Forces and Newton's first lawAQA A-Level Maths: Mind map

Exam questions on Forces and Newton's first law

1. A particle is acted on by two horizontal forces: one of magnitude $12$ N, and one of magnitude $5$ N at right angles to it.
   A third force $\mathbf{F}$ is now applied so that the particle moves with constant velocity. Find the magnitude and direction of $\mathbf{F}$.2 marks
2. A crate of mass $40$ kg is pulled along level ground by a horizontal rope. The tension in the rope is $150$ N and the crate moves at constant velocity. Take $g=9.8$ m s⁻².
   The tension is suddenly increased to $300$ N, with the resistance unchanged. Explain, using Newton's first law, why the crate no longer moves at constant velocity.2 marks
3. A particle is in equilibrium under the action of three forces $\mathbf{F}_1=(4\mathbf{i}+7\mathbf{j})$ N, $\mathbf{F}_2=(-9\mathbf{i}+2\mathbf{j})$ N and $\mathbf{F}_3$, where $\mathbf{i}$ and $\mathbf{j}$ are perpendicular unit vectors.
   Find $\mathbf{F}_3$.3 marks