problem 2.6 - express the force f in terms of x, y, and z components.
problem 2.6 - express the force f in terms of x, y, and z components.
Answer
Explanation:
Step1: Find the x - component
The angle between the force vector and the y - z plane is $25^{\circ}$. The magnitude of the force is $F = 81\mathrm{N}$. The x - component of the force $F_x$ is given by $F_x=F\sin70^{\circ}\sin25^{\circ}$. $F_x = 81\times\sin70^{\circ}\times\sin25^{\circ}\approx81\times0.9397\times0.4226\approx32.0\mathrm{N}$
Step2: Find the y - component
The y - component of the force $F_y$ is given by $F_y = F\cos70^{\circ}$. $F_y=81\times\cos70^{\circ}=81\times0.3420\approx27.7\mathrm{N}$
Step3: Find the z - component
The z - component of the force $F_z$ is given by $F_z=-F\sin70^{\circ}\cos25^{\circ}$. $F_z=- 81\times\sin70^{\circ}\times\cos25^{\circ}\approx - 81\times0.9397\times0.9063\approx - 68.4\mathrm{N}$
So the force vector $\vec{F}=F_x\vec{i}+F_y\vec{j}+F_z\vec{k}\approx32.0\vec{i}+27.7\vec{j}-68.4\vec{k}\mathrm{N}$
Answer:
$\vec{F}\approx32.0\vec{i}+27.7\vec{j}-68.4\vec{k}\mathrm{N}$