Hello, I'm Kimberly Palladino, a professor in the Physics Department and I'm joined here by my colleague Dan Hunt, and we'll be conducting a mock physics admissions interview. We're doing this online and we'll be using the Miro software for a shared whiteboard for writing on problems. And in the physics admissions interviews students are asked some basic physics and math questions, some of them are quite fanciful, some of them a little more day-to-day material but it's on topics that a student should be well grounded in but hasn't quite seen a problem quite like this before in their physics education. And what ... we're evaluating students on in these interviews is how they think about a problem, how they break it down, how they apply their knowledge, and when they know ... when to ask for direction, ... how they can take on board hints to move themselves forward when they get stuck. And a lot of those mimic what happens in a physics tutorial, which is the system that supports students during their studies at Oxford. So with that let's start our interview.
I'm Kimberly Palladino, a professor at the college you're interviewing at, and I've got my colleague Dan Hunt here who will be your second interviewer ... with us today. Hi Nina it's great to see you. Nice to see you, thank you. And so we're conducting this meeting online and so if there's any internet problems ... you know we'll try to reconnect and we'll see if there's anything we can do, if you miss anything I say please let me know and have me repeat it and I might need to do the same for you, in this modern era. And so we're going to be using the online whiteboard Miro for our interview and you've got technology to be able to write on it also and I do too, and so we'll get started. So we're just going to ask you some physics questions centred around a theme and move on from there as you help solve these problems. So Oxford as you might know is a bit of a cycling city, and so I get around by bicycle and I pull children in a trailer and it's quite exhausting, and so we're going to do some problems related to that. So here I am cycling on my bicycle and ... we're gonna treat our rider and the bicycle as ... as a single system so you know they've got a combined mass ... there's no, you know, forces, you know of course a pedal, you know I'm pedalling the bicycle, and the bicycle is holding me up, but we're not going to be able to neglect ... those okay.
We are moving to the left with our velocity and some acceleration, and there's no air resistance.
Of course we're cycling on the ground, can you ... in this problem draw what our force diagram for our cyclist bicycle ... system? So what what are the forces? And I've shown you that we are accelerating to the left. What are the forces at play here? Okay so let me just switch to try to write, so we said we're looking at it as a combined system right, so first of all we have the- oh that's way too big let me correct that-
so first we have the combined weight of the system ... so this is the gravitational force acting on it ... on the whole mass of the cyclist and the bike, times ... the earth's acceleration. We have a reaction force from the ground up and so the cyclist isn't accelerating in a vertical direction.
Yeah we have ... resistance from the ground, usually that's on ... the wheels but we're looking at the whole system so it's just some sort of resistance, and then ... you know ... the cyclist is exerting ... a force on the bike, and so there's a internal force for going forward, I guess. So there's a force from the cyclist to the bike, but that's internal, so how do we get, how does our whole system, accelerate with respect to the ground? Oh it actually does accelerate ... through the resistance force on the ... wheels of the bike. Yeah so how would you draw that? How do I, sorry? Yep so how would you, ... do you already have that shown in your force diagram? Okay I can make that clearer, so we have the force ... the resistance force acting in this direction on the wheels of the bike and so turning them in the correct direction.
I feel like I'm missing something, yeah? Yeah, so if the force, yeah if the force is going backwards on the wheel how can I still move forward if these are all of the external forces on my bicycle? ... I will say bicycles and rolling things incredibly hard force diagrams and that's why it's your interview question. Okay. So let me think what I'm missing, we don't have any air resistance, we're moving forward, we have... Maybe talk about that force: what's happening where the bicycle wheel touches the ground? So where the bicycle wheel touches the ground ... the bicycle, the only contact point, is between the wheel, right, and the ground. The wheel is turning in this direction so this point here is moving in that direction so the force is actually in this direction.
