A pulley with diameter 0.5 meter is being used to lift a box. How far will the box weight rise if the pulley is rotated through an angle of 5pi/3 radians?
2007-01-28 12:11:02 · 5 answers · asked by Mike R 2 in Science & Mathematics ➔ Mathematics
Since 6 pi /3 radians (2 pi) is a full rotation, you only have 5/6 of a rotation here. So the rope will lift the box 5/6 of the circumference of the pulley. C = pi d = 0.5 pi. Multiply this by 5/6 to get your answer.
2007-01-28 12:16:57 · answer #1 · answered by hayharbr 7 · 0⤊ 0⤋
Penny offered a headscarf for $5, spent a million/2 of her last money on footwear, commence quantity = X headscarf = 5 last after she offered the headscarf : X - 5 footwear= 0.5(x-5) lunch =2 remaining2 = remaining1 - footwear - lunch last 2 = x-5 - 0.5(x-5) - 2 recent 0.5*[ x-5 - 0.5(x-5) - 2 ] remaing2 - recent = 10 x-5 - 0.5(x-5) - 2 - 0.5*[ x-5 - 0.5(x-5)-2]=10 remedy this equation and also you've the quantity she began with. good luck
2016-10-16 05:50:45 · answer #2 · answered by pelt 4 · 0⤊ 0⤋
5pi/3 rads is equal to 300 degrees, which is 5/6 of a full turn.
The circumference is .5*pi meters. .5*pi*5/6 = 1.309 meters.
2007-01-28 12:16:43 · answer #3 · answered by giantsaholic 2 · 0⤊ 0⤋
It's an arc-length question, so you can use this simple formula:
(angle)(radius) = arc length
(5pi/3)(.25) = 1.3089
The formula is derived from the circumference formula
pi(d) = C
One diameter is equal to 2 radii, we can rewrite it this way.
2pi(r) = C.
Since 2pi is 360 degress, that's a full revolution of a circle, times the radius gives us the full arc.
A partial angle times the radius will give us a partial arc.
(angle)(radius) = (chunk of the arc)
OR
A*R = C, it spells arc, that's how I remember it.
2007-01-28 12:41:23 · answer #4 · answered by mirramai 3 · 0⤊ 0⤋
5 pi / 3 is .8333 of one revolution of a 1.57 meter pulley.
assuming the rope is taught and doesn't stretch, the box would be lifted (.83333)(1.57m) =1.3 meters
2007-01-28 12:32:03 · answer #5 · answered by davidosterberg1 6 · 0⤊ 0⤋