OCR H240/03 2018 June — Question 10

Exam BoardOCR
ModuleH240/03 (Pure Mathematics and Mechanics)
Year2018
SessionJune
TopicNewton's laws and connected particles

10 Three forces, of magnitudes \(4 \mathrm {~N} , 6 \mathrm {~N}\) and \(P \mathrm {~N}\), act at a point in the directions shown in the diagram.
\includegraphics[max width=\textwidth, alt={}, center]{d5ab20c8-afd5-473e-8238-96762bd3786d-7_604_601_306_724} The forces are in equilibrium.
  1. Show that \(\theta = 41.4 ^ { \circ }\), correct to 3 significant figures.
  2. Hence find the value of \(P\). The force of magnitude 4 N is now removed and the force of magnitude 6 N is replaced by a force of magnitude 3 N acting in the same direction.
  3. Find
    (a) the magnitude of the resultant of the two remaining forces,
    (b) the direction of the resultant of the two remaining forces.