Recent content by user240

Could you please explain/rephrase that part? I'm not sure I understand why it doesn't go to zero but the volume does (just so we're on the same page, you mean the blue part in the picture I attached, right?). Can we show this rigorously or more quantitatively? Also, why does using...

To find the surface area of a hemisphere of radius ##R##, we can do so by summing up rings of height ##Rd\theta## (arc length) and radius ##r=Rcos(\theta)##. So the surface area is then ##S=\int_0^{\frac{\pi}{2}}2\pi (Rcos(\theta))Rd\theta=2\pi R^2\int_0^{\frac{\pi}{2}}cos(\theta)d\theta=2\pi...

Could you please elaborate? I'm probably overlooking something very basic here but it's not obvious to me why the force from the rope is then given as ##2Tsin(\theta)## I'm not sure why the force happens to be ##2Tsin(\theta)## though.

Homework Statement I'm having trouble understanding an example given in K&K's Intro to Mechanics textbook. 'A string with tension ##T## is deflected through an angle ##\theta_0## by a smooth fixed pulley. What is the force on the pulley'. I don't understand how (in the first picture) they...

Homework Statement A hemispherical shell has radius ##R## and uniform charge density ##\sigma##. FInd the electric field at a point on the symmetry axis, at position ##z## relative to the center, for any ##z## value from ##-\infty## to ##\infty##. The Attempt at a Solution Let ##\theta## be...