15 Fig. 15 shows a particle of mass \(m \mathrm {~kg}\) on a smooth plane inclined at \(30 ^ { \circ }\) to the horizontal. Unit vectors \(\mathbf { i }\) and \(\mathbf { j }\) are parallel and perpendicular to the plane, in the directions shown.
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\caption{Fig. 15}
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- Express the weight \(\mathbf { W }\) of the particle in terms of \(m , g , \mathbf { i }\) and \(\mathbf { j }\).
The particle is held in equilibrium by a force \(\mathbf { F }\), and the normal reaction of the plane on the particle is denoted by \(\mathbf { R }\). The units for both \(\mathbf { F }\) and \(\mathbf { R }\) are newtons.
- Write down an equation relating \(\mathbf { W } , \mathbf { R }\) and \(\mathbf { F }\).
- Given that \(\mathbf { F } = 6 \mathbf { i } + 8 \mathbf { j }\),
- show that \(m = 1.22\) correct to 3 significant figures,
- find the magnitude of \(\mathbf { R }\).