A uniform rectangular lamina of mass 10 kg rests with one vertex A on a horizontal table. A force of 30.22 N acts along a side that makes an angle of 30^° with the vertical, so its vertical component is upward. Taking g = 9.81 mathrmms^-2, find the normal reaction at A in newtons, to 2 decimal places.

A uniform rectangular lamina of mass $10$ kg rests with one vertex A on a horizontal table. A force of $30.22$ N acts along a side that makes an angle of $30^\circ$ with the vertical, so its vertical component is upward. Taking $g = 9.81\,\mathrm{ms^{-2}}$ , find the normal reaction at A in newtons, to 2 decimal places.

Model answer

71.93

Also accepted: 71.93 N, 71.9, 71.932

Explanation

Resolve vertically for the whole lamina. The upward forces are the normal reaction

N

and the vertical component of the applied force,

30.22\cos 30^\circ = 30.22 \times 0.86603 = 26.17\,\mathrm{N}

. The downward force is the weight

10g = 98.1\,\mathrm{N}

. So

N = 98.1 - 26.17 = 71.93\,\mathrm{N}

. Friction at A is horizontal and so does not enter a vertical resolution.

Derived from ZIMSEC Additional Mathematics Paper 2, Specimen Paper, Q2

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