A particle of mass $1$ kg is threaded on a smooth circular wire of radius $0.5$ m fixed in a vertical plane. It is slightly disturbed from rest at the highest point. Taking $g = 9.81\,\mathrm{ms^{-2}}$ , find its speed in $\mathrm{ms^{-1}}$ at the lowest point, to 2 decimal places.

Model answer

4.43

Also accepted: 4.43 m/s, 4.4, 4.429

Explanation

The particle falls the whole diameter,

2 \times 0.5 = 1\,\mathrm{m}

. The wire is smooth so energy is conserved:

\dfrac12 mv^2 = mg(1)

, giving

v^2 = 2g

and

v = \sqrt{2g}

. With

g = 9.81

this is

\sqrt{19.62} = 4.43\,\mathrm{ms^{-1}}

(with

g = 9.8

it is

4.43

as well).

Derived from ZIMSEC Additional Mathematics Paper 2, Specimen Paper, Q3

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