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 consider the forces acting on it. In this case, the forces acting on the car are the weight force (mg) and the normal force (N). The weight force acts vertically downward and has a magnitude of mg, where m is the mass of the car and g is the acceleration due to gravity. The normal force acts perpendicular to the inclined surface and is equal in magnitude but opposite in direction to the component of the weight force that is perpendicular to the surface.
b) To calculate the linear velocity of the car, we can use the concept of circular motion. The centripetal force required to keep the car moving in a circular path is provided by the normal force. The centripetal force (Fc) is given by the equation Fc = m * v^2 / r, where m is the mass of the car, v is the linear velocity of the car, and r is the radius of the circular path.
In this case, since there are no friction forces present, the only force providing the centripetal force is the normal force. Therefore, we can equate the magnitude of the normal force with the centripetal force:
N = m * v^2 / r
We can then solve for the linear velocity v:
v = sqrt(N * r / m)
c) If a car is traveling on the same banked circular track but with a higher linear velocity, the centripetal force required to keep the car moving in a circular path will also increase. If the car's velocity exceeds the necessary value to maintain circular motion, it will move away from the circular path and may end up sliding or skidding on the track. In this scenario, friction forces become significant and can affect the motion of the car. It is important to ensure that the car's speed is within the appropriate range to maintain stable circular motion on the banked track.