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
Let the x-axis point toward the center of curvature and the y-axis point upward. Use Newton’s second law.
ΣFy = N• cos θ − mg − f •sin θ = 0
ΣFx = N• sin θ + f •cos θ = m•v²/R,
Solving the 1st equation for N, we obtain
N =( f •sin θ + m•g)/cos θ,
Substitute N to the 2nd equation and obtain friction force
f =m[(v²•cosθ/R) - g•sinθ].
f=0 =>
(v²•cosθ/R) - g•sinθ = 0,
v²•cosθ/R = g•sinθ,
v² /R•g = sinθ/cosθ = tanθ.
v =sqrt(R•g•tanθ) = sqrt (50•9.8•tan16º)=11.85 m/s
a) To draw a free body diagram of the car, we need to consider all the forces acting on it. In this case, there are three forces: the gravitational force (mg), the normal force (N), and the centripetal force (Fc). The gravitational force acts downward, the normal force acts perpendicular to the surface of the track, and the centripetal force acts towards the center of the circular motion.
b) To calculate the linear velocity of the car, we can use the equation v = √(rgtanθ), where v is the linear velocity, r is the radius of the track, g is the acceleration due to gravity (9.8 m/s²), and θ is the angle of banking.
In this case, the radius (r) is 50 meters and the angle of banking (θ) is 16 degrees. Plugging these values into the formula, we can calculate the linear velocity:
v = √(50 * 9.8 * tan(16°))
c) If a car is traveling on the same track but with a higher linear velocity, several things may happen. First, the car will experience a larger centripetal force, which means it will need more traction to maintain its circular path. If the grip of the tires is not sufficient, the car may start to slip or skid.
Additionally, the car will experience a greater outward force due to inertia. This force is commonly known as the "centrifugal force" (although it is not a real force). The car may feel like it is being pushed outwards, and the driver may need to steer more to keep the car on track.
Lastly, if the car exceeds the maximum speed it can handle on the banked track, it may start sliding or even lose control. Excessive speed can cause the car to move up too high on the banked surface, reducing the effective banking angle and ultimately leading to instability.
Overall, it is important for the driver to be aware of the track's limitations and adjust their speed accordingly to ensure safe and stable driving.