problem 2.6 - express the force f in terms of x, y, and z components. f = 8 kn
problem 2.6 - express the force f in terms of x, y, and z components. f = 8 kn
Answer
Explanation:
Step1: Find x - component
The angle between the force vector and the y - z plane is $70^{\circ}$, and the angle between the projection of the force on the x - z plane and the x - axis is $25^{\circ}$. The x - component of the force $F_x$ is given by $F_x = F\sin70^{\circ}\sin25^{\circ}$. Substituting $F = 8$ kN, we have $F_x=8\times\sin70^{\circ}\times\sin25^{\circ}\approx8\times0.9397\times0.4226\approx3.17$ kN.
Step2: Find y - component
The y - component of the force $F_y$ is given by $F_y=-F\cos70^{\circ}$. Substituting $F = 8$ kN, we get $F_y=- 8\times\cos70^{\circ}\approx - 8\times0.3420=-2.74$ kN.
Step3: Find z - component
The z - component of the force $F_z$ is given by $F_z=-F\sin70^{\circ}\cos25^{\circ}$. Substituting $F = 8$ kN, we have $F_z=-8\times\sin70^{\circ}\times\cos25^{\circ}\approx-8\times0.9397\times0.9063\approx - 6.87$ kN.
Answer:
$F_x\approx3.17$ kN, $F_y\approx - 2.74$ kN, $F_z\approx - 6.87$ kN