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December 19, 2014

December 19, 2014

Posted by **William** on Sunday, March 20, 2011 at 4:14pm.

With what maximum speed (in mph) can the car negotiate the turn with without losing equilibrium and starting to overturn? Use g = 10 m/s^2.

Hint 1: car is in circular motion with constant speed. Hint 2: car starts to rotate about its center of gravity when net torque about its center of gravity becomes non-zero. Hint 3: draw an extended free body diagram and identify two torques counteracting each other: torque due to friction force on the inner tire versus torque due to normal force on the outer tire (assume that at the moment the car lifts its inner tires, the normal force becomes equal to the car’s weight: N = mg). Hint 4: friction force is in perpendicular direction to the direction of car’s velocity (it is towards the center of the circle). So, Newton’s 2nd law: F_net = mv2/R. Hint 5: friction force is the only force acting on the car in horizontal direction: F_net = F_fr.

Given

Radius , r = 100 m

Height , h = 1 m

Width ,w = 2 m

We will find angle of banking

sinθ = 1 / 2

θ = 300

The speed of the car is

v = gr tan30

= 10 m/s^2 * 100 m *0.5773

v = 24 m/s

53.686471 mph

That answer is wrong, it has to be in MPH btw, please help me.

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