Three forces act on a particle of mass 4 kg. The forces are (5i+2j)(5\mathbf{i} + 2\mathbf{j})(5i+2j) N, (−3i+7j)(-3\mathbf{i} + 7\mathbf{j})(−3i+7j) N and (2i−4j)(2\mathbf{i} - 4\mathbf{j})(2i−4j) N, where i\mathbf{i}i and j\mathbf{j}j are perpendicular unit vectors in a horizontal plane.
Find the resultant of the three forces.
Find the magnitude of the acceleration of the particle.
Find the angle between the acceleration and the direction of i\mathbf{i}i.
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.