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

A car moves with a speed v on a horizontal circular highway turn of radius is R = 100. Assume the height of the car’s center of mass above the ground is h = 1 m, and the separation between its inner and outer wheels (car's width) is w = 2 m. The car does not skid (static friction works between tires and road surface).

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.

## Answer this Question

## Related Questions

- physics - A car moves with speed v on a horizontal circular track of radius R. ...
- physics - A race car is making a U-turn at constant speed. The coefficient of ...
- Physics - A race car driver drives her 1500 kg car around a circular turn, which...
- physics - A 1000 kg car is travelling on the highway at a constant speed of 110 ...
- Physics - A car is rounding an unbanked circular turn with a speed of v = 35 m/s...
- Physics - A car of mass = 1200 traveling at 60.0 enters a banked turn covered ...
- physics - A 625-kg racing car completes one lap in 14.3 s around a circular ...
- physics - A bumper car with mass m1 = 100 kg is moving to the right with a ...
- physics - A police officer in hot pursuit drives her car through a circular ...
- Physics help - A car travels in a circle whose radius is 31 m, with a speed of ...