Three forces act concurrently on a ring in a horizontal plane

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

Problem

Three forces act concurrently on a ring in a horizontal plane. Two of them are given in polar form and the third in component form:

\vec F_1 = 10\,\text{N}

30^{\circ}

above the positive

x

–axis,

\vec F_2 = 6\,\text{N}

200^{\circ}

measured anticlockwise from the positive

x

–axis,

\vec F_3 = 4\,\hat i - 2\,\hat j\,\text{N}

. (i) Express

\vec F_1

and

\vec F_2

in rectangular component form. (ii) Obtain the rectangular components of the resultant force

\vec F_{\text{res}}

. (iii) Calculate the magnitude of

\vec F_{\text{res}}

. (iv) Determine the direction of

\vec F_{\text{res}}

with respect to the positive

x

–axis, specifying the quadrant in which it lies.