Does that make sense? It does, right? Yeah, the force is going to be in the forward direction, yep. And, at that point what type of friction force is happening there? What type of friction? Yeah, is that point, you know if you've got your ...? Yeah it's static friction, yeah, so that's ... the coefficient of friction times the reaction force from the... yeah okay, makes sense, yeah okay. Oh ... we don't need the ground, that's okay. But do you want to add your little, your force? So I'm just going to put it in the middle generally on both wheels going in that direction. Ah yeah so let's talk about both wheels. Is there, so, we didn't draw this detail but when we pedal, you know, we're pedalling around there's some gears that attach to our pedal and it usually just attaches to the back wheel so our internally applied force is on the back wheel. Okay, true. What is happening on the front wheel? Okay so ... let me delete that as well again, so for the back wheel we know what's happening right? Yeah. From the front wheel it is just turning there's no force from you coming to the wheel, ... this applies again, this here, ... so when the wheel is turning there's again static friction in that single point there
...
let me think
I would say that the same force is acting on it, does that make sense? And so it's easier to ride a bike because you get this additional force which helps you.
... Let's think about that, how so, you know we've got a rigid bicycle frame, so you know our axles right if the one wheel is moving forward the other wheel ... is moving forward, but, so when the when the axle moves forward and the the wheel rotates because we've got static friction, we can have the same static friction with the wheel like turning, you know, either way, or vice versa right? We can have static friction that applies forwards or backwards when the wheel is turning forwards.
Okay yeah, there's... So this static friction on the front wheel, is it forward or backward? Just let me add, there's another force on the front wheel which, if that's the front wheel, is just going forward from the frame of the bike pushing it because of the force applied on the back wheel right? Yeah so this that's one of these internal forces to the system, yeah. Okay.
So we have this force going to the left and as you said ... the whole thing is turning, there is the static point and what you're implying is that there's ... friction force going backwards. Let me think why that is because what's the difference between the front and the back wheel in terms of the friction? Because the front wheel is turning the same way and it has the same ... point of contact with ... the ground right? It has, oh it has another force which is applied somewhere in it, so there's another force going backwards and this is why the whole thing is turning, okay, ... it's different. Yeah, so can you, so if I want a simple equation now for my, you know, my acceleration of my whole system, what is that ... acceleration of my system gonna look like? ... And you can leave it, ... you can have that total mass times our acceleration, you can set equal to something else. Yeah okay so let me just clear ... things up. So as we said, we have the two wheels, which are connected. On the back wheel we have the friction force going forward, on the front wheel we have the same friction ... force going backwards. Well does it...? So is it the same?
... Because this is one of the strange situations of how friction, and how especially static friction work. Does it actually have to be the same force?
No. Yeah, the coefficient could be different between the two. The coefficient could be different but ...
the static force you know if I'm ..., you know, I'm holding this pen and it's sitting on my hand and I push it really lightly and it doesn't move and I push it a little harder and it still doesn't move, ... what was happening with the static force between my pen and my hand? Okay yeah the static friction changes depending on the applied force, yeah ... until it becomes the dynamic friction when it starts moving, yeah okay, so those are different...
And so which of these two forces is going to be bigger?
Which of these is going to be bigger?
So the friction force on the back wheel is due to the pedalling and it drives the whole system, so I would expect it to be bigger than the front one. Yep, exactly, so as you said our acceleration is going to be caused ... by that that rear ... friction force. ... yeah so write that all up, for our our total acceleration.
I'm sorry just let me switch around stuff.
Okay so yeah the other two forces on the front wheel are internal from ... for the front wheel, so the whole bike rides forward because of this friction here. And if the mass of the whole system is 'a' this is what we have for the driving force.
Well that's our driving force, but what's our total force on the system? Yeah okay ... so we have the driving force on the back wheel on the, yeah on the front wheel
or ... yeah we're talking about the horizontal acceleration right? Yep. On the front wheel we have the force which comes from the frame, this one here, ... which pushes the forward ... yeah the other wheel forward, and that force, yeah that force should be the same as the friction force on the back wheel, so that they both accelerate at the same rate. Does that make sense? Yeah, when we talk about these internal forces it becomes ...
so it becomes a little convoluted, so let's just ... talk about ... the external, the forces external to the system. You already have them there, you're just missing it in your equation. Okay I'm missing something. So we've got our force from our pedalling that's pushing us forward on the back wheel and then we said we have a slowing, you know we have a force in the opposite direction from friction on the front wheel. Ah okay yeah cool. Yeah so our total accelerating force needs to take into account both of those. Yeah.
