Final Exam – ENS100 – Fusion of Engineering, Control, Coding, Machine Learning, and Science

General remarks

On the first page of your exam, clearly write your name, your student ID number, and the name of the class (ENS100).
You need to explain the complete procedure that you used to solve the problem. Final answers without the explained procedure will count 0 points.
Please do not cheat on the exam or ask someone else to complete the assignment for you. We can easily identify students that did not do the exam independently.
When submitting the assignment, follow the following guidelines. If you write the exam on sheets of paper, scan or take photos of all the pages. Then, transfer the photos to your computer. Then, open a new Microsoft Word file (or open a file in the text processor that you use) and copy and paste all the photos. On the first page of the Word document, write your name and the student identification number (employee ID number). Save the Word file as “yourname_yoursurname”. For example, if a person’s name is John Doe, the name of the file should be “john_doe”. Send the file as a single attachment to my email address. You can also save the file in the pdf file form. If you have a digital writing pad, you can also use the pad. In that case, you still need to combine the digital pages of your exam in a single file.
I will not accept the exam submissions after 3 PM on December 17, 2020. Submit your exam before 3 PM.

Question 1 (10 points). Interest rates.
Initially, you borrowed $$1000$ from a bank. If the monthly interest rate is $3\%$ , calculate the amount that you will have to return to the bank after 5 years.

Question 2 (10 points) Velocity and acceleration
An object is moving along a straight line. Its position that is a function of time is given by the following table.

Rendered by QuickLaTeX.com

Estimate
a) Velocity at the time instant $5 [s]$
b) Velocity at the time instant $6 [s]$
c) Acceleration at the time instant $5 [s]$

Question 3 (10 points). Moment of the force.

Given the force $F$ , angle, and distance $s$ , compute the moment of the force $F$ with respect to the point A for the cases given in the panels of the figure below.

Question 4 (10 points). Mechanical advantage
What is a mechanical advantage? Draw a sketch and provide a detailed explanation.

Question 5(10 points). Unit Conversion
Transform units:

a) $10 [\frac{miles}{hour}]$ to $[\frac{kilometer}{second}]$

b) $100 [\frac{centimeter}{second}]$ to $[\frac{milimeter}{hour}]$

c) $10^{4} [\frac{meter}{second}]$ to $\frac{miles}{hour}$

Question 6 (10 points)
Two cars are approaching each other. The velocity of the first car is $30 [\frac{meter}{second}]$ and the velocity of the second car is $20 [\frac{meter}{second}]$ . If the initial distance between the cars is $10 [miles]$ , compute the time it takes until two cars reach each other. What is the distance the first car traveled? Provide a sketch of the problem and all the graphs.

Question 7(20 points).

A force $F$ is acting on a box of the mass $m=200 [kg]$ (see the figure below). The coefficient of friction between the surface and the box is $\mu=0.2$ .

a) Sketch a free body diagram of the box?
b) What is the maximal intensity of the force $F$ that can be applied to the box such that the box remains still (at rest)?

Question 8 (20 points)
A force $F$ is acting on a box of the mass $m=200 [kg]$ on an inclined plane with an angle of $30$ degrees. The inclined plane is without friction (no friction force).
a) Sketch a free body diagram of the box.
b) What is the force $F$ (the force is horizontal) that needs to be applied to the box such that the box does not move.

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