The Official Mechanics A Revision Thread

x max and min values should occur at dx/dt = 0, i.e. v = 0. I get $x_0$ and $\infty$ for the first, and $x_1$ and $\frac{1}{2} x_1$ for the second if you want to check.

Using that information I could make a guess on the orbits, the first being either parabolic or hyperbolic, and the second being elliptic (or a circle if it's a special case).

cheers i think i get it now, did you mean $\frac{1}{3} x_1$ for the min of the second part, or is it as you said $\frac{1}{2} x_1$. i might've done an earlier part wrong though.



ok, do u see a way of how we can guess the orbits from the speed formulaes. i'm guessing that's what they expect us to do, in the way that the quesiton ordered, but i can't see how!

I get $\frac{1}{2} x_1$ but my velocity function might be wrong. I did $\frac{1}{2}mv^2 = - \Delta U(x)$ and $U(x_1) = -\frac{2\alpha}{x_1 ^2}$, which if you miss that then you can get $\frac{1}{3} x_1$.
You could check by substituting x = x1 and seeing if you get 0.

wow, i got different, i got $\sqrt{\frac{2\alpha}{m{x_1^2}}({(\frac{x_1}{x})^2}-\frac{3x_1}{x})}$

yeah i didn't sub in $U(x_1)$ like you did, i thought it would be simple and just a replica of the method we had to do for the first part for $x_0$.

Yeah that's exactly what you get if you ignore the U(x1) bit in mine. Technically it is the same as the first method, but in that method the initial potential energy is 0. It's kind of like conservation of energy, the potential energy is transferred to kinetic, so the change in potential is equal to the change in kinetic.

Anyone got any idea why my 'Access is denied' for the 2004/05 and the 2003/04 past papers on the past exam papers site?

Dont suppose you saved it at all? The page doesnt exist apparently

has anyone done question 3b) on the 2005 paper, because i don't have a clue.

a belt drives the circumference of a cylindrical wheel of radius R and mass M with no slipping. The tension in the belt is T. Friction in the wheel bearing causes an effective torque N to act on the wheel.
i) if the velocity of the belt is constant, what is T in terms of N.
ii) the bearing is lubricated removing all significant friction and the velocity of the belt then increases with uniform acceleration a. write down T in terms of M, R and a.

[hint:]

i did get r_0mv for 3a)

for 2b) let the velocity of the particle of mass m after the collision be v_1 and the velocity of the particle of mass km after the collision be v_2 i got the following 3 equations

by conservation of momentum mu + kmu = mv_1 + kmv_2

by resolving momentum in the x direction and y direction respectively gives mu = 1/root2 [mv_1 + kmv_2]
and kmu = 1/root2 [mv_1 - mv_2]

(note because the collision is elastic kinetic energy is conserved which could give you another equation if necessary)

use equations 1 and 2 sub root2 [mu] = mv_1 + kmv_2 and you get k = root2 -1 as required

...
More questions for anyone that still comes here, Q3, 2006...

hey, i remeber discussing this question with aksan a while ago, look back to page 2 in this thread, i think.

i'm not sure what's up with the non-conservative thing.

A quick question off the 2004-05 paper, question 1c)
Which quantities are conserved in a system free from external forces and torques, and bound internally by a central inverse square law field.

what did you guys put for this???

Thanks I'll check.

The inverse square law hints that you should think of gravity as an example. I put energy (all energy should be conserved to the system as far as I can tell. Thermal/Light energy radiated from the system is what's bugging me, but we never did anything like that in lectures...), momentum (always conserved so long as no body of mass leaves the system) and mass. I guess total net force and total net torque might be conserved too, since the only force is the inverse square law. Energy conservation could also be because the inverse square field is a conservative force field, somewhere in the notes he shows this so maybe thats what the question wants you to remember (and newton's 3rd law to prove conservation of momentum).

Frustration.
For the 2007-2008 paper question 1c) how do you get v_tan = 0.63m/s?

Because v_tan = rw where r = 0.25m and at t=0.2s, w = 0.4rev/s (from part a) therefore shouldnt:

v_tan = 0.25*0.4 = 0.1m/s ?

EDIT: Im so stupid v_tan = 0.1rev/s = 0.1*2pi m/s = 0.63 m/s

What kind of sick twisted physicist uses revolutions per second over radians per second?