Two forces F1\mathbf{F}_1F1 and F2\mathbf{F}_2F2 act on a particle of mass 4 kg.
It is given that F1=(5i−2j)\mathbf{F}_1 = (5\mathbf{i} - 2\mathbf{j})F1=(5i−2j) N and F2=(ai+bj)\mathbf{F}_2 = (a\mathbf{i} + b\mathbf{j})F2=(ai+bj) N, where a a\,a and b b\,b are constants.
The particle has acceleration (2i+3j)(2\mathbf{i} + 3\mathbf{j})(2i+3j) m s−2^{-2}−2.
Find the value of a a\,a and the value of bbb.
Find the magnitude of F2\mathbf{F}_2F2.
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.