Cambridge Engineering Interview

Cambridge Engineering Interview

Hi, my name is Madeleine and I’ve just finished
my second year of Engineering at Jesus College, Cambridge. I applied in 2012 and matriculated
in 2013. I’m going to go through 2 interview questions which are taken from the website
I want to study which is a website which has hundreds of engineering
interview type questions with worked through answers and occasionally videos too. The two
questions that I’m going to do are similar to the kind of questions that I got during
my interviews. So hopefully this will help. So the first question reads as follows. On
a clear day, you are on an airplane which is 38,000 ft above the middle of Pacific Ocean.
Taking the radius of the Earth to be 6,400km, what is the approximate distance between you
& the horizon of the Earth? You are also given that 1 foot is equivalent to 0.3048 meters. So the first thing that I would do is convert
the 30000 feet into meters using the given conversion. So 38 000 ft times by 0.3084 meters
is roughly, using a calculator, 11.6km So now that you have all of the figures in meters
or km, you can then draw a diagram of the earth with the center here and you can say
that the airplane is hereish. So now marking the distances on, you know that this, the
radius of the earth, is 6400km. I’m just going to say all the distances are in Km.
Then the distance from the plane to the Pacific Ocean is, as we calculated here, 11.6kms.
So now we need to think about where the horizon is. So the horizon is the line of sight from
where you are in the airplane to the first point you can see. By definition or by intuition,
you can say that point has to be at right angles with the radius of the earth because
if you are looking at this way and say that this is your line of sight and this is with
the horizon and it’s essentially where your line is horizontal with the circumference
of the earth. So if we then draw the radius of the earth on to this point you know this
has to be a right angle and, so from then on, it’s essentially a Pythagoras question.
So again this is the radius of the earth and you are trying to find the approximate distance
between you and the horizon. So if we call this x (that’s the distance here). So then
if we redraw the triangle, we have x here, 6400km here and, in total, 6411.6 here and
so by Pythagoras which in full of course is this and by rearranging this to get x; as
the result, you find the x, the approximate distance between you and the horizon of the
earth is roughly 386km. The second question which is I’m going to
go through goes as follows. A rocket of mass m is to be launched from the surface of a
rogue planet with mass M and radius R and no atmosphere. By making reasonable assumptions
about the distance between the planet and any nearby galaxies, find the escape velocity
required for the rocket to overcome the gravitational field of the planet. You might be wondering what the reasonable
assumptions mentioned in the questions might mean. And you just really need to think about
what the effect of other planets close by to this planet might be. So if there are planets
close to the rogue planet, it’s likely that their gravitational field that have an effect
on the motion of the rocket. Therefore, the assumption that you need to make is the distance
between this planet and any nearby planets is very, very large and, therefore, only the
gravitational field of the rogue planet is important in this question. So for this question,
I’ll go straight into drawing a diagram as it might make it clearer as to what you
need to do to solve this problem. Say this is the planet and we can mark on here that
this is the radius big R. Now if we draw the rocket to be here at any moment in time, we
can label the distance from the rocket to the center of the earth as little r. So this
is just something that we can define. Say in another given time, the rocket has now
moved. So it’s got a little further and we are going to say that the distance between
this instance and this instance is delta r (just to symbolize a little distance). So
we know that as the rocket is moving, there must be a force due to the gravitational field
of this planet acting on the rocket and this force is going to be in this direction which
we can call big F and we know in this instance it will also be acting obviously with a different
value which is given by the formula F equals big G and then the mass of the planet which
is capital M, the mass of the body upon which the force is acting which is the little m
over the distance between the two bodies which we have to find as r2. Now with kinetic energy
questions, you often immediately think of energy balancing equations. So this might
help in this problem. One energy balance equation that we know is that the work done is equal
to force times distance. Although we don’t quite know how we are going to get to kinetic
energy through this, it might be worth a try. We know that the force on the rocket is going
to be given by the equation that we just wrote down and if you don’t remember this equation
in the interview or you haven’t seen it before just as an example in an interview
if you can’t think of the equation or you really don’t know it; if you just state
it, say “I’m really sorry I don’t think I can’t quite really remember the formula
of the equation” They will usually give it to you as it will help you solve the question
and they just don’t want you to stop in your tracks so they will help you if you forget
things that might be useful. So yes force times this force times the little distance.
