Recent content by bshoor

I have tried in different ways. But the integral becomes more and more complicated. Anyway the identity can be modified to : $\int_{0}^{\frac{\pi }{2}}{\sqrt {\sin \theta cos\theta}k(\theta) K[k(\theta)]}d\theta=\pi \sqrt{ \frac{Rh}{R^2 + (h+Z)^2}} $ by multiplying both side by $ 2 \sqrt{Rh} $

Please make correction of the post: $\int_{0}^{\frac{\pi }{2}} {\frac{\sin \theta}{\sqrt{Z^2+(R+h \tan \theta)^2}} K[k(\theta)]}d\theta=\frac{\pi }{2\sqrt{R^2 + (h+Z)^2}} $

How to prove: $\int_{0}^{\frac{\pi }{2}} {\frac{\sin \theta}{\sqrt{Z^2+(R+h \tan \theta)^2}} K[k(\theta)]}=\frac{\pi }{2\sqrt{R^2 + (h+Z)^2}} $ where \[ k(\theta)=\sqrt\frac{4Rh \tan \theta}{Z^2+(R+h \tan \theta)^2}\] and $ K[k(\theta)] $ is the complete elliptic integral of the first kind...

In = an+3 + (a+1)2n+3 , when n=-1 and n=0 it can be shown that it is divisible by a2+a+1 In+1 = an+4 + (a+1)2n+5 In+1 - In = (an+4 - an+3) + [(a+1)2n+5 - (a+1)2n+3] which can be ultimately reduce to In+1 = a.In + (a2+a+1).(a+1)2n+3 So, by induction method u can prove. Not true for n less than -1.

From 9810 N you can find the mass of the ball by just dividing 9.81, and mas becomes simply 1000 kg. Now you can find Kinetic Energy of the ball. When the winch is suddenly stopped, the cable gets elongated and a potential energy develops which resist the ball. Now Youngs Modulus gives you the...