A high-precision surgical micro-robot of mass mmm grams is being navigated through a fluid medium under the influence of two primary forces, P\mathbf{P}P and Q\mathbf{Q}Q.
The forces are defined as follows:
P=(0.7i−3.2j) N \mathbf{P} = (0.7\mathbf{i} - 3.2\mathbf{j}) \text{ N} P=(0.7i−3.2j) N Q=(ki+0.5kj) N \mathbf{Q} = (k\mathbf{i} + 0.5k\mathbf{j}) \text{ N} Q=(ki+0.5kj) Nwhere kkk is a constant scalar.
The resulting acceleration of the micro-robot is measured to be (2.4i+0.8j) m s−2(2.4\mathbf{i} + 0.8\mathbf{j}) \text{ m s}^{-2}(2.4i+0.8j) 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.