There we go, because they're in different directions and acceleration is forward. Yep. If we assume the acceleration is forward. Okay. Fantastic, okay so that's our ...
our situation ... on a flat surface. So now I'm going to ask you to do the same thing, and we might have to be careful with with our drawings, ... I'm going to move, oops, I'm going to move ...
there we go. If I want to move, how do I move along the screen now?
You have to select the cursor up top, yeah. Ah there I go, I was just touching too close to any of our writing before. There we go, okay, so I'm gonna go back, so now I'm gonna draw a situation
and I'm gonna have my same cyclist on a bike
and they're now going to be on an incline
and they're going to be pulling a trailer up the incline
so
now ... so we've added something else to our system
can you draw ... and we are still ...
... now we get to go, but now we have to go up a hill. Can you work towards solving what that total, you know, the force that's going to give us our acceleration up the hill is now in this system on the hill? Yeah okay ... so we'll be looking at the projections of the forces along this line so that we, yeah, don' look at other projections up and down ...
so we still have
let me just fix this, we still have the forces, we still have the friction forces on the wheels as starters
oh nope the other way around
I'm gonna delete your hill though. That's fine. Okay I mean ...
we still have those forces, however they are smaller, okay, let's come back to that later. First of all another, right now the weight of the whole system, there's a projection of it along ... the hill slope in this direction, ... which is
sine theta
times the width, which we had. Right.
Yeah we also have now the weight of this thing, which we'll denote with a small m and we have its projection as well.
What else do we have? We have friction on it's wheels, which it, following the same logic ... , for ... the front wheel, the friction here goes backwards, and it's dragged forwards by the friction on the back wheel of the bike, so we'll call this f double prime we have f prime here and f here
... is that all?
Is there something else new coming from the setup?
Nope I think that's everything else would be internal to the system. Yeah exactly. Okay so our final equation of motion would be ... m plus small m. They are riding at the same acceleration equals their driving force minus the two friction forces minus
... the two projections
of the gravitational force. Okay yeah.
Now let's go back to something you started to mention before, what, how do our f and f primes relate to our forces before when we were flat? ... What will be different for those forces now? Our frictional forces. Okay so those frictional forces are some coefficient times ... the reaction of the ground. This time ... when we have an incline, yeah when we have an incline, this is the system ... we have the ...
we have the weight or the gravitational force going downwards, we have some projection of it in this direction, and so ... the reaction force from the ground is smaller going upwards, compensating only for this component, which is the cosine theta of mg right or m plus small mg so those friction forces will be smaller this time but this is for the f prime and ... f double prime the driving force however, yeah it depends on the drive, yeah it depends on the power input, so to keep driving with the same acceleration you would need a larger force
yeah because those components here become small ...
wait what, I said those components will become smaller yeah, but we have those components okay yeah. Yep you've got it right. Excellent, so, ... let's maybe put some numbers ... this a little, but I'll do very very easy numbers, okay, ... unrealistic numbers one would say, so let's ... assume that ...
you know oops
so, you know, our g can just be a perfect 10 meters per second squared, and let's say our theta is 0.1 radians which is about 5.7 degrees. Our big m is going to be a whopping 10 kilograms - I was on a diet - and our little m will be six kilograms, and our coefficient of static friction for all of these is gonna be a half. Okay
so the idea is to calculate the driving force yeah? The idea is to calculate the driving force or the resulting acceleration. Yeah okay ... we're looking at the second scenario right? Yeah yeah we have the... Let's look at our second scenario. Yeah so our acceleration times those 16 kilograms will equal the driving force minus the two friction forces. Now we have a coefficient, oh yeah okay, let's just put in the ... yeah let's just put in the numbers, ... we have the coefficient
fixed in the width
... and I said that one of them was a cosine theta times
yeah times ... the acceleration
So one of them is for the big mass, the other one is for the small mass, right.
So this is the coefficient times the projection of the gravitational force for both of the masses, and then we have sine theta
Oh I forgot to give you a number. Yeah I thought so okay. Which is our ... your little f
The driving force? Yeah. Yeah okay. That's gonna be 400 newtons okay?
