A precision-controlled submersible of mass m m\,m is being tested in a deep-water tank. It moves under the influence of two horizontal forces, F1\mathbf{F}_1F1 and F2\mathbf{F}_2F2.
It is given that
F1=(2.5i−14.8j) N \mathbf{F}_1 = (2.5\mathbf{i} - 14.8\mathbf{j}) \text{ N} F1=(2.5i−14.8j) N F2=(0.4ki+1.2kj) N \mathbf{F}_2 = (0.4k\mathbf{i} + 1.2k\mathbf{j}) \text{ N} F2=(0.4ki+1.2kj) Nwhere k k\,k is a constant.
The submersible experiences an acceleration of (1.5i+2j) m s−2(1.5\mathbf{i} + 2\mathbf{j}) \text{ m s}^{-2}(1.5i+2j) m s−2.
Determine the value of kkk.
87 exam-style questions on OCR (MEI) A Level Maths 3.4 Forces, covering 3.4.1 Language relating to forces, 3.4.2 Acceleration due to gravity, 3.4.3 Identify forces and draw force diagrams, 3.4.4 Resultant of concurrent forces, 3.4.5 Equilibrium of a particle, 3.4.6 Resolve a force into components (A-level only), 3.4.7 Equilibrium condition for resultant zero (A-level only), 3.4.8 Forces in equilibrium sum to zero (A-level only), 3.4.9 Equations for a particle in equilibrium (A-level only), 3.4.10 Frictional force and normal contact force (A-level only), 3.4.11 Model friction with F ≤ μR (A-level only), and 3.4.12 Apply Newton's Laws to friction problems (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.