Question

A uniform meter rule AB is balanced on a knife edge placed 58cm from A when a mass of 20.0Kg is placed 25cm from B. Calculate the mass of the rule and the force exerted on the rule by the knife edge

Answer 1

$AB = 1m$

$g= 9.8\frac{m}{s^2}$

$\text{let }K\text{-point where the knife is located}$

$AK = 58cm = 0.58m$

$BK = AB-AK = 0.42m$

$\text{let }M\text{-point where the mass is located }m_1=20kg$

$BM =25cm = 0.25m$

$KM = BK-BM= 0.18m$

$\text{let point } O \text{ midpoint of the ruler}$

$m - \text{this is the mass of the ruler}$

$AO = \frac{AB}{2}=0.5m$

$KO = AK-AO = 0.08m$

$KO*mg=KM*m_1g$

$m= \frac{KM*m_1}{KO}=\frac{0.18*20}{0.08}=45kg$

$N = mg+m_1g= 637N$

$\text{Answer: }$

$\text{the mass of the rule }45kg$

$\text{the force exerted on the rule by the knife edge }637N$