A 40 N block is supported by two ropes. One rope is...

A $40 \mathrm{~N}$ block is supported by two ropes. One rope is horizontal and the other makes an angle of $30^{\circ}$ with the ceiling. The tension in the rope attached to the ceiling is approximately: (a) $80 \mathrm{~N}$ (b) $40 \mathrm{~N}$ (c) $34.6 \mathrm{~N}$ (d) $46.2 \mathrm{~N}$

A $40 \mathrm{~N}$ block is supported by two ropes. One rope is horizontal and the other makes an angle of $30^{\circ}$ with the ceiling. The tension in the rope attached to the ceiling is approximately:
(a) $80 \mathrm{~N}$
(b) $40 \mathrm{~N}$
(c) $34.6 \mathrm{~N}$
(d) $46.2 \mathrm{~N}$

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Key Concepts

Force Decomposition

Force decomposition involves breaking a force vector into its perpendicular components, typically horizontal and vertical. This method simplifies the analysis of forces, especially in systems where forces are applied at angles, by allowing each component to be examined independently in satisfying equilibrium conditions.

Trigonometric Analysis in Mechanics

Trigonometric analysis in mechanics uses sine, cosine, and other trigonometric functions to relate the magnitude of force vectors and the angles they form. This is essential for determining the individual force components when a force is applied at an angle, and is a key step in solving static equilibrium problems.

Static Equilibrium

Static equilibrium refers to a state where an object is at rest or moving at a constant velocity, which means that the net external forces and net torques acting on it are zero. This concept is crucial for analyzing forces in structures or systems where motion does not occur.

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