Mechanics

Topic overview

Particle motion, constrained motion, momentum and impulse

Key concepts

Verify STEP 2/3 separately. Complex numbers and 2×2 matrices may belong to STEP 2; De Moivre, general complex roots, planes and vector products, etc. belong to STEP 3.

Key points

◆Follow the prerequisite knowledge requirements given by the examination body; new concepts may only be used when the question provides sufficient guidance.
◆The examples on this site are training with a limited scope and do not represent full syllabus coverage or official difficulty.

Worked examples

Try each example yourself before checking the explanation.

1Written examples within the scope

A particle of mass $m$ is projected vertically upwards from the ground with initial speed $u$ . The particle experiences a drag force of magnitude $mkv^2$ where $v$ is its speed and $k > 0$ is a constant.

Show that while the particle is moving upwards, $v\dfrac{dv}{dx} = -g - kv^2$ , where $x$ is the height above the ground. Hence find the maximum height $H$ reached.

Write the equation of motion for the particle as it falls from height $H$ . Find the speed $V$ when it returns to the ground.

Show that $V < u$ and explain this physically.

Find the limit of $V$ as $k\to0$ , and describe the behaviour of $V$ as $k\to\infty$ .

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