Exam-Style Problem

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Nov 2014 p42 q2
3690

Three coplanar forces act at a point. The magnitudes of the forces are 20 N, 25 N, and 30 N, and the directions in which the forces act are as shown in the diagram, where \(\sin \alpha = 0.28\) and \(\cos \alpha = 0.96\), and \(\sin \beta = 0.6\) and \(\cos \beta = 0.8\).

(i) Show that the resultant of the three forces has a zero component in the \(x\)-direction.

(ii) Find the magnitude and direction of the resultant of the three forces.

(iii) The force of magnitude 20 N is replaced by another force. The effect is that the resultant force is unchanged in magnitude but reversed in direction. State the magnitude and direction of the replacement force.

problem image 3690
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