Quote:
Originally Posted by Pazuzu
As for the 467 pounds, I think it must be a derivation error coming from the fact that jyl forgot that the measurement "pounds" is a force, not a mass, so he has an extra factor of "g" floating around.
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"lb" is not a unit of force and I'm not calculating that the force on the pulley is "467 pounds" or that the pulley "sees" a force of 467 lb. "lb" is a unit of mass. Force is mass x acceleration ( F = m *a ) and the unit of force is "lb * ft / sec^2". When we use "pounds" as a shorthand expression for force, we are implicitly leaving out the relevant acceleration.
I calculated the force vector on the pulley is -14,933 ft lb / sec^2. But no manlift is load rated for a
force expressed in
ft lb / sec^2. The manlift is rated for a given
mass expressed in
lb and that rating applies if stationary in Earth gravity.
So I'm saying the manlift (that the pulley is mounted to) has to be rated for "467 lb" of mass, to withstand the force of -14,933 ft lb / sec^2 on the pulley. (And then I'm assuming you'd want a big safety factor which I guessed at 3X, because you're lifting humans and because we're ignoring shock/dynamic loading.)
If I were simply off by a factor of "g", then my scalar 467 would be 467 * 32 or 467 / 32, both of which would be obviously wrong, plus the units would be obviously wrong.
From above post
The force on the pulley, which we'll call P for pull, is 2 * - T
P = 2 * - T
= -14,933.3333 ft * lb / sec^2
The pulley is attached to a platform, which must support "X pounds". That means X pounds in Earth's gravity g, so
-14,933.333 ft * lb / sec^2 = X lb * 32 ft / sec^2
X = [ -14,933.333 ft * lb / sec^2 ] / [32 ft / sec^2 ]
= -466.6667 lb
Hugh, if your intuition is having a hard time w/ the idea that the force on the pulley depends on the ratio of the weights (M / m ), not merely on the total weight ( M + m ), maybe do an experiment. With a nylon string (rope), a pencil (pulley), and some fruit in plastic grocery bags (stuntmen). Hang 5 oranges on one side and 4 on the other, have your helper let go of the bags, you feel the force on the pencil that you're holding as the heavier side descends slowly. Now hang 8 oranges on one side and 1 on the other, and feel the difference in the force as the heavier side drops rapidly. In the second case, the force should feel smaller. I haven't done this (we don't eat enough fruit) but that's what the math says. You can even make the ratio more and more extreme (get a knife and make it 8.75 oranges vs 0.25 oranges). If you can discern a difference at an extreme ratio (must be non-zero and non-infinity), then you know there is a difference at a less extreme ratio, because the system is linear (the formulas have no polynomials).
Now, it's been >30 years since the last physics class, so I could certainly have gotten this wrong.
If so, it'd be helpful for me to point it out
specifically, since I'll have to be helping my daughter through high school physics pretty soon so I actually need to review/relearn all this stuff over the next year - basic mechanics, electromag, thermodynamics, etc. My copy of Halliday & Resnick is falling apart so badly that I need to buy a new one.