The tongs are used to grip the ends of the drilling pipe P ....

The tongs are used to grip the ends of the drilling pipe $P .$ If a torque (moment) of $M_{P}=800 \mathrm{lb} \cdot \mathrm{ft}$ is needed at $P$ to turn the pipe, determine the cable force $F$ that must be applied to the tongs. Set $\theta=30^{\circ}$.

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Key Concepts

Force Resolution

Force resolution involves decomposing a force into its components based on the angle at which it is applied. This process is important when the force is not applied perpendicular to the lever arm because only the component of the force acting perpendicularly contributes to the torque.

Torque

Torque is a measure of the turning effect produced by a force. It is calculated as the product of the force and the perpendicular distance from the pivot point (lever arm) to the line of action of that force. Understanding torque is fundamental when examining how forces cause rotational motion.

Lever Arm

The lever arm is the shortest or perpendicular distance from the axis of rotation to the line along which the force is applied. It plays a critical role in determining the magnitude of the torque, as a larger lever arm increases the moment generated by a given force.

Static Equilibrium

Static equilibrium refers to the state where all forces and moments acting on a body are balanced, meaning there is no net acceleration. In problems involving rotational systems, ensuring static equilibrium means that the applied forces and moments are sufficient to counteract or achieve a desired balance of torques.

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