A rod A B of mass 10 kg tied with a string at C such that A C=A B. A θ=30^∘: (a) rod is in equi

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A rod A B of mass 10 kg tied with a string at C such that A...

A rod $A B$ of mass $10 \mathrm{~kg}$ tied with a string at $C$ such that $A C=A B$. A $\theta=30^{\circ}:$
(a) rod is in equilibrium
(b) the force of friction on the rod by ground is $25 \mathrm{~N}$
(c) the force of friction acts in the forward direction
(d) all the above

Key Concepts

Tension in the String

Tension is the force conducted along a string, cable, or rope when it is pulled tight by forces applied at either end. When analyzing equilibrium problems, the tension in a string contributes to the overall balance of forces and moments, and must be considered alongside other forces such as weight and friction.

Friction Force

Friction force is the force that resists the relative motion or tendency of such motion between two surfaces in contact. In the context of static equilibrium, static friction adjusts to balance other forces acting on the body, and its direction is determined by the requirement to oppose the net effect of those forces to maintain equilibrium.

Torque (Moment) Analysis

Torque, or moment, is the measure of the tendency of a force to rotate a body about a pivot or axis. In problems of static equilibrium, calculating the torques about a chosen point is critical, as it enables the determination of unknown forces when the algebraic sum of the moments is set to zero.

Free-Body Diagram

A free-body diagram is a simplified representation of a body isolated from its surroundings, with all the external forces and moments acting on it drawn as vectors. This tool is essential for analyzing static problems as it helps to clearly identify and balance the forces (such as weight, friction, tension, and reaction forces) and moments acting on the body.

Static Equilibrium

Static equilibrium refers to the state of a rigid body in which the sum of all forces and the sum of all moments (torques) acting on the body are zero. This concept is fundamental in mechanics, ensuring that the body does not translate or rotate, and is used to set up the equations that allow for the calculation of unknown forces and moments in structures.

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