3. A laboratory balance essentially uses the method of moments to compare an unk

Question

3. A laboratory balance essentially uses the method of moments to compare an unknown mass with a known mass. Some balances have constant and equal lever arms, and others do not. Fig. 4(a) shows the balance used in our lab. Its sketch diagram is shown in Fig. 4(b), where mi is the unknown mass, m2 is the known mass and m, is the mass of the metal scale bar. rz pivot point me ma mI Fig. 4(a) Fig. 4(b) (a) Explain how the condition =o is satisfied for the balance in Fig.4 (b). (b) Explain how the condition -0 is satisfied fo the balance in Fig 4 (b) The torques are calculated about the rotating axis through the pivot point O. Does the individual torque depend on the position of the rotating axis? Does the second equilibrium condition ( 4. 0) ofa ngid body depend on the position of the rotating axis? why? 63

Explanation / Answer

3 )

a )

the normal force on lever at " O " in upward

N = m1 g + m2 g + mc g

m1 g + m2 g + mc g - N = 0 --------------------- i

b)

moment is acts on Point " O "

r1 m1 g = rc mc g + r2 m2 g

r1 m1 g - rc mc g - r2 m2 g = 0 ------------------- ii

4 )

"NO"

because

AX = OA + OX

AM1 m1 g + A M2 m2 g + A Mc mc g + OA ( -N )

( OA + r1 ) m1 g + m2 g ( OA - r2 ) + mc g ( OA - rc ) + OA ( -N )

OA ( m1 g + m2 g + mc g - N ) + ( r1 m1 g - r2 m2 g - rc mc g )

OA X 0 + 0 = 0 ( ZERO )

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