A Block Initially At Rest Is Given A Quick Push

The Physics of a Quick Push: From Rest to Motion and Back Again

Imagine a wooden block sitting motionless on a rough tabletop. You give it a swift, sharp shove with your finger. For a split second, it springs to life, skidding across the surface before grinding to a halt. This deceptively simple scenario—a block initially at rest is given a quick push—is a cornerstone of classical mechanics. It encapsulates fundamental principles governing force, motion, and friction. By unpacking this everyday event, we gain profound insights into the invisible forces that dictate the movement of everything from a coffee cup sliding off a dashboard to a spacecraft coasting through the void. This journey from stillness to sliding stop is a masterclass in Newton’s laws and the relentless, often underestimated, power of friction.

The Foundation: Newton’s First Law and Inertia

Before the push, the block is at rest. According to Newton’s First Law of Motion, an object at rest stays at rest, and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force. This tendency is called inertia. The block’s inertia is its resistance to any change in its state of motion. To overcome this inertia and initiate movement, an external force must be applied. Your quick push provides that unbalanced force.

The moment your finger contacts the block, you impart a force over a very short time and distance. This force does work on the block, transferring energy to it and giving it kinetic energy—the energy of motion. The block accelerates from zero velocity to a certain speed during the brief contact period. The magnitude of this initial speed depends on two key factors from Newton’s Second Law (F = ma): the net force applied (how hard you push) and the mass of the block (a heavier block accelerates less for the same force).

Crucially, the push is quick. This means the applied force is not sustained. Once your finger loses contact, the only horizontal forces acting on the block are those arising from its interaction with the table surface. The story of the block’s motion after the push is entirely the story of these remaining forces.

The Antagonist: The Role of Friction

The primary force opposing the block’s sliding motion is kinetic friction (also called sliding friction). Kinetic friction is a force that acts parallel to the surfaces in contact and opposes their relative motion. Its magnitude is given by the equation: f_k = μ_k * N where:

• f_k is the force of kinetic friction.
• μ_k (mu-k) is the coefficient of kinetic friction, a dimensionless number representing the roughness of the two surfaces (e.g., wood on carpet has a higher μ_k than wood on ice).
• N is the normal force, the perpendicular force exerted by the surface on the block. On a horizontal table, N equals the block’s weight (mg).

This frictional force is the reason the block doesn’t glide forever. It is a non-conservative force, meaning it dissipates mechanical energy (kinetic energy) into thermal energy (heat) and sometimes sound. The block’s kinetic energy is steadily converted into heat at the interface between the block and the tabletop, causing it to slow down.

The Motion Phases: A Detailed Timeline

1. Phase 1: The Acceleration (During the Push). For the milliseconds your finger is in contact, two horizontal forces act: your applied push (F_push) forward and a smaller static friction force backward (since the block isn’t sliding yet, static friction adjusts to match your push up to a limit). The net force (F_push - f_s) causes acceleration. Once the block starts sliding, the friction switches to kinetic friction, which is typically lower than the maximum static friction.
2. Phase 2: The Deceleration (After the Push). The instant your push ceases, F_push becomes zero. The only horizontal force is kinetic friction (f_k), acting