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Old Mar 4th 2012, 08:24 AM   #1
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the rate of falling ladder

there is a contradiction between Mathematics and Physics. When a ladder lean over a wall and the bottom point move to the right (in x direction) with constant speed of k, the top of the ladder moves down with the rate of
Vy= -k* x/y
when y approach to the floor then the rate goes to infinity which is physically impossible.
nobody knows how to explain and solve this question. and what is the real rate of y in y=0?

Last edited by toyota11; Mar 5th 2012 at 05:51 AM.
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Old Mar 15th 2012, 11:54 AM   #2
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The explanation is not that difficult. Indeed a mathematican would say that Vy = - Vx * (x/y). At y = 0 it seems that Vy becomes infinite. And the rotational velocity of the ladder (in radians per second) also becomes infinity.

But a physicist would tell you that as the velocity of the ladder approaches the speed of light the mass of the ladder increases according to the rules of general relativity: m = m0/sqrt(1 - (v/c)^2)). At v = c the mass becomes infinite. The result is that it is impossible for the x coordinate of the ladder to move at a constant velocity - it must slow down because otherwise an infinite force would be required to maintain Vx at a constant rate. So the condition as stated that that Vx = constant is impossible.

Last edited by ChipB; Mar 16th 2012 at 12:34 PM.
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