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Problem 67 Hard Difficulty

Why might tall narrow SUVs and buses be prone to "rollover"? Consider a vehicle rounding a curve of radius $R$ on a flat road. When just on the verge of rollover, its tires on the inside of the curve are about to leave the ground, so the friction and normal force on these two tires are zero. The total normal force on the outside tires is $F_{N}$ and the total friction force is $F_{f r}$ . Assume that the vehicle is not skidding. (a) Analysts define a static stability factor $S S F=w / 2 h$ where a vehicle's "track width" $w$ is the distance between tires on the same axle, and $h$ is the height of the cM above the ground. Show that the critical rollover speed is
$v_{C}=\sqrt{R g\left(\frac{w}{2 h}\right)}$
[Hint: Take torques about an axis through the center of mass of the SUV, parallel to its direction of motion. (b) Determine the ratio of highway curve radii (minimum possible) for a typical passenger car with $\mathrm{SSF}=1.40$ and an SUV with $\mathrm{SSF}=1.05$ at a speed of 90 $\mathrm{km} / \mathrm{h}$ .

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Physics 101 Mechanics

Physics for Scientists and Engineers with Modern Physics

Chapter 11

Angular Momentum; General Rotation

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Video Transcript

this question, we are asked to consider the, uh, the situation when a bigger that is rounding a curve of radius R and then it's possible that you may roll over. OK, so you're considering, uh uh ah. Suv. Okay. And then you have two tires. Okay, This is the view from the back. Okay, so you assume that it's, uh, turning to the left. So the contributor force is pointing to the left. Okay, So the two tires, uh, the distance between the two tires is W uh huh. Distance of the central mess from the ground is h um, this is, you know, to and then this is the ark attire. Okay. On the when, When it is at a critical, uh, over speed. Okay. The inner tire will be raised up. And so there are only two forces acting on the outer tire. Okay, he saw the two forces are the frictional force and the normal force. Of course, there's a weight, but this weight will be Uh huh. Will come later. Okay. And then this is the CME. Okay. Okay. So in part, a want to show you want to show that the critical role was being given to the, uh, given by the expression. Okay, So in prime area asked to consider the top about the access through the center of mass of the S U V K. So and then we are going to say the talk that's pointing out of the page to be positive. Okay. And then consider the tarp, uh, about access through the center to the cm of the SUV came. Okay, so, um, this means that we will be, uh, the net talk about the center man to be, uh, f n times uh, w two minus ah. And friction times each. Okay. And then from the free body diagram, uh, fn would be, uh, g. And then the frictional forces the centrifugal force. The Emmy Square are okay. And then critical speed. You see, um, we have natural because zero so M g w two is equal to, uh, e square. Are times age cancer, the m it arranged equation. You have V c equals two our g and w over to h square root Sean. Okay, then in part B. Um, we want to You are given two vehicles. One is a passenger car with S s F 1.40 and s U V s uh, S S F 1.5 Okay, so the s s f is, uh, uh, static 70 80 factor. Okay, so this is equal to W two h. So our V c is equal to r G s s f square it. And then you can, uh, we write the whole thing become like this. And so our is university proportional to S f k. Okay, so, um, we have one to be the passenger car, okay? And then to be the SUV. So, uh, are one divide by our two. You want to find the ratio of the radio? I Okay, so, uh, this would be, uh, s f two right? By s f one across. The rest are constant. Uh, we see is constant Jews constant. So the ratio of the radio so only depends on only depends on ssf The ratio of ssf. So s s F two is 1.5 ssf one is 1.40 How quick This you get 0.750 Okay, so this is the answer for part B. And that's all for this question.

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A spherical asteroid with radius $r=123 \mathrm{m…

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Physics for Scientists and Engineers with Modern Physics

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Watch More Solved Questions in Chapter 11

Video Transcript

Douglas C. Giancoli

Physics for Scientists and Engineers with Modern Physics

Zachary Mitchell

Aspen Fenzl

Jared Enns

Meghan Miholics

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Physics for Scientists and Engineers with Modern Physics

Zachary Mitchell

Aspen Fenzl

Jared Enns

Meghan Miholics

Douglas C. GiancoliPhysics for Scientists and Engineers with Modern Physics

Zachary Mitchell

Aspen Fenzl

Jared Enns

Meghan Miholics

Douglas C. Giancoli

Physics for Scientists and Engineers with Modern Physics