An \"asymmetrical object\" is created using a ruler whose length is 27.5 cm and

Question

An "asymmetrical object" is created using a ruler whose length is 27.5 cm and whose mass is 44.0 g, plus a brass weight of mass 40 g that is taped to the ruler at xM = 24.8 cm. The center of mass of the ruler is at its geometrical center.

Calculate the location of the center of mass XCM for this asymmetrical object.

XCM =

Part 2 - Use the asymmetrical object to weigh an unknown Next, a "test mass" is placed on the ruler at the point xT = 9 cm, and the assembly is positioned on a fulcrum so that it balances at xF = 16.1 cm. Given this information, find the mass mT of the "test mass".

mT =

Explanation / Answer

(a) x cm = (1/total mass) ( m1 x1 + m2 x2) =

= (1 / 44 + 40) (44 * 13.75 + 40 * 24.8) =

= 19.01 cm

(b) now you are given that the cm is at x = 16.1 So use the same idea

x cm =    (1/total mass) ( m1 x1 + m2 x2 + m3 x3)

16.1 = (1 / 44 + 40 + m) ( 44*13.75 + 40*24.8 + m*9)

simplify

16.1 * (84 + m) = 1597 + 9m

7.1 m = 244.6

m = 34.45 grams is the unknown mass

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