Just ran through it trying splitting the triangle and i got
OB = kmg(4a\cos\theta -4a\cos\frac{\theta}{2})
As this is equal to the GPE of the rod.
mga\cos\theta = kmg(4a\cos\theta -4a\cos\frac{\theta}{2})
V = mga[(4k - 1)\cos\theta - 4k\cos\frac{\theta}{2}]
Which is the correct...
Hmm. Since the triangle OAB is isosceles, could i split it into 2 right angled triangles to get the length of the extension in terms of \cos\frac{\theta}{2}?
I'm not too clear why the sine of the angle theta can't just be used. Is there a fundamental flaw in my understanding of mathematics...
Just come across a question and I'm at a point where i see no further.
A uniform rod AB, of mass m and length 2a, is free to rotate in a vertical plane, about the end A. A light elastic string of modulus kmg and natural length a, has one and attached to B and the other end to a fixed point O...
A particle P of mass 0.2kg is attatched by an elastic spring of modulus 15N and natural length 1m to a point A of the smooth horizontal surface on which P rests. P recieves an impulse of magnitude 0.5Ns in the direction AP. Show that while the string is taught, the motion of P is simple harmonic...
This is probably a really easy question. But alas the answer has eluded me thus far. Anyway, here is the question:-
Points O, A and B lie in that order on a straight line. A particle P is moving on the line with S.H.M period of 4s, amplitude 0.5m and centre O. OA is 0.1m and OB is 0.3m. When...
Hmm, Ive cancelled it all down to get
\frac{3mgl}{4} - \frac{2mgl}{3} + \frac{mgl}{3} = \frac{3mg(y - l)^2}{4l} - (Y - l)mg
Which goes to:-
3(y - l)^2 - 4l(y- l) - \frac{20l^2}{12}
Which after applying the quaratic formula, equates y - l = \frac{10l}{6}. (y - l) is the distance i...
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EPE = \frac{3mg(\frac{2}{3}l)^2}{4l}
The string is initially stretched by 2/3L as natural length is L and stretched length is 5/3L.
I really appreciate your help Doc Al, this question has been giving me trouble for the last couple of days.
Thank's once again.
I'm calling the entire length of the string (at maximum stretch after projection) Y. The energies are measured from the equilibrium point.
Before projection:-
KE = \frax{3mgl}{4}
EPE = \frac{3mg(\frac{2}{3}l)^2}{4l}
PE = 0
After projection:-
KE = 0
EPE = \frac{3mg(y -...
In my book, Lambda is defined as \lambda = \frac{mgl}{x} where x is the compression/extension. As the equilibrium length is \frac{5l}{3} the extension is \frac{2l}{3}.
Subbing that into the above gives:
\lambda = \frac{3mg}{2}
Why is this wrong?
Ok, We've only been taught the elastic modulus, so i assume the question should be able to be done using that. Do i use K and i would use lambda in the EPE equation?
Thanks once again,
Bob
A particle P of mass m is attached to one end of a light elastic string of natural length L whose other end is attached to a point A on a ceiling. When P hangs in equilibrium AP has length \frac{5l}{3}. Show that if P is projected vertically downwards from A with speed \sqrt(\frac{3gl}{2}), P...
A particle P of mass m is attached to one end of a light elastic string of natural length L whose other end is attached to a point A on a ceiling. When P hangs in equilibrium AP has length \frac{5l}{3}. Show that if P is projected vertically downwards from A with speed \sqrt(\frac{3gl}{2}), P...
\frac{dv}{dt}= -x^{-3}
\frac{1}{2}v^2 = \frac{x^-2}{2} + C
As at rest when x = 1, v = 0
then C = -1
v = \sqrt(x^-2 - 1)
Then i continue to integrate as above.
\frac{dv}{dt}= -x^{-3}
when t=0, the particle is at rest with x=1
Therefore by integrating i get
v = \sqrt(x^-2 - 1)
\frac{dx}{dt}= \sqrt(\frac{1 - x^2}{x^2})
dx\frac{x}{(/sqrt(1 - x^2))} = dt
-\sqrt(1 - x^2) = t + C
C=-1
Therefore:-
t = 1 - \sqrt(1 - x^2)
However i cant...
Multiply the numbers out first. Then you will have just one complex number. Then just find the modulus and argument using pythagoras and arctan like you mentioned.
When i integrate i get t = 1 - (1 - x^2).
I'm getting confused by this now, i think my brain's just died, ah well. Sorry for keeping asking questions, i can see how annoying it would be if the answer was so obvious yet i dont grasp it.
Thanks,
Bob
I've integrated to t = \sqrt(x^2 - 1) but cant get the answer correct. Find t when x = 1/4, which gives the root of a negative number, not real. But the book's answer is \sqrt(15) which i notice is \sqrt(x^-2 - 1). How is this possible?
Thank you,
Bob
Hey.
I've been doing more mechanics recently - further kinematics in M3. I've come across another question i'm confused by.
A particle moves on the positive x-axis. When its displacement from O is x meters, is acceleration is of magnitude x^-3 m/s^2 and directed towards O. Given that...