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 travelling on a banked circular racetrack, we need to identify the forces acting on the car. In this scenario, the only force acting on the car is the gravitational force (weight) which can be resolved into two components:
- The vertical component (mg*cosθ), where m is the mass of the car and θ is the angle of inclination of the banked curve.
- The horizontal component (mg*sinθ), which provides the centripetal force required to keep the car moving in a circular path.
So, the free body diagram of the car would depict an arrow representing the weight of the car pointing vertically downward, with two components: one pointing downward at an angle θ, representing the vertical component, and one pointing inward towards the center of the circle, representing the horizontal component.
b) To calculate the linear velocity of the car, we can use the concept of centripetal force. The centripetal force is given by the equation:
Fc = m * v^2 / r
Where Fc is the centripetal force, m is the mass of the car, v is the linear velocity, and r is the radius of the track.
In this case, the only force providing the centripetal force is the horizontal component of the weight (mg*sinθ). Therefore:
mg*sinθ = m * v^2 / r
Rearranging the equation, we can find the value of v:
v^2 = g * r * tanθ
v = √(g * r * tanθ)
where g is the acceleration due to gravity (approximately 9.8 m/s^2).
So, substituting the given values into the equation, 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, there are a few things that will happen:
1. The car will experience an increased centripetal force to maintain its circular motion. This increased force will be achieved by increasing the horizontal component of the weight (mg*sinθ).
2. The car may experience a higher sideways force (friction) between the tires and the track, which can help it maintain traction and prevent slipping or skidding.
3. The car will tilt toward the center of the track due to the increased centripetal force, resulting in a wider angle between the vertical component of the weight and the vertical direction.
Overall, as the linear velocity increases, the car will need to generate more centripetal force to stay on the track without skidding or slipping.