Find the differential equation and velocity

Alexiy
Messages
6
Reaction score
0

Homework Statement


probs_Untitled.jpg


Homework Equations


3. The Attempt at a Solution [/B]
rijes_Untitled.jpg
Hello guys,I posted images since its easier to write equations.Please can someone help me check this, if this is correct so far, then i should be able to find the velocity at C, using kinetic energy?
 
Physics news on Phys.org
Looks good to me.
 
Chestermiller said:
Looks good to me.
velocity_Untitled.jpg


Edit: Work done from A to C is the difference of the potential energy between these two points, am i wrong?
 
Last edited:
By the way in the problems text i translated R as circumference, but its actually a radius R.
 
In my judgment, you did all this correctly. I think you should have more confidence in your ability. Your analysis was very nice, perceptive, and mathematically talented.

Chet
 
Chestermiller said:
In my judgment, you did all this correctly. I think you should have more confidence in your ability. Your analysis was very nice, perceptive, and mathematically talented.

Chet
Thank you very much Chet, I can't help it,I always had some difficulties to translate "physics thoughts" into math language so maybe I am overly cautious, sometimes i even waste time writing code for motion simulations to make sure something behaves like its supposed to, but it seems I'm getting the hang of it.Thanks again for your support.
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
Back
Top