And here I'm loosely calling it the applied pedal force, there's clearly a lot, you know, there's more, right we'd be dealing with our gear system in talking about our actual pedalling force, but so this is the equivalent number that you wanted, of what's along the ground. Yeah okay ... so we have the acceleration ... gravitational acceleration and then the sum of the masses ... I'm putting in numbers kind of partially, sorry about that. No problem, so with an angle like this how can we quickly figure out the sine? Let's do the sine first. Yeah ... so we have 5.7 degrees we have 0.1 radians or we're looking for the sine of that or the cosine.
Yeah let me think...
so 0.1 radians
... is this a big angle or a small angle to have? A small angle.
... there's a small angle ... Oh yeah we can use an approximation that sine theta is approximately the value of theta and radians and then cosine theta is approximately one, yeah thank you.
... that's all right, right? Yeah. Yeah okay so if we plug in the numbers
we have that 16 times our acceleration which we're looking for equals those 400 newtons minus 0.5 times cosine is 1, g is 10, this is 16, 160 divided by 2 is 80. So we'll just put this in
and then minus
the sine times 160, the sine is one-tenth, so that's 16.
Our acceleration will be 320 over 16 minus 1,
which is 19 meters per second and I think the yeah everything's in kilograms it's in psi units so that's our... Yeah great job checking your units, and actually quite conveniently because of how you've written it, what would have been our situation on the flat ground compared to this? So on the flat ground we wouldn't have, yeah, we wouldn't ... have the sine theta argument at all and ... the f prime and the f double prime wouldn't have the cosine, but the cosine is, we take it as one, so it's the same so we just don't have the last ... term which is one which isn't a big difference
Yeah we ended up with, you know, flat. Yeah so numerically flat we'd be at at 20 meters per second instead of 19. Now that's a little bit due to the numerical choices here,
but, you know, my legs certainly feel more tired than that. Yeah. Okay okay, cool. Excellent ... we could, let me briefly ask you one more question, so now ... let me move us over again
Okay
Sitting still, and I'm gonna simplify it. I'm not gonna bother to draw the front wheel, I'm actually just going to draw the pedals.
So the pedals are 180 degrees off so they're up and down and now I'm going to come in and I'm not...
that would be darker
I'm now going to push against that bottom ... sorry I'm trying to show it turning. That bottom pedal, I'm gonna push it backwards. So we've got a bicycle sitting there and usually when we pedal you know we in this view we would pedal around clockwise and so ... in usual pedalling to move forward I, that bottom pedal ... moves backwards and the bike moves forward, but now I'm not sitting on the bike I am an external to the system and I push that pedal backwards. What's going to happen to the bicycle?
Okay ... we push the pedal like forwards right, so that it rotates in the wrong direction. Well the way ... the arrow is shown. Yeah okay okay okay, so what will happen? Both of the wheels on the, are on the ground right? Both the wheels are on the ground. Yeah, we have ... the, why don't we have the back wheel? Okay let me think ...
So first of all are the pedals, when they turn they're turning ... this chain here, right, oh yeah the one I just moved
... and the chain starts going in that direction yeah and so this ... the chain is connected to some, not sure how bike works, to some inner part of the wheel, of the front wheel, so this smaller circle here turns in that direction, so this is the whole bike right yeah? It's not some complicated system, yeah okay, so this wheel should be turning backwards
... how is the back wheel connected to all of this? This is the back wheel, so there's no, the front wheel is just like a free spinning wheel, it's attached but this is, the middle part is the the gear system that the pedal is attached to, so the pedal attaches to the back wheel right- our pedalling will turn our back wheel. But now we are not on the bike doing the pedalling, we're just a person standing next to the bike pushing.
Okay.
I'm trying to see the difference between us standing on a bike and us not being on a bike. Well yeah, so let's... Obviously the weight is beginning... The weight will be part of it.
