\"Give me a place to stand, and I shall move the Earth with it\". (A remark of A
ID: 1418622 • Letter: #
Question
"Give me a place to stand, and I shall move the Earth with it". (A remark of Archimedes. 3rd century BC) This is an engraving from Mechanics Magazine published in London in 1824 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 m_1 is the unknown mass, m_2 is the known mass and m_c is the mass of the metal scale bar. Explain how the condition sigma F vector = 0 is satisfied for the balance in Fig. 4 (b). Explain how the condition sigma tau vector = 0 is satisfied for the balance in Fig. 4 (b). The torques are calculated about the rotating axis through the pivot point O.Explanation / Answer
A) The resultant of the forces is equal to zero as the weight of the blocks is balanced by the normal reaction offered by the pivot at point O.
m1g + m2g = N (normal reaction by pivot)
B) The net torque about the point O is equal to 0 as the torque of the weight of block 1 is balanced by the torque of the weight of block 2 which is in opposite direction. The torque of block 1 tends to turn the scale in counter-clockwise direction whereas the torque of block 2 tends to rotate the scale in clockwise direction.
m1 * r1 = m2 * (r2 +r3)
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