You want to design a circular racetrack of radius R such that cars of mass m can

Question

You want to design a circular racetrack of radius R such that cars of mass m can go around the track at speed v without the aid of friction or other forces other than the perpendicular contact force from the track surface.

1)Find an expression for the required banking angle of the track, measured from the horizontal. Your answer should be expressed in terms of m, R, v, and g.

2)Suppose the racecars actually round the track at a speed u > v. What additional radial force is required to keep the cars on the track at this speed? Express your answer in terms of m, R, v, u, and g.

Explanation / Answer

Here ,

radius of racetrack = R

let the required banking angle is theta

m * g * sin(theta) = m * v^2/R

theta = arcsin(v^2/(g * R))

the expression for the required banking angle theta is arcsin(v^2/(g * R))

b) for additional radial force needed is

F = m* v^2/R - m*g * d * sin(theta)

F = m * (v^2 - u^2)/R

the additional radial force required is m * (v^2 - u^2)/R

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