The angle θ refers to the banking angle of the road, which is the angle at which the road is tilted from the horizontal. If the road is frictionless, the car can only rely on the centripetal force provided by the banked curve to turn and avoid sliding off the road.
The centripetal force required to move the car in a circular path of radius 100m at a speed of 40.0 m/s can be calculated as:
Fc = mv²/r
where Fc is the centripetal force, m is the mass of the car (900kg), v is the speed of the car (40.0 m/s), and r is the radius of the curve (100m).
Plugging in the values, we get:
Fc = (900kg)(40.0 m/s)²/100m
Fc = 1,440,000 N
The centripetal force is provided by the horizontal component of the normal force (N) acting on the car, which is given by:
N*cos(θ) = Fc
where θ is the banking angle of the road.
Solving for θ, we get:
θ = arccos(Fc/N)
θ = arccos((900kg)(40.0 m/s)²/100m)/(9.81 m/s²)(cos(θ))
θ = 53.1°
Therefore, the road needs to be banked at an angle of 53.1° for the car to navigate the curve frictionlessly at a speed of 40.0 m/s.
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. what does the angle θ has to be if the road is frictionless?
1 answer
1 answer