A $200\text{ kg}$ crate is suspended by two cables, AB and AC, attached to a ceiling. Cable AB makes an angle of $45^\circ$ with the horizontal, and cable AC makes an angle of $30^\circ$ with the horizontal. Determine the tension in each cable to keep the crate in equilibrium.

A particle is acted upon by three forces:

Determine the components of $\mathbf{F}_3$ required for the particle to be in equilibrium.

A particle is suspended by three cables anchored to walls. The forces acting on the particle in equilibrium are $W = \{-200\mathbf{j}\}\text{ N}$ (weight), $\mathbf{F}_A = F_A\{0.8\mathbf{i} + 0.6\mathbf{j}\}\text{ N}$, and $\mathbf{F}_B = \{-50\mathbf{i} + F_{By}\mathbf{j}\}\text{ N}$. Find $F_A$ and $F_{By}$.

Two spring scales are hooked end-to-end. One end is attached to a wall, and a person pulls the other end with a force of $50 \text{ N}$. What will each spring scale read, assuming they are light enough to be considered massless? Explain your reasoning.

A person hangs a very heavy wet blanket exactly in the middle of a tightly strung horizontal clothesline. The clothesline sags slightly. Why is it impossible to pull the clothesline perfectly horizontal again without breaking it, no matter how hard you pull? Explain using the equilibrium equations for the point where the blanket hangs.