Question

a.    You came across a picture of three coplanar forces acting at a point, P. The first force is 200N and acting at 20° to the horizontal; the second 400N and acting at 165° to the horizontal; the third 500N acting at 250° to the horizontal. Draw what you saw in the picture using an appropriate scale. Use protractor for the angles.                                                                              

                                                                                                      AP [5 Marks]

b.   With the information in a); determine by resolution of forces:

i.      The magnitude of the resultant of the three coplanar Forces.

ii. The direction of the resultant of the three coplanar forces.

Answer 1

i. $F_x=200\cdot\cos20°+400\cdot\cos165°+500\cdot\cos250°=-369.4\ (N)$

$F_y​=200⋅\sin20°+400⋅\sin165°+500⋅\sin250°=−298 (N)$

$F=\sqrt{369.4^2+298^2}=475\ (N)$ .

ii. $\theta=\tan^{-1}\frac{298}{369.4}=219°$