Figure P 12.10 shows a claw hammer being used to pull a nail...

Figure $\mathrm{P} 12.10$ shows a claw hammer being used to pull a nail out of a horizontal board. A force of 150 $\mathrm{N}$ is exerted horizontally as shown. Find (a) the force exerted by the hammer claws on the nail and (b) the force exerted by the surface on the point of contact with the hammer head. Assume the force the hammer exerts on the nail is parallel to the nail.

Key Concepts

Force Decomposition

Force decomposition involves breaking a force into its orthogonal components, typically horizontal and vertical. This technique is essential when analyzing situations where forces are applied at angles, as it allows each component to be considered separately in applying equilibrium conditions or Newton’s laws.

Torque and Moment Equilibrium

Torque (or moment) is the rotational effect of a force, calculated by multiplying the force magnitude by the perpendicular distance from a pivot point. Establishing moment equilibrium—ensuring that the sum of all torques is zero—is crucial in problems involving levers or any system where forces cause rotation.

Static Equilibrium

Static equilibrium refers to a state where a body is at rest, with all forces and torques balanced so that there is no net linear or angular acceleration. This principle is fundamental in analyzing situations where different forces are acting on a system, as it leads to a system of equations that determine unknown forces.

Reaction Forces

Reaction forces are the forces exerted by supports or contact surfaces in response to applied forces. In mechanical systems, these forces arise in accordance with Newton’s third law and are essential for ensuring that structures and components remain in equilibrium.

Lever Systems

A lever system is a simple machine that amplifies an input force through a rigid bar pivoting about a fixed point, known as the fulcrum. Understanding how forces are distributed and amplified in lever systems is key to analyzing tools and mechanisms that rely on rotational equilibrium to perform work.

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