Recent content by gelfand

OK ##F = - \frac{dU}{dx}## sorry , I'm still unsure about the question

Homework Statement potential energy function of : $$ U(x) = 4x^2 + 3 $$ And have to i) Work out the equation of motion ii) Prove explicitly that the total energy is conservedHomework Equations$$ F = \frac{dU}{dt} $$ The Attempt at a Solution I'm not too sure how to go about this...

OK cool - thanks for the help

Hrm ok - i'll think about how to apply that to this (i'm not sure on first read) is the rest of the problem sound now though? thanks

Thanks - so that's this question done then?

Sorry - that answer is correct but Its in thousands. I'd be unlikely to trust any boss who gave me a job anyway tbh :)I thought that I had accounted for the frictional force during that, damn. OK $$ \text{Force net} = 10 - mg\mu_k $$ Then we have that $$ F_n = ma $$ So $$ a =...

So we have $$ \frac{1}{2}mv_1^2 - \frac{GMm}{r_1} = \frac{1}{2}mv_2^2 - \frac{GMm}{r_2} $$ Here we want to solve for ##M##, and can see that every term has ##m## in it (nice!) so can just drop that :) Dropping ##m## and multiplying through by 2 gives $$ v_1^2 - \frac{2GM}{r_1} = v_2^2 -...

So I have ##a = 100, v = 300## after three seconds. Then I remove the force that's pushing the object and friction slows it to a stop. Then at three seconds I have the kinetic energy $$ \frac{1}{2} m v^2 $$ And this is all spent on work against friction (so that the object comes to a stop...

Ah yes >.< , whoops. So that the force of friction would be ##0.1 \times 9.81 \times 0.2 = 0.1962##. The means that during the acceleration phase (from ##t = 0 ## to 3) I have the net Force would be $$ F_n = 10 - 0.1962 = 9.8038 $$ Given this I have the work done against friction over...

Thanks - are you just using ##\vec{h}## here to represent angular momentum for this case? (I've not seen ##\vec{h}##, just making sure that's what this was for here). Then from this we have that $$ h = rv $$ So for this problem we have, for the perihelion position (where the object is...

Homework Statement A block of mass 100 grammes was stationary on the flat surface at ##x = 0##. At time ##t = 0## a horizontal force of 10 Newtons was applied on the block in the positive x direction during ##\Delta t = 3## seconds. Find at what x position the block will stop, if the...

OK - so I have that ##f =\sqrt{21}##, and this is the distance from the star to the 'origin' (where major / minor meet). So from this I can say that the distance from the star to the orbiting body is $$ dist = major - f $$ Which here is $$ dist = 5 - \sqrt{21} = 0.417242305 $$ So that...

cheers - so for part 4 if I consider the angular momentum ##\omega## then: ##v = \omega r##, and here we have ##r = a##, the semi-major axis and the speed is ##100##km/s. So we have $$ \frac{v}{r} = \omega $$ Which gives us ##\omega = \frac{100}{5} = 20##. But this doesn't take into...

Homework Statement A comet moves around a stat in ##xy## plane along elliptical orbit, described by $$ 0.16 x^2 + y^2 = 4 $$ where ##x, y## are in ##AU## 1) Sketch the comet in the ##x,y## coordinate system denoting all orbit parameters 2) Find the semi major and minor axes of the orbit...

Calculus made easy , by Thompson