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.
139 exam-style questions on AQA A Level Maths 3.3 R: Forces and Newton's laws, covering 3.3.1 Concept of a force and Newton's first law, 3.3.2 Newton's second law, 3.3.3 Weight and motion under gravity, 3.3.4 Newton's third law and equilibrium, 3.3.5 Addition of forces and resultants (A-level only), and 3.3.6 Friction (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.