Question

Determine (a) the x, y, and z components of the 900-N force. (b) the angles theta_x, theta_y, and theta_z that the force forms with the coordinate axes.

Answer 1

The force in the x, y, z graph is shown below, 900 N 30° T25 x According to the figure, to find the component of the force on x axis, first find the component of the force on the blue line and then find the component of this component on x axis. Therefore, the component of force on blue line is, F =(900 N) cos 30° =(900N). = 779.422N

Now, take the component on x axis, F, =F' cos 25° Substitute 779.422 N for F'. F = (779.422 N) cos 250 = (779.422N)0.906 = 706.396N The component of force in y axis is, F, =(900 N)sin 30° =(900N).V3 = 450N The component of force in z axis is, F, =F' sin 25°

Substitute 779.422 N for F. F, =-(779.422 N) sin 25° =-(779.422 N)0.4226 =-329.38N Therefore, the components of force in x, y and z directions are 706.396 N, 450 N and -329.38N respectively. (b) The angle , is calculated by the following expression. Fy =(900 N) cos Substitute 706.396 N for F. 706.396 N =(900 N)cos

@ = cos? 706.396N) 900 N = 38.29° The angle 0, is calculated by the following expression. F, =(900 N) cos , Substitute 450 N for F,. 450 N =(900 N)cos, 0 = Cos- 1450N) 900 N) cos = 60° The angle is calculated by the following expression. F, = (900N)cos , Substitute -329.38 N for F,

-329.38N=(900N)cos , 0, = cos+ -329.38N) 900 N =111.46° Therefore, the value of 0, 0, and 0, are 38.29°, 60° and 111.46° respectively.