The center of gravity of an irregular object is shown in (see figure). You need

Question

The center of gravity of an irregular object is shown in (see figure). You need to move the center of gravity 2.36 cm to the left by gluing on a tiny 1.48-g mass, which will then be considered as part of the object. Where should you attach this additional mass? (Take the mass of the irregular object to be 4.50 g. The origin is at the original center of gravity of the object, and +x is to the right.)
_____ cm

PART TWO:

Two people are carrying a uniform wooden board that is 6.00 m long and weighs 220 N. If one person applies an upward force equal to 50 N at one end, at what point does the other person lift?
____m (distance from point of application of 50 N force)

Explanation / Answer

a)

let

object mass m1=4.5 g which at origin

a tiny mass m2= 1.48 which is attached at x

center of gravity xcg=2.36 cm

use,

xcg=m1*x1+m2*x2/(m1+m2)

xcg=m1*0+m2*x/(m1+m2)

xcg=m2*x/(m1+m2)

2=1.48*x/(4.5+1.48)

====>

x=8.08 cm left of the c.m

b)

length of the wooden board l=6m

weight w=220N

upward forec F1=50 N (by one person)

let, other person applies F2 force

use,

W=F1+F2

220=50+F2

==>

F2=170 N

use,

torque w.r to center,

F1*d1=F2*d2

50*3=170*d2

==> d2=0.88 m

force F2 applied at d2=0.88m

or

Force F2 applied at (3+0.88) =3.88m (from point of application of F1)

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