A force F\mathbf{F}F of magnitude 42 N42 \text{ N}42 N acts on a charged particle. The direction of the force relative to unit vectors i\mathbf{i}i (representing the positive horizontal direction) and j\mathbf{j}j (representing the positive vertical direction) is such that the force vector points into the second quadrant. The angle between the force vector and the positive j\mathbf{j}j direction is 62∘62^\circ62∘.
The force can be expressed as a vector [F1F2] N\begin{bmatrix} F_1 \\ F_2 \end{bmatrix} \text{ N}[F1F2] N.
Find the correct expression for F1F_1F1.
F1=42sin62∘F_1 = 42 \sin 62^\circF1=42sin62∘
F1=42cos62∘F_1 = 42 \cos 62^\circF1=42cos62∘
F1=−42sin62∘F_1 = -42 \sin 62^\circF1=−42sin62∘
F1=−42cos62∘F_1 = -42 \cos 62^\circF1=−42cos62∘
139 exam-style questions on OCR A Level Maths 3.3 Forces and Newton's Laws, covering 3.3.1 Concept and vector nature of a force, 3.3.2 Newton's first law, 3.3.3 Newton's second law in a straight line, 3.3.4 Newton's second law with vectors (A-level only), 3.3.5 Newton's second law with resolved forces (A-level only), 3.3.6 Weight, 3.3.7 Gravitational acceleration, 3.3.8 Newton's third law, 3.3.9 Normal reaction force, 3.3.10 Smooth contact model, 3.3.11 Equilibrium with connected particles and pulleys, 3.3.12 Newton's third law with resolved forces (A-level only), 3.3.13 Equilibrium by resolving (A-level only), 3.3.14 Equilibrium of forces in two dimensions using vectors (A-level only), 3.3.15 Resolving forces for advanced problems (A-level only), 3.3.16 Resultant forces and components (A-level only), 3.3.17 Dynamics of a particle in a plane (A-level only), 3.3.18 Concept of a frictional force (A-level only), 3.3.19 Contact force components (A-level only), 3.3.20 Coefficient of friction (A-level only), 3.3.21 Static and limiting equilibrium on a rough surface (A-level only), 3.3.22 Motion of a body on a rough surface (A-level only), and 3.3 Forces and Newton's Laws. Each one has a worked solution and a mark scheme showing where the marks go.