acts perpendicular to the surface of the track, directed toward the center of the circular path.
- The centrifugal force (F_c) acts radially outward, perpendicular to the direction of motion.

b) To calculate the linear velocity of the car, we can use the concept of the equilibrium of forces. In equilibrium, the sum of the forces acting on the car in the horizontal direction is zero.

To calculate the linear velocity (v), we can use the following formula:

mg * sinθ = m * v^2 / r

where:
m is the mass of the car,
g is the acceleration due to gravity,
θ is the angle at which the track is banked,
r is the radius of the track.

Rearranging the formula, we get:

v = sqrt(g * r * sinθ)

Plugging in the values (θ = 16 degrees, r = 50 meters, g = 9.8 m/s^2), we can calculate the linear velocity of the car.

c) If a car is traveling on the same track but with a higher linear velocity:
- The magnitude of the centrifugal force (F_c) will increase since it is directly proportional to the square of the linear velocity (v^2).
- The normal force (N) will decrease because the track is banked, and the vertical component of the normal force will decrease.
- The gravitational force remains unchanged.

As a result, the car will experience a net inward force, causing it to move closer to the center of the circular path. At higher velocities, the car will be more likely to lose traction (depending on the coefficient of friction between the tires and the track) and slide off the track.