Three$-$Step Cycle

List all the relevant information you have gathered from the problem. Based on this information,

state what you need to know to solve the problem. As new information comes in$,$ you will want to

summarize and update the relevant information you have gathered and ask new questions.

List the following: Questions

List the two tasks that you have to work on$,$ based on the CEO's request.

Sketch the gradual, circular merge between Highway $15N$ and Route $174W.$ Give the dimensions of the circle that you have chosen and explain your choice with both qualitative $($i$.$e$.,$ words$)$ and quantitative $($i$.$e$.,$ equations$)$ arguments.

What is the role of friction in determining the speed limit$?$ Does friction help or prevent cars from moving along the circle?Draw a $2-$D force diagram of the vehicle on the circle showing all forces in that plane $($i$.$e$.,$ as if you are a bird looking down upon the car, showing neither gravitational force nor normal force$).$

Are there any measurements you could make or collateral information you could get that would help you determine the speed limit on the exit? If so$,$ state explicitly what you are trying to measure and give a detailed description $($i$.$e$.,$ an experimental protocol$)$ of any measurements you would carry out. Hint: There are tire treads and concrete blocks available.Get Out! Designing a Highway Exit

Context

You have just obtained a well$-$paid summer internship in the renowned civil engineering firm Highways$-$R$-$

Us$.$ This firm recently received a substantial amount of money from the government to design and build

an extra exit on Highway $15$ North. With a little excitement, you enter the headquarters of the firm

awaiting your project. The boss clarifies your initial assignment in the following letter:

Dear New Intern,

There are numerous tasks to carry out in the construction of a highway exit

like Exit $43$B$.$ We must evaluate the type, quality and structural patterns of

the soil before we lay down any concrete. Furthermore, effects of thermal

expansion on the concrete must also be evaluated. There are also many

choices to make when it comes to design. The partners in our firm have

opted for a flat, circular, clockwise exit, mostly for purposes of cost$-$

effectiveness.

As an intern, you will have to determine what portion of a circle we will

need, as well as the optimal dimension of the circle. Security being of

utmost importance, you will have to calculate the maximum speed limit on

the exit. Note that the maximum speed on the highway is $100k\frac{m}{h},$

although speeds of up to $120k\frac{m}{h}$ are common. As a designer, it is almost

a rule of thumb that excesses of $20\%$ over the speed limit are to be

expected.

Your calculations should be thorough enough to include different

scenarios, such as exiting in rain and snow. Minimizing the number of

accidents on our exit is a critical part of obtaining future contracts.

Trusting the quality and thoroughness of your work,

Y$.$ Bada B$.$ Ing

CEO, Highways R Us

You have little experience with blueprints, so you decide to travel to the location of the future exit. You

find that the government has bought out a square plot of land measuring $5,000m^2$ adjacent to the exit.

The exit must gradually lead $($no stops or right$-$angled turns$)$ onto a perpendicular road $($Route $174$ West$)$

that crosses above the highway on a bridge. You also find out that the average stretch before entering an

exit is $300m$ and that vehicles taking this exit may range in masses from $100kg($e$.$g$.,$ motorcycles$)$ to

$100,000kg($e$.$g$.,$ fully loaded trucks$).$