A particle on a smooth horizontal table is subjected simultaneously to two constant…

PHYSICS · Subjective · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

A particle on a smooth horizontal table is subjected simultaneously to two constant forces while it slides

10\,\text{m}

due east. The forces are:

\vec F_1 = 40\,\text{N}

acting

30^{\circ}

north of east,

\vec F_2 = 30\,\text{N}

acting

120^{\circ}

measured counter-clockwise from east. Take the

+x

-axis eastward and the

+y

-axis northward. (a) Calculate the work done separately by

\vec F_1

and by

\vec F_2

during the displacement. Indicate the sign of each. (b) Hence obtain the net work done on the particle. (c) If the magnitude of

\vec F_2

could be adjusted while keeping its direction fixed at

120^{\circ}

from east, determine the value of

|\vec F_2|

for which the net work done over the same displacement would be zero.