Month: February 2015

098 Electromagnetic Induction: Race to the Bottom

Since the rods experience a changing magnetic flux as the magnets make their descent, emf is induced in the rods. The resulting eddy current creates a magnetic field that opposes the descent of the magnets, resulting in a retardation force on the magnets.

Assuming all four magnets are identical, then the induced emf in all the four rods should be exactly the same. However, the induced current is different due to the different resistivities of the four rods. Copper, with the lowest resistivity, has the largest induced current and thus experiences the largest retardation force. Plastic is basically an insulator and has zero induced current (despite the same induced emf). It thus suffers practically no retardation force.

097 Friction: Till Death Do Us Part

 

The friction between two pages is quite weak. So how did friction grow to be so incredibly strong in this demonstration? 2 reasons:

(1)

When we interleave N pages on one side with N+1 pages on the other side, each side now experiences a total of 2N frictions.

(2)

Remember also that friction depends on how hard the two surfaces are pressed perpendicularly into each other. Consider the bottom page: it is now weighed down by 2N pages instead of just one. The next bottom-most page is weighed down by 2N-1 pages. And so on until the top page where the normal contact force is back to the weight of one single page.

So the total friction is multiplied by (1+2+…2N). The sum of this arithmetic progression is about 2N2.

 

It takes just over 30 pages on each side to amplify the friction by about 2000 times!