- #1

reshmaji

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1. How far from the woman is the center of mass of the woman + plank system?

a. 0.0m, b. 2.5m, c. 5.0m, d. 7.5m, e. 10m

regarding center of mass m

A 60kg woman walking at a speed of 1.0 m/s steps onto a long plank that has a mass of 60kg. Upon stepping on the plank, both she and the plank begin to slide with speed v and spin with angular rate ω on a frictionless surface.__Problem__A 60kg woman walking at a speed of 1.0 m/s steps onto a long plank that has a mass of 60kg. Upon stepping on the plank, both she and the plank begin to slide with speed v and spin with angular rate ω on a frictionless surface.

1. How far from the woman is the center of mass of the woman + plank system?

a. 0.0m, b. 2.5m, c. 5.0m, d. 7.5m, e. 10m

__Relevant equations__regarding center of mass m

_{1}x_{1}= m_{2}x_{2}, x is center of mass from side of plank where woman is standing__The attempt at a solution__for woman+plank: [60 kg + (x/10)*60kg] * x

& for plank on other side: [60 kg + ((10-x)/10)*60kg] * (10 - x)

These 2 equal each other by definition of center of mass

We get 60x + 6x

^{2}= 1200 - 120x - 60x + 6x

^{2}

60x = 1200 - 180x

240x = 1200

x = 5m

This doesn't conceptually seem right to me, but I'm not sure how else to go about this. 5m is the center of the 10m plank, that would be the center of the mass without the woman standing on one end, no? So I'm thinking it wouldn't be with her there? But what is wrong with my calculations if this is true?