The figure below shows a uniform rod AB, 100.0 cm long, with a mass m of 225 g hung from the end A. The rod is balanced on a knife edge place 20.0 cm from A.
(i) Explain carefully why the rod, with the mass attached rests in a horizontal position.
(ii) Calculate the mass of the rod
(iii) If m is increased to 260 g, where should the knife-edge be placed such that the rod remains balanced.
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Answer:
(i) The total anti-clockwise moments about the knife-edge is equal to the total clockwise moments about the knife-edge.
(ii) Let the mass of rod = y
Note: The centre of gravity of the rod is 50 cm - 20 cm = 30 cm from the knife-edge
The mass m is 20 cm from the knife-edge
Using the principle of moments,
total anti-clockwise moments about the knife-edge = total clockwise moments about the same knife-edge
0.225 * 10 * 0.20 = y * 10 * 0.3
y = 0.15 kg
Hence, mass of rod is 150 g
(iii) Let the new distance of the knife-edge from A = d
Hence,
0.260 * 10 * d = 0.15 * 10 * (0.5 - d)
2.6d = 0.75 - 1.5d
4.1d = 0.75
d = 0.183 m
Knife-edge should be placed 18.3 cm away from A.
