You will be allowed three submissions for this question. Assume: - the ruler is

Question

You will be allowed three submissions for this question. Assume:
- the ruler is exactly 1 m long and has mass 396 g
- the mass hangers have negligibbe mass.

a) Suppose the ruler in procedure 2 is asymetrical, and it is balanced on a fulcrum at the 45.4 cm mark (at the center of mass). Now, mass M is hung on the ruler at the 100 cm mark.
- Where must you hang mass 2.02M so the system remains in equilibrium?
At the ______ cm mark

- If M = 66.3 g, find magnitude of the force exerted by the fulcrum on the ruler.
Ffulcrum = ______ N

b) The method of procedure 2 can be used to accurately determine the mass of a light coin (as in procedure 4). Suppose the ruler is now perfectly symmetrical, and it is balanced on a fulcrum at the center. The coin of unknown mass is placed at the 0 cm mark, it is balanced by a mass m = 24.6 g placed at the 72.8 cm mark. Find the mass of the coin.
mcoin = ________ g

Explanation / Answer

m = 396 g
l = 1 m

For system to remain in equilibrium, Torque about the center of mass = 0
M * (100 - 45.4) = 2.02 M * x
x = 27.03 cm

Mass 2.02M, should be hung at x = 27.03 cm Mark.

M = 66.3 g
Ffulcrum = (M + 2.02*M + 396) * 10^-3 * g
Ffulcrum = ( 66.3 + 2.02 * 66.3 + 396 ) * 10^-3 * 9.8
Ffulcrum = 5.84 N

(b)

mcoin = ?
m = 24.6 g @ x = 72.8 cm

For system to be in equilibrium,
mcoin * (50) = 24.6 * (72.8 - 50)
mcoin = 11.22 gm

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