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Put units A carousel (a powered merry-go-round), 5.0 m in diameter, started brak

ID: 2145234 • Letter: P

Question

Put units

A carousel (a powered merry-go-round), 5.0 m in diameter, started braking 10 s ago; in a total of 15 s of uniform change it will have stopped from its "full speed" motion of 6 revolutions per minute. You are riding the carousel, 2.0 m east of its axis, going north, and a fly (20 g) landed on the top of your head 1 second ago and is riding along with you. Find the total contact force by your hair (assuming you're not bald nor wearing a cap) on the fly now. Old MacDonald (900 N) needs to remove a large boulder from his level field. He has a long (5 m) rigid board (60 N) as a lever, there is a low rock 1.5 m from the boulder which he is using as a pivot. What force does the rock exert on the board if one end of the board is braced under the boulder and Mac is standing on the other end, trying to move the boulder?

Explanation / Answer

6 rpm = 6 / 60 = .1 rev/sec

wi = 2 * pi * f = .628 / sec     where wi is initial angular speed

a = .628 / 15 = -.0419 / sec^2   where a is the "angular acceleration"

wf = wi - 10 * a = .209 / sec    angular speed after 10 sec

Fc = m * w^2 * R = .02 * .209^2 * 5 = .00438 N   centripetal force

Ft = m a R = .02 * .0419 * 5 = .00419 N    tangential force

Fg = m g = .02 * 9.8 = .196 N

F = (.00438^2 + .00419^2 + .196^2)^1/2 = .196 N

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W * 1.5 = 60 * 1 + 3.5 * 900    balancing torques about pivot

W = 2000 N on the rock