A race car driving on a banked track that makes an angle theta with the horizont

Question

A race car driving on a banked track that makes an angle theta with the horizontal rounds a curve for which the radius of curvature is R There is one speed V_eritical at which friction is not needed to keep the car on the track. What is that speed in terms of theta and R Express your answer in terms of the variables R, theta, and the acceleration due to gravity g. If the coefficient of friction between tires and road is Mu_1 what maximum speed can the car have without going into a skid when taking the curve Express your answer in terms of the variables R, theta, Mu and the acceleration due to gravity g.

Explanation / Answer

Here ,

for No friction on the track ,

for Vcritical

centripetal force = gravity force down the plane

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

Vcritical = sqrt( g * R * sin(theta))

the Vcritical is sqrt( g * R * sin(theta))

part B)

when there is friction present also

for maximum velocity Vmax

centripetal force = gravity force down the plane + frictional force

m * Vmax^2/R = m * g * sin(theta) + u * mg * cos(theta)

Vmax= sqrt( g * R * sin(theta) + u * g * R*cos(theta))

the Vmax is sqrt( g * R * sin(theta) + u * g * R*cos(theta))

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