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

We can use the following formula to solve this problem:

centripetal force = mv^2/r

where m is the mass of the car, v is its speed, and r is the radius of the curve.

In this case, the centripetal force is provided by the horizontal component of the normal force, since there is no friction. So we can write:

centripetal force = N sin(θ)

where N is the normal force and θ is the angle of banking.

Equating these two expressions for the centripetal force, we get:

N sin(θ) = mv^2/r

Solving for θ, we get:

θ = sin^-1(mv^2/(Nr))

Substituting the given values, we get:

θ = sin^-1((900 kg)(40.0 m/s)^2/((900 kg)(9.81 m/s^2)(100m)))

θ ≈ 32.83 degrees

Therefore, the angle θ has to be approximately 32.83 degrees if the road is frictionless.