Two forces act on a ring: and

PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

Two forces act on a ring:

\mathbf{F}_1=3\hat{i}-2\hat{j}\,\text{N}

and

\mathbf{F}_2=-1\hat{i}+5\hat{j}\,\text{N}

. A third force is applied in the form

\mathbf{F}=F\bigl(\cos\theta\,\hat{i}+\sin\theta\,\hat{j}\bigr)

. The net force on the ring is required to be

\mathbf{R}=4\hat{i}+1\hat{j}\,\text{N}

. (a) Determine the magnitude

F

of the third force. (b) Find the angle

\theta

(measured from the positive

x

-axis) that this force makes.