Question

Dr. C. #2. (PHYS 121 engineering design exercise) You have seen why cars inherently accelerate quicker in a straight line and have better fuel mileage than an SUV with the same engine; it's because of air drag and the smaller frontal area and better drag coefficient of the car. Now let's think about why cars handle (take turns, change lanes and make other quick maneuvers) better than an SUV. We'l1 simplify our analysis by considering a vehicle of mass M that is trying to go around a flat circular track of radius R at a constant speed v. We'11 simplify the problem further by considering only the rear wheels, as shown in the figure below. The 'track of the car, defined as the spacing between the two rear wheels, is W, assuming the tires themselves have negligible width. The other critical parameter is the height of the vehicle's center of mass above the ground, let's call this H. We can analyze this situation more conveniently in the rest frame of the car, where the centripetal acceleration a vR results in an apparent force MR pushing outward, away from the center of the circle, acting at the center of mass of the car center of mass A. Draw a Free Body Diagram showing all the forces acting on this system when the inner tire has just begun to lose contact with the groundr0). Note that Feal seems real in this frame of reference. B. If the car tries to go around the circle too fast, the inner tire will lift off the ground. In other words, the car will tend to rotate (flip over) about a pivot point formed by the contact of the outer tire with the ground. This assumes, of course, that your tires are sticky enough that friction isn't the critical factor, but you can put sticky tires on an SUV as well as on a car Calculate the maximum speed the vehicle can take a curve' before the inner tire lifts. Your answer for v can include M, g, R, W, H, and numerical factors, although you might not need every one of these parameters. C. Given the following values for a Porsche 911 and a Cadillac Escalade SUV, what are the safe speeds of each for rounding a curve of radius 30 m? Give your answer in both m/s and miles per hour, mph Mp 1500 kg. Wp-1.54 m. Hp 0.45 m Mc 2720 kg, Wc1.74 m, Hc 0.91 m D. Once the inner tires lift off the ground, angular momentum would tend to make the vehicle tip even further, another problem for the heavier SUV. It would help, however, if the net torque got smaller or reversed direction as the vehicle begins to tip. Does either of these happen or does the net torque get worse (bigger), so the vehicle continues to tip over even faster and becomes more dangerous? How does your equation from part B show this?

Answer 1

Fantisf Ferrovit w う As the speed increases torque of centrifugal force increases while torque of gravity remains constant. for maximum safe speed for safe U "Mg-τcentrifugal Safe speed for Porsche 1.54x 30 x 9.8 2 × 0.45 Un-22.43 × m/s

Safe speed for Cadillac Escalade SUV x30 x 9.8 2 x 0.91 vp 16.76x m/s If speed increases from this safe speed torque of centrifugal force increases while torque of gravity remains constant. This makes the net torque worse (bigger). this makes the situation more dangerous as vehicle topples This can be seen from the equation from part B t Mg centri fugal τcentri fuga! ner et increases