# Work Done by a Force 3

https://isaacphysics.org/questions/work_done3?stage=a_level

Could someone explain what the question is saying - I got the answer for all the parts but don't really understand what is going on.
I understand what r is but no idea about F.
r = xi+yj which makes sense to me because the axis for both lines up
but for F...
I initially tried to write F as a column vector so F = (F_0*y/r,-F_0*x/r) - but unsure why y is multiplied by i - shouldn't that be x?
(edited 3 weeks ago)
Original post by mosaurlodon
https://isaacphysics.org/questions/work_done3?stage=a_level
Could someone explain what the question is saying - I got the answer for all the parts but don't really understand what is going on.
I understand what r is but no idea about F.
r = xi+yj which makes sense to me because the axis for both lines up
but for F...
I initially tried to write F as a column vector so F = (F_0*y/r,-F_0*x/r) - but unsure why y is multiplied by i - shouldn't that be x?

You could think of it in polar form and x=r*cos(theta), y=r*sin(theta). So r would make an angle theta with the x axis and F would be perpendicular as the dot is zero, so it would be acting tangentially to (the point on) the circle which is probably what you want?

If youre unsure, pick an angle like theta=30 degrees, r=1 and sketch it out.
(edited 3 weeks ago)
so something like this?

I still don't really understand how you get original equation for F
Original post by mosaurlodon
so something like this?

I still don't really understand how you get original equation for F

F is given and its always perpendicular to the displacement (x,y), so thats why you have zero work done. It must be something like (y,-x) or (-y,x) to get a zero dot product with (x,y).
(edited 3 weeks ago)
ah I see so you cannot work F out by the diagram itself

the diagram actually makes sense and I guess the reason its flipped to (-y,x) is just so it mathematically works out with the dot product like you said.

Thank you
(edited 3 weeks ago)
Original post by mosaurlodon
ah I see so you cannot work F out by the diagram itself
the diagram actually makes sense because it has to go a little left (negative) and up (positive) for it to be perpendicular (for this angle anyway) - and I guess the reason its flipped to (-y,x) is just so it mathematically works out with the dot product like you said.
Thank you

Actually, Im unsure about the whole question. The F.s formula (which they tell you to use) really refers to the work done in applying a force over the displacement s. Here the motion lies on a circle and the force is acting tangentially to the circle so work will be done along the circumferece as the instantenous displacement is in the same direction. So the work done along that path should be something like
Int F ds = Int F.ds/dt dt = Int F.v dt
and the velocity is parallel to the force.

Either Im completely misunderstanding something or there is a problem with the question.

Edit - as an example, centripetal force which generates circular motion acts along the radial direction (negative) however no work is done as the radial displacement does not change. Its perpendicular to the tangential velocity and all that would be in keeping with Int F.v dt rather than F.r
(edited 3 weeks ago)
So just to like reiterate what you said to check If I understood...

usually with circular motion since the centripetal force acts towards the centre, and not in the direction of the displacement (ie going around the circle) then no work is done,
but with this scenario the force IS acting in the direction so work is done.

and the only way to get that work done would be using an integral rather than a dot product?
i might contact Isaac Physics to see if there is something Im missing.
Original post by mosaurlodon
So just to like reiterate what you said to check If I understood...
usually with circular motion since the centripetal force acts towards the centre, and not in the direction of the displacement (ie going around the circle) then no work is done,
but with this scenario the force IS acting in the direction so work is done.
and the only way to get that work done would be using an integral rather than a dot product?
i might contact Isaac Physics to see if there is something Im missing.

I dropped them a line last night as it seems like an obvious mistake (famous last words) and will let you know what they say. Im surprised that noone has picked it up before, though its easy just to chug through the question without thinking about it and I was guilty of that in the first couple of replies. The question is a maths one (rather than physics) and Id guess it was churned out. The question is incomplete as there is no indication of the length of arc the force acts for which is important as the infinitesimal work done is constant (not zero).

https://phys.libretexts.org/Bookshelves/University_Physics/University_Physics_(OpenStax)/Book%3A_University_Physics_I_-_Mechanics_Sound_Oscillations_and_Waves_(OpenStax)/07%3A_Work_and_Kinetic_Energy/7.02%3A_Work
is a bit long, but has most of the arguments.
(edited 3 weeks ago)
Thank you so much - lets hope they give us an apology rather than a lecture
(although in my case I wouldnt mind a new lesson)
Original post by mosaurlodon
Thank you so much - lets hope they give us an apology rather than a lecture
(although in my case I wouldnt mind a new lesson)

Had a very brief reply from isaac a day or so ago and their last observation about because the particle does not speed up, then no work is done .... is best left uncommented on. Though I have queried their reply.

However, I looked over the previous two work sheets and they both (correctly) refer to work done as the dot of F with the change in displacment or the (integral of) instantaneous displacement. In particular part c) in sheet 2
https://isaacphysics.org/questions/work_done2?board=1ae25da7-3108-48fc-9a50-2c6acc68a471&stage=all
is very similar to the circular motion set up, although the force is in radial direction (in sheet 3 its tangential) and they correctly make the observation that as the dot of that with the (instantaneous) displacment is zero, then work done is zero. Which is the centripetal force (radial direction) argument, but the opposite of what is done in sheet 3. Ho hum ... Cambridge physics (fill in a suitable phrase here) ...
(edited 2 weeks ago)
I see... from what ive noticed they rarely go into detail - they must get a lot of other questions from a lot of people regarding their challenge questions which would explain the brief comment.
Anyways, thank you for that and all your help and I look forward to seeing what they reply with
Original post by mosaurlodon
I see... from what ive noticed they rarely go into detail - they must get a lot of other questions from a lot of people regarding their challenge questions which would explain the brief comment.
Anyways, thank you for that and all your help and I look forward to seeing what they reply with

Just had a reply where they now accept that both the worksheet and their original reply were wrong. So work is done when the force is in the tangential direction which should have been obvious as you could unroll the circle into a straight line and the constant force would always be heading along that line and this is pretty much textbook definition of (simple) work done.
I see.. thank you, so are they going to change the question/previous worksheet?

I also might have time to thoroughly go through the libretext you sent, just so I can confidently understand why/why not work done occurs when the force is either tangential or radial (and to know when to use integration of Int F.v dt)
Original post by mosaurlodon
I see.. thank you, so are they going to change the question/previous worksheet?
I also might have time to thoroughly go through the libretext you sent, just so I can confidently understand why/why not work done occurs when the force is either tangential or radial (and to know when to use integration of Int F.v dt)

The guy said he was looking at adapting the text, though then it would pretty much become question c) on worksheet 2, but its their problem now tbh.

Im not sure Id spend lots of time going through that page (its decent but Im sure there are more concise ones) and thinking of it as
Int F.v dt
is a bit beyond a level.