What else, what can be happening, so what other external force, I've drawn only a very small part of this system, what other ...
what other force can be acting on this bike, right, because we're we're trying to say, you know, how is this bike going to move? It was still and we're pushing on a pedal so we expect it to accelerate in some direction, so it'll start moving in some direction, what other forces could be applied, you know, what other external forces are going to be acting on this bike system, and here we just care about this rear tyre, that will affect which direction this bike goes. Yeah okay I'm trying to think, so yeah we know about ... the friction force on the back wheel again going in this direction because the wheel is turning, and that yeah
... we are not sitting on the bike
let me think what is different between the previous setup and this setup. The only difference is that, ... the force is coming from an external place and this time we're looking at the system by its parts, so we're looking at the pedals, ah, so the force is applied here and there's a torque around this point in the middle of the pedalling gear
Yep, so we could, I think, let's try and, we could analyze this through the full torques and that would give us our full understanding and I think I'm gonna try and have you leap over that, to just think about .. in this situation
what
how should we be thinking about our different forces? Yeah okay, so in the filling gear we're applying the force from outside we're pushing the down, yeah the bottom pedal to the back, and with this, apart from turning it, we are also applying force on the whole system which is
is it resisted by some, or could we say that we are just applying, yeah, so apart from turning it along its direction of rotation we also apply ... some projection of our force straight to the left of the system, yeah, so effectively we have some force going to the back of the bike's acceleration if we want to accelerate it forwards, okay. And we've got only, and on the back we only have static, you know, we have our extra sub part of the force that that pedalling force that we would have had in the first case pushing us forward ... but
is it going, I mean, I think you've gotten most of the way there. If you imagine a bike and you just try to turn the wheel you're probably going to push it backwards. Exactly so now you can amaze your friends and family and anyone standing around with a bike. It's actually called the bicycle paradox, that we're used to thinking about pedalling our wheels, you know, pedalling, and that would move us forward but if you apply this force externally from the system it'll move it backwards. Okay yeah nice. And you know none of our friends and family are really amazed by this but that's what happens in your physicals. Well thank you so much for answering bicycle questions ... and working on some physics problems with us today ,so this will conclude our interview and we'll move on.
See you. Thank you so much.
I'm Professor Palladino and this is my colleague Dan Hunt and we'll give a brief review of the interview you've just seen as a physics interview. So this is an approximate question of an Oxford admissions interview question, and our student Nina is a third year Oxford student, who had never seen this question ... before, and overall she did an excellent job ... and I'll ask my colleague Dan to give his impressions of the interview first. Okay ... I think that Nina handled the question very well, there were definitely some points where she was grappling with the kind of material that we were discussing, in particular with the bike paradox, but she was then very quickly able to rehabilitate and reorient to understand what we were actually asking with the question. With a lot of topics such as these it's, we're not looking for people to get the question in an instant, we're looking for people who are very quickly able to understand and adapt to the situation and who seem very eager to kind of pick up on the topics that we're actually discussing, so I was very impressed by how that was handled and how we came to a solid answer right at the end there, absolutely. Yeah I agree, I think Nina did ... a really wonderful job and ... really very much what we expect, and you know even talking to another professional physicist, when you first start with a brand new problem you might not see all of the the effects that are going on, you might have to ask questions to better understand the setup and why you're being asked the question ... Her process of verbalizing everything she was thinking and including drawings of how she was thinking about things really let us have a really good sense of how she went about tackling the problem and that really lets us evaluate her knowledge ... in a strong way it helps us give her feedback about what she's thinking early on, so that she can maybe adjust her thinking. And that's, again, our interview process lets us, as future tutors to a student, think about what the tutoring process would be like. Does the student know when to struggle with an idea, when to maybe ask if they're going in the right direction and when to use a hint correctly to move them more forward and Nina did a really wonderful job in all of that. She would be near close to perfect marks, maybe a student who is a little bit faster through everything, perhaps especially with the first bicycle on the flat ground and what happens to the front wheel and the fact that it's frictional force ... is opposing our direction of motion ... is maybe the type of thing that we would, if a student got that immediately they would score a little higher, but almost in all cases when that happens it's because that student has maybe worked on a bicycle problem before and already knew that that's the situation ... because that's how these these physics problems ... usually work. We want to see some general math skills so you don't need a calculator but you might have to do some simple arithmetic or ... you know, basic variable manipulation ... maybe a bit more than ... than was shown here but we're really trying to give students in an interview a question where they should know enough to go in and solve it but it's a brand new question and Nina handled that really well in how she interacted with us and with the Miro white board.