Recent content by chingcx

If you take upper div EM classes, there'll be extensive use of vector calculus.

Homework Statement A 0.2 kg disc slides down from smooth track of height 1.8m. It arrives at a rough 1 kg block resting on a smooth surface. The friction between them is 1.2N. Find the distance traveled by the disc on the block before it comes to rest relative to the block. Homework...

so you mean work done on the box = Fs work done by friction = -fs so no net work done on the box? All work done (both by me and the friction) dissipated as heat energy? it sounds reasonable to me. so what does "work done against friction" mean?

ya, thanks, I get your meaning, but if the box is moving, for example, at a constant velocity. It is evident that the friction balances the applied force, but on the other hand the box's KE is not increasing. So the work done converts to heat energy again? But in this case, the box is really...

If I push a heavy box on the ground but it doesn't move at all (due to friction), the work done on the box is of course zero. But where does the work I done go? From a website, it says the work is done on myself (in the muscle whatsoever), which I find weird because once it moves, the work is...

<p> is the integral of the product of a real function and its first derivative, multiplied by an imaginary number. But why <p> is real?

Homework Statement A mass follows the path of a cardioid r=1+sinφ with given speed, what is its period? Homework Equations The Attempt at a Solution I attempt to do an integral on polar coordinates to find the distance covered by the mass first. The integral I derived is \int_0^{2\pi}...

Homework Statement This is from Prob. 2.25 Two point charges with separation d, P is a point at a distance z above the mid-point of the charges. The last sentence asked if one of the positive charges is changed to a negative one, what is the potential at P? What field does it suggest? Explain...

Thanks, but it doesn't make sense... when N is very large, the peak should be very narrow, but from the equation, N becomes larger then the exponential decreases much slower.

Homework Statement Flip N fair coins. The distribution for different numbers of heads and tails should be peaked at N/2. When N is very large, the peak will be very high. Let x = N(head)-N/2, required to find an expression for this distribution near the peak, i.e. x<<N. Homework Equations...

Solved.

Homework Statement A rigid circular ring (M) of radius R is hanged from a string. Two equal mass beads (m) are released from rest simultaneously from the top of the ring and begin to slide down opposite sides. Show that if the mass of the bead exceeds 1.5 times of the ring, the ring will...

ya, sorry, I mean divergence of curl of vector function is always zero. Why is that true?

(Sorry, the title should read "...why curl of gradient of a scalar "function" is zero) Of course I know how to compute curl, graident, divergence. Algebrically I know curl of gradient of a scalar function is zero. But I want to know the reason behind this...and also the reason why gradient of...

x=a tan(ay) 1= a sec^2(ay) d(ay)/dx