a) If the road is frictionless, the only force acting on the car is the force of gravity and the normal force. The normal force is perpendicular to the surface of the road, and since the car is on a banked curve, it will have a component pointing towards the center of the curve, providing the centripetal force. Therefore:
N cosθ = mg
N sinθ = mv^2/r
where m is the mass of the car, g is the acceleration due to gravity, v is the speed of the car, and r is the radius of the curve.
Solving for θ, we get:
tanθ = v^2/(rg)
tanθ = (40.0 m/s)^2 / (900 kg x 9.81 m/s^2 x 100 m)
θ = 23.3 degrees
Therefore, the angle θ has to be 23.3 degrees if the road is frictionless.
b) If the car is moving at constant speed, the net force on it must be zero. Thus, the friction force must exactly balance the component of the normal force pointing down the slope:
f = N sinθ - mg cosθ
Using the same values as before, we get:
f = (900 kg x 9.81 m/s^2 x sin23.3°) - (900 kg x 9.81 m/s^2 x cos23.3°)
f = 198 N
Therefore, the friction force the car is experiencing is 198 N.
A car is moving in curved bank ,the 900kg car is moving at speed of 40.0 m/s through
this curve of radius 100m, a) what does the angle θ has to be if the road is frictionless?
b) If a car moving at constant speed, calculate friction force the is experiencing
1 answer
1 answer