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2 problems tagged with Statics
P0422
Beginner Mechanics › DynamicsStatic Equilibrium of a Mass with Rope and Rod
A rope has one end fixed at point A on a vertical wall. The other end supports an object of mass $m$. A horizontal wooden rod BC holds the rope away from the wall, with point B on the rope and point C on the wall. The system is in static equilibrium. The segment of the rope AB makes an angle $\theta$ with the horizontal rod. The weights of the rope and the rod are negligible.
- Find the tension in the rope segment AB.
- Find the compressive force in the rod BC.
P0356
Intermediate Mechanics › DynamicsSymmetric Rope System with Complementary Angles
An object of weight $W$ is held in static equilibrium by a symmetric system of ropes as shown. A central point C is supported by two ropes AC, each making an angle $\beta$ with the vertical. Each connection point A is in turn supported by a rope AB attached to a horizontal ceiling, with each rope AB making an angle $\alpha$ with the horizontal. Let the tensions in the ropes be $T_{CG}$, $T_{AC}$, and $T_{AB}$. The system is in static equilibrium.
- Find the tension $T_{CG}$ in the rope supporting the weight.
- Find the tension $T_{AC}$ in the ropes AC.
- Find the tension $T_{AB}$ in the ropes AB. Simplify the result for the special case where the angles are complementary, i.e., $\alpha + \beta = \pi/2$.
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