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
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