In the figure, an external force F⃗ is holding a bob of mass 500 . g in a station ary position.

Step 1:u000AFirst, we need to understand that the bob is in equilibrium, which means the net force a

In the figure, an external force F⃗ is holding a bob of mass...

In the figure, an external force $\vec{F}$ is holding a bob of mass $500 . \mathrm{g}$ in a station ary position. The angle that the massless rope makes with the vertical is $\theta=30.0^{\circ}$ a) What is the magnitude, $F$, of the force needed to maintain equilibrium? b) What is the tension in the rope?

In the figure, an external force $\vec{F}$ is holding a bob of mass $500 . \mathrm{g}$ in a station ary position. The angle that the massless rope makes with the vertical is $\theta=30.0^{\circ}$
a) What is the magnitude, $F$, of the force needed to maintain equilibrium?
b) What is the tension in the rope?

Key Concepts

Equilibrium Condition

In physics, a body is in equilibrium when the net force acting on it is zero. This principle, derived from Newton's First Law, is used to set up equations for the balance of forces in different directions, ensuring that the object remains at rest or moves with constant velocity.

Free-Body Diagram

A free-body diagram is a graphical illustration used to visualize all the forces acting on a single object. It is essential for understanding and solving problems in statics as it helps identify the directions and magnitudes of individual forces, such as gravitational force, tension, and any applied external force.

Force Decomposition

Force decomposition involves breaking a force vector into its horizontal and vertical components using trigonometry. This technique is vital when dealing with forces acting at an angle, as it simplifies the analysis of equilibrium by allowing the application of Newton's laws independently along each axis.

Gravitational Force

The gravitational force (or weight) is the force exerted by gravity on an object, typically calculated as the product of the object's mass and the acceleration due to gravity. This force acts vertically downward and is a key component when analyzing the balance of forces in statics.

Tension Analysis

Tension in a rope or string is the pulling force transmitted along its length, acting away from the object along the direction of the rope. In equilibrium problems, the tension must counteract both the component of the gravitational force and any additional applied forces, making its determination crucial to understanding the system's overall balance.

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