Force given resultant and one force

Given the resultant of two forces and one of the forces, find the other force or its properties using vector addition or the triangle/parallelogram of forces.

4 questions · Moderate -0.1

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CAIE M1 2009 November Q3
4 marks Moderate -0.3
3 \includegraphics[max width=\textwidth, alt={}, center]{a9f3480e-7a8a-497d-a26a-b2aba9b05512-2_462_721_1672_712} Two forces have magnitudes \(P \mathrm {~N}\) and \(Q \mathrm {~N}\). The resultant of the two forces has magnitude 12 N and acts in a direction \(40 ^ { \circ }\) clockwise from the force of magnitude \(P \mathrm {~N}\) and \(80 ^ { \circ }\) anticlockwise from the force of magnitude \(Q \mathrm {~N}\) (see diagram). Find the value of \(Q\).
Edexcel M1 2008 June Q5
9 marks Standard +0.3
5. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{9dbbbc01-fb66-460d-a42e-2c37ec8b451a-07_357_968_274_484} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Two forces \(\mathbf { P }\) and \(\mathbf { Q }\) act on a particle at a point \(O\). The force \(\mathbf { P }\) has magnitude 15 N and the force \(\mathbf { Q }\) has magnitude \(X\) newtons. The angle between \(\mathbf { P }\) and \(\mathbf { Q }\) is \(150 ^ { \circ }\), as shown in Figure 1. The resultant of \(\mathbf { P }\) and \(\mathbf { Q }\) is \(\mathbf { R }\). Given that the angle between \(\mathbf { R }\) and \(\mathbf { Q }\) is \(50 ^ { \circ }\), find
  1. the magnitude of \(\mathbf { R }\),
  2. the value of \(X\).
Edexcel M1 2024 January Q4
8 marks Moderate -0.3
4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{e59a66b8-c2ad-41fd-9959-9d21e9455c37-08_399_889_246_587} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} Figure 3 shows two horizontal forces \(\mathbf { P }\) and \(\mathbf { Q }\) acting on a particle.
The angle between the direction of \(\mathbf { P }\) and the direction of \(\mathbf { Q }\) is \(150 ^ { \circ }\) Force \(\mathbf { P }\) has magnitude \(X\) newtons.
Force \(\mathbf { Q }\) has magnitude \(5 \sqrt { 3 } \mathrm {~N}\).
The resultant of \(\mathbf { P }\) and \(\mathbf { Q }\) has magnitude \(\sqrt { 129 } \mathrm {~N}\).
Find
  1. the value of \(X\).
  2. the angle between \(\mathbf { Q }\) and the resultant, giving your answer to the nearest degree.
Edexcel M1 2006 January Q4
9 marks Moderate -0.3
Two forces \(\mathbf{P}\) and \(\mathbf{Q}\) act on a particle. The force \(\mathbf{P}\) has magnitude \(7\) N and acts due north. The resultant of \(\mathbf{P}\) and \(\mathbf{Q}\) is a force of magnitude \(10\) N acting in a direction with bearing \(120°\). Find
  1. the magnitude of \(\mathbf{Q}\),
  2. the direction of \(\mathbf{Q}\), giving your answer as a bearing.
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