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yrelhan4
A block on a rough inclined plane..... Question attached.
What the heck is that ? Sry i only understand english
Ignore the hindi part. Its just the translation of the question.
For the first question?
Its a. Might me some minor mistake.
Here Suppose the block has moved a distance x
then at position x balance the forces i.e. mgsin(-) - umgcos(-) = 0 Integrate this from 0 to x
u get the answer on simplification.
Well i get this sin(-)=mu*x^2/2*cos(-) Doesnt give me the required answer? @lordcyborg
there is no m term on RHS
and u missed an 'x' term on LHS
There is. You see the coefficient of friction given is mu=mu(not)*x. Ah, so we are not balancing forces, we are conserving the work. I get it. But that still doesnt give me a ?
hey man/woman................. on integrating u get mgsin(theta)*x=u.mgcos(theta)*(x^2)/2 Cut mg and 'x' on both sides.......... U get the answer........now try it fast
Oh. But you cant balance forces for the body to stop right? You have to conserve the work done?
When you balance forces, it means there is no acceleration. It doesnt necessarily mean that the body is at rest? And a man.
lol.........Dont go too deep...........i'm balancing forces when body is at rest
I dont think you can balance force for the body to be at rest.
ya we cannot all times.........bt we can
Why doesnt conservation of energy give me the answer?
coz u can apply dt when there are conservative forces.......in this case friction is not acting as a conservative force..........Now dont make me bore
You can leave if you are getting bored. You chose to answer my question. I didnt tell you to come here and help me. Thank you.
C'mon man............I gave u the perfect(i suppose) reasons.........now go and sleep it 2:15 a.m.
Yeah you did. Thank you.
|dw:1364764688058:dw| a = gsin@ - u0 x gcos@ vdv = (gsin@ - u0 xgcos@)dx => 0 = gsin@ x - u0 gcos@ x^2/2 x=0 and x = 2tan@/u0
for 2nd part, limit of v will be from 0 to v, of x will be 0 to tan@/u0 ^_^
:O mere dimaag me kabhi nhi aata ye, 2nd part konsa? Heat produced?
oh sorry, nahi 3rd part me ye. heat produced me work energy lagayenge (SHAYAD) :/
Hmm. Equation likh do 2nd part ke liye. :/
|dw:1364765247915:dw| mgh + integral (mg sin@ - u0x mgcos@) dx = change in kinetic energy + heat change in KE = 0 hai x ka limit 0 to max tak jayega.
check kar lena, maine bola hai to high probability hai ki galat hoga. 3 baj gaya! :O gtg bye
Acha ruk.. Sahi hoga. :/ Ke 0 kyun hai? x to lamit 0 se x/2 tak nhi jayega?
@Vincent-Lyon.Fr We got the first and the last part. For the second part what would be the work energy equation?
Answers to all 3 questions are no 1. I solved 1st question by dynamics 3rd question is just substituting cos and sin. 3rd question is computing the decrease in mechanical energy.
1st one by 1=v*dv/dx right?
For the first question, N's 2nd law gives : \(\ddot x+(\mu_og\cos\theta) x=g\sin\theta\) If you use \(\omega ^2=\mu_og\cos\theta\) the solution is \(x(t)=\Large\frac{\tan\theta}{\mu_o}\normalsize (1-\cos\omega t)\)
I'll try solving it by work-energy theorem tomorrow, but now I have to go to bed.
Yeah i am looking for that solution. Alright. Thank You.
At the top, \(\cos \omega t=1\) At the bottom, \(\cos \omega t=-1\) Halfway, \(\cos \omega t=0\) The rest is easy.
Right. I'll try and get back. And please see if we can do it by work energy theorem too.
if i use work energy theorem i get some weird answer.. Net work done = change in K.E since Initially its at rest and finally also at rest.. change in K.E = zero hence net work done = zero now there are two forces doing work, gravity Wg = mgcos(theta) x and friction Wf = - mgsin(theta)ux^2 Wg + Wf = zero but solving that gives a weird answer for x .. none of them listed :P..
sorry i flipped sin and cosine terms... so the answer should be 4 like someone said earlier.. :-/..
you cannot balance forces.. why!? cause when forces are balanced.. the body will not stop.. it ll only stop ACCELERATING.. after that point it will start to decelerate .. and then ulimately stop :P.. thats how i see it..
and the answer can't be a) for the first part cause if it is.. then in second part none of them would satisfy the answer..
ahh.. there is definitely something wrong with what i did.. :-/... the answer should be ONE itself.. for the first question :(
Here is the solution using work-energy theorem. It is nicer than the one using N's 2nd law, because time does not appear in the equations. But you would need N's laws if one of the questions had been: "How long does it take the body to stop?" \(KE=1/2 \,m\,v^2\) \(PE=mgh=-mg(x\sin\theta )\) Elementary work done by friction: \(dW=-f\,dx=-\mu \,mg\cos\theta\,dx=-(\mu_o\,x) \,mg\cos\theta\,dx\) Total work done by friction: \(W=-m\,(\mu_o\,g\,\cos\theta)\,\int{x\,dx}\) Let's use: \(\mu_o\,g\,\cos\theta=\omega^2\) \(W=-m\,\omega^2\,x^2 /2 \) Now work-energy theorem goes: (KE + PE) - (0 + 0) = W leading to : \(\color{red} {v^2=x(2g\sin\theta -\omega^2\,x)}\) So v = 0 for x = 0 and \(x=2\tan\theta /\mu_o\) The rest follows from new value \(x_1=\tan\theta /\mu_o\)
damn.. so stupid.. thats where i went wrong.. :-/.. i forgot to consider the work done by friction as a variable.. and integrate
By the way, "balancing forces" will not lead anywhere, as forces are only balanced at one point where the body is halfway down the plane; and you can find out that only in the end.
yea logically i got that.. i was just wondering where i went wrong with my work energy theorem :P.. thanks man.. !!