4 Three forces act on a hook Determine the magnitude of the

4. Three forces act on a hook. Determine the magnitude of the resultant of the forces. Neglect hook bending.

Solution

Total horizontal components of forces acting on the hook
(Forces acting along +ve X axis direction is considered as +ve components)

Fx = F1*cos(30) - F2*cos(20) - F3*cos(15)

= 1000*cos(30) - 1500*cos(20) - 750*cos(15)

= 866-1409.5-724 = -1267.94 N
Total vertical components of forces acting on the hook,

(Forces acting along +ve Y axis direction is considered as +ve components)

Fy = F1*sin(30) + F2*sin(20) - F3*sin(15)

   = 1000*sin(30) +1500*sin(20) - 750*sin(15)
= 818.92 N
Total force on Hook = -1267.94 i^ + 818.92 j^ N

                                 = 1509<147.14⁰ N