Physics
posted by William .
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 nonzero. 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.
Respond to this Question
Similar Questions

physics
A car moves with speed v on a horizontal circular track of radius R. The height of the car's center of mass is h, and the separation between the inner and outer wheels is d. The road is dry, and the car does not skid. Find the maximum … 
Physics
A race car driver drives her 1500 kg car around a circular turn, which is banked at an angle of 20 degrees to the horizontal. If the car is traveling around the frictionless curve of radius 100m, a) What is providing the centerseeking … 
physics
A police officer in hot pursuit drives her car through a circular turn of radius 305 m with a constant speed of 83.5 km/h. Her mass is 55.0 kg. what are the magnitude and the angle of the net force of the officer on the car seat? 
physics
A 625kg racing car completes one lap in 14.3 s around a circular track with a radius of 55.0 m. The car moves at constant speed. (a) What is the acceleration of the car? 
physics
A race car is making a Uturn at constant speed. The coefficient of friction between the tires and the track is μs = 1.0. If the radius of the curve is 40 m, what is the maximum speed at which the car can turn without sliding? 
Physics
A car of mass = 1200 traveling at 60.0 enters a banked turn covered with ice. The road is banked at an angle , and there is no friction between the road and the car's tires.What is the radius of the turn if = 20.0 (assuming the car … 
physics
A 1000 kg car is travelling on the highway at a constant speed of 110 km/h. The highway makes a turn that is banked at an angle of 10o and has a radius of 160 m. What is the coefficient of friction between the car tires and the pavement … 
Physics
A car is rounding an unbanked circular turn with a speed of v = 35 m/s. The radius of the turn is r = 1500 m. What is the magnitude ac of the car’s centripetal acceleration? 
physics
A bumper car with mass m1 = 100 kg is moving to the right with a velocity of v1 = 4.6 m/s. A second bumper car with mass m2 = 86 kg is moving to the left with a velocity of v2 = 3.8 m/s. The two cars have an elastic collision. Assume … 
physics
A car with mass (452) kg attempts to make a turn with a radius of (31.8) m at a speed of (21.5) m/s on a horizontal surface. What is the minimum value for the static coefficient of friction between the tires and the roadway necessary …