Three coplanar vectors

PHYSICS · Multi-part · CBSE · Physics · Motion in a Plane · Motion in a Plane

Problem

\mathbf{A}

\mathbf{B}

and

\mathbf{C}

act on a ring that is free to move only in the x-y plane. The vectors are given below: (i)

\mathbf{A}

has a magnitude of

40\,\text{N}

and acts at

20^{\circ}

above the positive x-axis. Resolve

\mathbf{A}

into its rectangular components. (ii)

\mathbf{B} = -25\,\mathbf{\hat{i}} + 30\,\mathbf{\hat{j}}\,\text{N}

. Write its components explicitly. (iii) The ring is in translational equilibrium so that

\mathbf{A}+\mathbf{B}+\mathbf{C}=\mathbf{0}

. Using the condition of equilibrium, determine the x and y components of

\mathbf{C}

. (iv) Express

\mathbf{C}

in magnitude-angle form, quoting the angle it makes with the positive x-axis and specifying whether the direction is above or below the axis. (v) Show graphically, on a rough sketch of the component axes, how the three vectors form a closed triangle in equilibrium.

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