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
11.97m/s
a) To draw a free body diagram of the car, we need to consider the forces acting on it. The two main forces are the gravitational force (mg) acting vertically downward and the normal force (N) acting perpendicular to the surface of the track. Since the track is banked at an angle, there is also a component of the gravitational force acting along the track's surface. This component of the gravitational force provides the centripetal force required to keep the car moving in a circle. Hence, we have the following forces:
- Weight (mg) acting vertically downward
- Normal force (N) acting perpendicular to the track's surface
- Centripetal force (Fc) acting inward towards the center of the circular path
b) To calculate the linear velocity of the car, we can use the formula:
Fc = (mv^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 circular track.
In this case, since there is no friction, the centripetal force is provided solely by the component of the weight along the track's surface:
Fc = mg * sin(θ)
where θ is the angle of the track's inclination.
Equating the centripetal force to the formula above, we have:
mg * sin(θ) = (mv^2) / r
Simplifying the equation, we can solve for v:
v = sqrt(g * r * sin(θ))
where g is the acceleration due to gravity.
Plugging in the given values:
g = 9.8 m/s^2 (approximate)
r = 50 m
θ = 16 degrees
We convert the angle from degrees to radians:
θ = 16 * π / 180 = 0.279 radians
Now 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, several things can happen:
1. The car may start skidding or sliding due to insufficient friction. This is because the centripetal force required for circular motion increases with higher velocity, and if the available friction force is not enough, the car will not be able to make the turn safely.
2. The car may experience a higher reaction force from the track's surface. This is because the normal force acting perpendicular to the track's surface increases as the velocity increases in order to provide the necessary centripetal force.
3. The car may tilt outward more. As the velocity increases, the car tends to lean outward due to the inertia acting in the outward direction. This is witnessed in high-speed racing where cars have significant tilting angles.
It's important to note that in this scenario, we assumed no friction forces present. In real-world situations, additional factors like friction and air resistance should be considered, and these can affect the car's behavior.