- A particle \(P\) rests in equilibrium on a smooth horizontal plane.
A system of three forces, \(\mathbf { F } _ { 1 } \mathrm {~N} , \mathbf { F } _ { 2 } \mathrm {~N}\) and \(\mathbf { F } _ { 3 } \mathrm {~N}\) where
$$\begin{aligned}
& \mathbf { F } _ { 1 } = ( 3 c \mathbf { i } + 4 c \mathbf { j } )
& \mathbf { F } _ { 2 } = ( - 14 \mathbf { i } + 7 \mathbf { j } )
\end{aligned}$$
is applied to \(P\).
Given that \(P\) remains in equilibrium,
- find \(\mathbf { F } _ { 3 }\) in terms of \(c\), \(\mathbf { i }\) and \(\mathbf { j }\).
The force \(\mathbf { F } _ { 3 }\) is removed from the system.
Given that \(c = 2\) - find the size of the angle between the direction of \(\mathbf { i }\) and the direction of the resultant force acting on \(P\).
The mass of \(P\) is \(m \mathrm {~kg}\).
Given that the magnitude of the acceleration of \(P\) is \(8.5 \mathrm {~m} \mathrm {~s} ^ { - 2 }\) - find the value of \(m\).