- the ruler is exactly 1.00 m long and has mass M = 284g - the mass hangers have

Question

- the ruler is exactly 1.00 m long and has mass M = 284g - the mass hangers have negligibbe mass.

NOTE: Watch out for units!!!

a) Suppose the ruler in procedure 2 is asymetrical, and it is balanced on a fulcrum at the 45.8 cm mark (at the center of mass). Now, mass m1 = 57.9g is hung on the ruler at the 100 cm mark exactly (with no uncertainty).

- Where must you hang mass m2 = 164.4 g so the system remains in equilibrium (in cm)?

- Find magnitude of the force exerted by the fulcrum on the ruler.

b) The method of procedure 2 can be used to accurately determine the mass of a light coin. Suppose the 100 cm ruler is now perfectly symmetrical, and it is balanced on a fulcrum exactly at the center (with no uncertainty). The coin of unknown mass is placed exactly at the 0 cm mark (again, no uncertainty), and it is balanced by a mass m = 43 g placed at the 79.6 cm mark. Find the mass of the coin in grams.

Explanation / Answer

A) For the system to be in equilibrium, the net Torque on the ruler must be 0.

Since the ruler it is balanced on a fulcrum at the 45.8 cm.

Then Torque from this point must be 0.

m1g(100 - 45.8) = m2g(x)

57.9(54.2) = 164.4x

=> x = 19 cm to the other end from the equillibrim position.

Force exerted on the fulcrum = (M + m1 + m2)g = (284+57.9+164.4)*9.8 = 4961.74 N

B)

Since the ruler it is balanced on a fulcrum at the 50 cm mark

Then Torque from this point must be 0.

Let mc be the mass of the coin

mc*g(50) = 43*g(79.6-50)

mc = 25.45 g

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