In certain cities, parking spaces are at a premium and anyavailable surface will be used for parking, even highly slopedroofs. Consider the SUV parked in the picture above. If you are thedriver, how can you be sure that your car wonât flip overbackwards?

The schematic diagram below gives a simplified model of thesituation with the SUV on the slope. We are approximating the SUVas a uniform cube three meters long and two meters high, mounted ontires a half-meter in diameter that are set in a half meter fromthe edges of the vehicle. The SUV has a mass of 1500 kg. Forsimplicity, we will ignore the mass of the tires. Assume that thecoefficient of static friction between the tires and the road is0.8. Using the principles of static equilibrium, letâs determinewhether the car will stay on the slope. In order to maintain staticrotational equilibrium, the magnitudes of the normal forces on theforward and rear wheels must adjust to create a situation of zeronet torque. In order to maintain static translational equilibrium,the static friction forces between the tires and the road mustadjust to create a situation of zero net force. If the angle Î¸ getstoo big, we will have a problem...

1. First, letâs assume that the angle Î¸ is 30 degrees (note thewheels are locked and donât roll) and the car is not moving. Whatis the magnitude of the normal force from the road on the frontwheels (top of incline)? On the back wheels (bottom of incline)?These normal force are unequal- why?

2. Now letâs take the situation to the extreme: what is the maximumvalue of the angle Î¸ which is possible, if the SUV is to remain instatic equilibrium? First, determine the maximum angle that the carwonât slide, and then determine the maximum angle that the carwonât rotate. What happens to the SUV first if the angle isexceeded? What is the normal force on the front (top of incline)wheels in this situation?

3. Assume that it rains, and the coefficient of static friction isreduced from 0.8 to 0.5. Now what is the maximum value of the angleÎ¸ for which the car can remain in static equilibrium? If the angleÎ¸ exceeds this value, what happens to the SUV?

In certain cities, parking spaces are at a premium and anyavailable surface will be used for parking, even highly slopedroofs. Consider the SUV parked in the picture above. If you are thedriver, how can you be sure that your car wonât flip overbackwards?

The schematic diagram below gives a simplified model of thesituation with the SUV on the slope. We are approximating the SUVas a uniform cube three meters long and two meters high, mounted ontires a half-meter in diameter that are set in a half meter fromthe edges of the vehicle. The SUV has a mass of 1500 kg. Forsimplicity, we will ignore the mass of the tires. Assume that thecoefficient of static friction between the tires and the road is0.8. Using the principles of static equilibrium, letâs determinewhether the car will stay on the slope. In order to maintain staticrotational equilibrium, the magnitudes of the normal forces on theforward and rear wheels must adjust to create a situation of zeronet torque. In order to maintain static translational equilibrium,the static friction forces between the tires and the road mustadjust to create a situation of zero net force. If the angle Î¸ getstoo big, we will have a problem...

1. First, letâs assume that the angle Î¸ is 30 degrees (note thewheels are locked and donât roll) and the car is not moving. Whatis the magnitude of the normal force from the road on the frontwheels (top of incline)? On the back wheels (bottom of incline)?These normal force are unequal- why?

2. Now letâs take the situation to the extreme: what is the maximumvalue of the angle Î¸ which is possible, if the SUV is to remain instatic equilibrium? First, determine the maximum angle that the carwonât slide, and then determine the maximum angle that the carwonât rotate. What happens to the SUV first if the angle isexceeded? What is the normal force on the front (top of incline)wheels in this situation?

3. Assume that it rains, and the coefficient of static friction isreduced from 0.8 to 0.5. Now what is the maximum value of the angleÎ¸ for which the car can remain in static equilibrium? If the angleÎ¸ exceeds this value, what happens to the SUV?