20 practical engineering math problems to demonstrate the important of math proficiency in engineering & science
Are you ready?
Below is a list of carefully curated questions from technical textbooks that demonstrates the need for math proficiency for Science, Business and Engineering. Be challenged.
As Medium doesn’t have a show/hide feature, you are advised to scroll slowly to see the questions you are going to attempt without revealing the answer that follows.
I hope such questions can prepare you for any technical exam regardless of any formal qualifications or not.
Good luck!
Warm-up Algebra (Q1 — Q5)
Question
1.If cast iron weighs 450 pounds per cubic foot, the weight of a solid cast iron manhole cover 2 feet in diameter and 1 inch thick is most nearly ____ pounds.
Answer:
Thought Process:
The first question that comes to mind would be what shape the manhole cover is? Manhole covers are commonly round in shape, although other shapes do exists! Nevertheless we cannot just assume, so we need to pay careful attention to the question. The question states the diameter, so we can go ahead and assume a round manhole.
Because the manhole diameter is given in inches, lets calculate the entire volume in cubic inches. However the weight of cast iron is given in pounds per cubic foot. So we shall convert that to cubic inches and work out the aspect ratio.
Tip: Be familiar with metrics and SI units conversion!
Question
2.A single-phase diesel AC generator produces 60 Hz and it’s driving engine speed is 450 rpm. How many poles does it have?
Answer:
Thought Process:
Frequency of diesel generator is given as
Remember this formula — some technical exams are closed book or restrict the texts you are allowed to have and do not provide this formula. Once you have remembered it, the question can ask you for any unknowns. With basic algebraic skills, just rearrange the numbers to make the variable the subject.
Tip: Also worth remembering 450 x p can be expressed as 450p
Question
3.A fixed-wing aircraft has a wing area of A = 16.2 m² and lift coefficient around C₀ = 1 (at moderate angles relative to the wind) What is the lift produced by the wings when taking off at sea level, with wind density D = 1.25 kg/m³, at a speed of v = 36 m/s? And, compare this to the gravitational pull on the aircraft given the take off mass of m = 1000 kg.
Answer:
Thought Process:
Remember the lift formula! For the aircraft to ascend its lift force needs to offset the forces of gravity. Hence, the difference between the two forces of F₀ and F₁. Lift coefficient is denoted by C₀ (is given in this case) is a dimensionless quality (having no units) and doesn’t affect the calculation. It is any value between 0 and 1. Unless otherwise given, for all practical purposes, we assign it a value of 1. When we worked out the net force, we are able to calculate lift velocity/climb rate in meters. Again SI units are used, you you need to be familiar and pay attention to what’s given and convert them if necessary.
Tip: For a level flight, the aircraft constantly needs to balance lift with gravitational pull which will allow it to maintain an altitude. Modern aircraft auto-pilot system handles this process without the intervention of a human operator (the human pilot) when activated once cruising altitude is reached. Increase in altitude results in a decrease in surrounding air pressure requiring an increase in horizontal speed to maintain the balance. Also, an increase in mass by a factor of 2² = 4, the speed of the aircraft will need to be doubled. That new velocity is determined by the following formula
Question
4.If a fuse is protecting the circuit of an 15 ohm electrical heater and the fuse’s current rating is at 10 amperes, the maximum voltage that should be applied to the terminals of the heater is_____volts?
Answer:
Thought Process:
Pay attention to the question. Unless otherwise stated, a heater appliance is purely a resistive load ie. It generates heat from electricity via resistance. It different for other appliance that uses inductive loads or a combination of resistive and inductive loads. Its internal resistance is given as 15 ohms
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I = E * R would give us 150 volts at maximum.
Tip: However most of US household current is at 110/120 volts and Europe is at 220/240 volts, so the correct answer is 120 volts. Most countries conform to either one of the standards. If you live in a 220/240 volt zone, you will need either a 1) higher rating fuse or b) voltage converter. You should also pay attention to the maximum power ratings for the heater. Exceeding that posses a safety and fire risk! As mentioned earlier, this calculation is only applicable to purely resistive loads such as heaters.
Question
5.Implement a computer a program or algorithm to display the distance an object falling under the force of gravity (acceleration of gravity is defined as 9.8 m/s²) after a 10 seconds from release. Do not factor weight or air resistance into the equation. BONUS: Simulate animation for each second of free-fall in your application.
Answer:
Link to the program: https://onlinegdb.com/ttOTxWzgV
Thought Process:
There are 2 formulas dealing with the kinematics of free-fall and acceleration of an object caused by gravity. One determines the velocity (speed) of an object after a period of time in t seconds,
V₀ = g x t
While the other determines distance
d = 0.5 x g x t²
Since the question asked you to determine the distance after 10 seconds, the 2nd formula should give us the correct answer of 490 meters!
Tip: Don’t let the code confuse you! The algorithm part to calculate fall distance from gravity is
in the main() function
While the first function serves to delay the output of data on a computer console every 1 second!
The delay() function is actually calling a system procedure call to create the delay in the computer program by counting n seconds x 1000 milliseconds. You can see the effect when you run the software on a PC (not the online version). The code conforms to the ANSI C standard. This means that is guaranteed to behave the same on different Operating Systems (Mac, Windows and Linux) as well as mobile (Android, iOS) and embedded systems (hardware) without retooling the software or installing dependent software components. Practical applications of this software would be in avionics and missile guidance control
Bonus Qn: A free-fall gravity bomb is released from an aircraft flying 8500 m above ground level. Calculate the time of impact of the bomb on target. Again gravity = 9.8 m/s².
More to come, stay tuned!
Resources
I would like to end off by leaving you with 2 resources to explore to encourage learning and critical thinking in a scientific field.
1.Here are 2 useful Telegram channel links for Maths, Science and Engineering resources (e-books included). Disclaimer: I’m not affiliated to the channels creators and I can’t guarantee this channel’s availability at any time.
2.My StackExchange profile. See how I ask questions on StackExchange network of scientific and non-fiction Q&A sites. As long as you are inquisitive and willing to learn, there is no such thing as a stupid question to ask on Stack-Exchange!
Conclusion
Many times, math challenges are asked in the context of an examination or interview test. Hence, given time constrains, it is imperative to quickly understand what the question is asking and whether enough data is provided to use a certain equation. By following the tips provided, you should identify the areas that require improvement and obtain practice to improve proficiency
