Answer to Question #118099 in Physics for Abba

Question #118099
A uniform metre rule balanes on a knife edge placed at the 60cm mark whem a weight of 2N is suspended from one end calculate the weight of the metre rule
1
Expert's answer
2020-05-25T11:04:37-0400

The ruler weights m kilograms.



(there is nothing interesting on the 60-cm end, that is why it is not shown)


Since the ruler is uniform, we can say that the centre of mass of the 60-cm long side is at the centre, or the lever 30 cm. The 60-cm long part weights


P60=mg60100.P_{60}=mg\frac{60}{100}.

The centre of mass of the 40-cm end is at the centre as well, the lever for this is 20 cm. The weight is


P40=mg40100.P_{40}=mg\frac{40}{100}.

On the 40-cm end, there is 2 N attached at the 100-cm mark. The lever for 2 N is 40 cm. The system is in equilibrium, which means


di leftPi left=di rightPi right30P60=20P40+40P2N,30mg60100=20mg40100+402,m=0.82 kg.\sum d_{i\text{ left}}P_{i\text{ left}}=\sum d_{i\text{ right}}P_{i\text{ right}}\\ 30P_{60}=20P_{40}+40\cdot P_\text{2N},\\ 30\cdot mg\frac{60}{100}=20\cdot mg\frac{40}{100}+40\cdot2,\\ m=0.82\text{ kg}.

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