A boy holds a 30 cm metal ruler between three fingers of one hand, pushing down with the middle finger and up with the other two, at the points marked \(5 \mathrm {~cm} , 10 \mathrm {~cm}\)
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and \(x \mathrm {~cm}\) and exerting forces of magnitude \(11 \mathrm {~N} , 18 \mathrm {~N}\) and 8 N respectively. The ruler is in equilibrium in this position. Modelling the ruler as a uniform rod, find
the mass of the ruler, in grams,
the value of \(x\).
State how you have used the modelling assumption that the ruler is a uniform rod.
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A small packet of mass 0.3 kg rests on a rough horizontal surface. The coefficient of friction between the packet and the surface is \(\frac { 1 } { 4 }\). Two strings are attached to the packet, making angles of \(45 ^ { \circ }\) and \(30 ^ { \circ }\) with the horizontal, and when forces of magnitude 2 N and \(F \mathrm {~N}\) are exerted through the strings as shown, the packet is on the point of moving in the direction \(\overrightarrow { A B }\).
Find the value of \(F\).