The system in Fig. 12-77 is in equilibrium. The angles are θ1=60^∘ and θ2=20^∘, and the ball has

step 1 Here in this given problem these are the 2 digit supports horizontal ceiling and vertical wall.

The system in Fig. 12-77 is in equilibrium. The angles are...

The system in Fig. $12-77$ is in equilibrium. The angles are $\theta_{1}=60^{\circ}$ and $\theta_{2}=20^{\circ},$ and the ball has mass $M=2.0 \mathrm{kg} .$ What is the tension
in (a) string $a b$ and (b) string $b c ?$

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Key Concepts

Static Equilibrium

Static equilibrium refers to a state in which all the forces and moments acting on a system balance each other out so that there is no net force or torque, and the system remains at rest. This principle is essential for setting up equations that relate various forces, including tensions, in systems that are not accelerating.

Tension Force

Tension is the force transmitted through a string, rope, or similar medium when it is pulled tight by forces acting from opposite ends. Analyzing the tension in different parts of such a system is crucial for understanding how the weight and any applied forces are distributed along the string.

Free Body Diagram

A free body diagram (FBD) is a visual representation that isolates a system or a component and depicts all the forces acting on it. This tool is key in solving equilibrium problems as it helps identify and resolve forces in various directions, particularly in scenarios with angled forces.

Force Resolution

Force resolution involves breaking down forces into their horizontal and vertical components, typically using trigonometric functions like sine and cosine. This process is vital when dealing with forces acting at angles, as it allows for the application of equilibrium conditions separately in each direction.

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