The lower end of the thin uniform rod in Fig. 𝐏 2 7 . 7 2 is attached to the floor by a friction

step 1 The rod is in rotational equilibrium, so the torques must balance. So balancing torques gives yo

The lower end of the thin uniform rod in Fig. 𝐏 2 7 . 7 2 is...

The lower end of the thin uniform rod in Fig. $\mathbf{P 2 7 . 7 2}$ is attached to the floor by a frictionless hinge at point $P$. The rod has mass $0.0840 \mathrm{~kg}$ and length $18.0 \mathrm{~cm}$ and is in a uniform magnetic field $B=0.120 \mathrm{~T}$ that is directed into the page. The rod is held at an angle $\theta=53.0^{\circ}$ above the horizontal by a horizontal string that connects the top of the rod to the wall. The rod carries a current $I=12.0 \mathrm{~A}$ in the direction toward $P$. Calculate the tension in the string. Use your result from Problem 27.66 to calculate the torque due to the magnetic-field force.

Key Concepts

Magnetic Force on a Current-Carrying Conductor

A current-carrying conductor in a magnetic field experiences a force given by the equation F = I L × B, which depends on the current, the length of the conductor in the field, and the orientation of the rod relative to the field. Understanding this concept is essential to calculate the magnetic torque acting on the rod.

Free-Body Diagrams

Free-body diagrams are used to visually represent all forces acting on an object, including applied forces, gravitational forces, tension, and magnetic forces. They are critical tools for setting up the equations of equilibrium and analyzing both translational and rotational effects in the problem.

Static Equilibrium

This concept involves analyzing an object where the sum of all forces and the sum of all torques (moments) are zero, ensuring that the object remains at rest. In this problem, static equilibrium is used to balance gravitational, tension, and magnetic forces, as well as their associated torques about the pivot point.

Torque and Moment Arm

Torque is the measure of the rotational force applied to an object, calculated as the product of the force and the perpendicular distance (moment arm) from the pivot point. Here, torque calculations are crucial to determine the effects of gravitational force, magnetic force, and the tension in the string about the hinge.

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