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JAMB Physics 2020 Paper

Question : 23

Total: 38

Consider the three forces acting at O and in equilibrium as shown in the figure. Which of the following equations is/are CORRECT?

I. P ${}_1$ cos $\theta_1$ = p ${}_1$ cos $\theta_2$

II. P ${}_3$ = P ${}_1$ cos $\theta_4$ + P ${}_2 \cos_2$

III. P ${}_1 \sin \theta_1 = P_2 \sin \theta_2$

Solution:

resolving $P_1$ , $P_2$ and $P_3$ into x and y component

$P_x$ = $P_1 \cos \theta_1$

$P_y$ = $P_1 \sin \theta_1$

$P_x$ = $P_2 \cos \theta_2$

$P_y$ = $-P_2 \sin \theta_2$

$P_x$ = $- P_3 \cos \theta_0$

therefore

total $P_x$ = $P_1 \cos \theta_1$ + $P_2 \cos \theta_2$ + $- P_3 \cos \theta_0$ = 0

total $P_y$ = $P_1 \sin \theta_1$ + $-P_2 \sin \theta_2$ = 0

so that $P_1 \sin \theta_1$ = $P_2 \sin \theta_2$

$P_3 \cos \theta_0$ = $P_1 \cos \theta_1$ + $P_2 \cos \theta_2$

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