So we are working out the work that’s done for the rocket moving from here to here. So
we will do times delta r. Now this here is just an equation for the little amount of
work done moving the rocket from this position to this position which is just an arbitrary
small distance. So to get the total amount of work that will be needed to get the rocket
from the surface of the earth as specified in the question all the way to outside the
gravitational field of the planet we will need to sum all these little works done from
bigger to infinity which is where the gravitational field of the planet will end. Now if this
isn’t an intuitive step and you don’t get it in the interview, they may again the
interviewers may again help you so that you might be able to proceed further with the
question. So don’t panic. Therefore the total work done which I’m
going to write as w will be equal to the integral between big R (so the radius of the planet)
and infinity of this. And now you can see it’s just an integral but we need to calculate
to get the work done. So to do the integral, you can rewrite the over r2 as r to the power
of -2 which makes it easier and then you can see that by adding 1, dividing by the new
power you get minus … r to -1 which you can put on the bottom again between r to infinity.
Now this when you put the limits in, the first limit you put in is infinity obviously dividing
by infinity is going to give you zero and then the next step is you are doing is minus
and then inserting large R; so you end up with a minus minus big G big M little m over
big R. Now this is just the total work done. So I’ve just moved the result of this integral
up here to save space for the next bit of the question. As I have said in the beginning,
when you think of kinetic energy questions you may think of work done and energy balance
equations. So now we have the total work needed to get the rocket from here to outside the
gravitational field. Through energy balance, you know that the work done that is needed
to do this must be equal to the initial kinetic energy that the rocket has when it’s at
the surface of the planet. Therefore, we can write that the result of our integral must
be equal to half mv squared. From now on, it’s just rearranging to find the v which
is the escape velocity, as specified in the question. So mv2 is 2GFm over big R; therefore,
in the end you get v as equal to 2GbigM/R as the two ms cancel and the whole thing square
rooted. And this is the formula for the escape velocity. So these were the two interview
questions. I hope you found them useful. If you want to see anymore, go to the website
that I mentioned earlier, I want to study But if I were to give any
tips for the interview, I would say try not to panic I know it’s really hard and obviously
you are going to feel stressed. But if you forget anything in a spark of moment, if you
misremember an equation or if you literally can’t see where this question is going,
don’t be afraid to admit that. The interviewers are there to help and I’m sure teacher or
whoever might have been telling you that already. You may not believe but it is true they will
try and help you through a question they won’t just leave you in a alert they just want to
test you with things that you haven’t seen before so maybe using equations that you might
have seen in Math and Physics for example the gravitational force equation and then
use it in a way that you might not be familiar with. So they just want to see how well you
pick up new concepts or at least that’s the idea that I got from my interview and
speaking to my interviewers who are now also my supervisors. That is generally the thing
that they are trying to do or, at least in my college, that’s what they are trying
to do. So try and not to panic and don’t be afraid to admit if you don’t know something.
I quoted FM=ma in my interview and they still let me in. So don’t worry if you slip
up. Try and enjoy it these are some of the most renowned academics in the engineering
field who will be interviewing you probably. They really are there to try and test you
obviously but they will also help you through it. So they are not the enemy. So hopefully
that was useful and I wish you all good luck.

29 Replies to “Cambridge Engineering Interview

  1. If you havnt been given the oppertunity to study m1 or m2 as part of maths/further maths will you be at a disadvantage because that 2nd question made no sense to me

  2. Thanks for this! It was really helpful. The interviews this year are drawing near. I've used some of the free resources on gurume which were good but now I'm really thinking of engaging a tutor. Are they good for running through mock interview sessions? Anyone care to share their experiences?

  3. I'm glad that people find this useful – if you would like more information on Engineering, Cambridge interviews, A-Levels, or would potentially like some tutoring from me (I'm Madeleine, the girl in the video), please visit my tutoring profile on the GuruMe website! 🙂

  4. If those were the questions to get into Cambridge then it would be ez, also second problem could be solved easier. Also, rly not knowing simple equations could turn out to be bad.

  5. Hey! This was great, just one question – for the second question couldn't you directly use the equation for potential in a gravitational field, that is 1/2mv^2=Gmm/R and then do the last few steps?

  6. When I saw the second question, my instinct was to just simply use the equation v= (2GM/R)^1/2 instead of deriving it. Would I be penalised?

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