Mechanics of Individual Forces

Gravitational Force

A field force that acts over a distance without physical contact, typically represented by weight (F_g or W).

Mass (m)

A measure of an object's inertia, quantified in kilograms (kg), and remains constant regardless of location.

Weight (F_g or W)

The gravitational force exerted on an object, measured in Newtons (N), and is a vector quantity.

Formula for Gravitational Force

F_g = mg, where m is mass in kg and g is gravitational field strength (9.8 m/s^2 on Earth).

Normal Force (F_N or N)

A contact force exerted by a surface, perpendicular to the surface, preventing an object from penetrating it.

Common Scenario for Normal Force on Flat Surface

F_N = mg when there are no other vertical forces.

Normal Force on Incline

F_N = mg cos(θ), where θ is the angle of incline.

Static Friction (f_s)

The frictional force that acts to keep an object stationary when subjected to an external force.

Maximum Static Friction Formula

F{s, max} = μs FN, where μs is the static coefficient of friction.

Kinetic Friction (f_k)

The frictional force that acts when two surfaces slide past each other.

Kinetic Friction Formula

F{f,k} = μk FN, where μk is the kinetic coefficient of friction.

Coefficient of Friction (μ)

A unitless value representing the interaction between two surfaces, with μs for static and μk for kinetic friction.

Hooke's Law

A principle stating that the force exerted by a spring is proportional to its displacement from equilibrium (F_s = -kΔx).

Spring Constant (k)

Measured in N/m, indicates the stiffness of a spring; higher values indicate stiffer springs.

Displacement in Hooke's Law (Δx)

The distance a spring is stretched or compressed from its natural length.

Direction of Gravitational Force (F_g)

Always points towards the center of the massive body, typically vertically downward.

Force due to External Push (F_{push})

When a downward push is applied to an object, the normal force becomes FN = mg + F{push}.

Force Balance in Static Friction

Static friction only matches the applied force up to its maximum limit; it adjusts to maintain equilibrium.

Difference between Mass and Weight

Mass is a measure of inertia (kg) while weight is a force caused by gravity (N).

Pitfall: Normal Force Equals Weight

F_N = mg is only true on level surfaces without additional forces; otherwise, adjustments must be made.

Pitfall: Kinetic Friction vs. Static Friction

Kinetic friction is constant, whereas static friction varies to match the applied force until the maximum is reached.

Negative Sign in Hooke's Law

Indicates that the spring force acts in the opposite direction of displacement, restoring the spring to its equilibrium.

Spring Force vs. Displacement Graph

The linear relationship between spring force (F_s) and displacement (x) where the slope represents the spring constant.

Effect of Incline on Normal Force

On an incline, the normal force is reduced due to the angle, represented by F_N = mg cos(θ).

Static vs. Kinetic Friction

Static friction occurs when no sliding takes place, while kinetic friction acts during sliding motion.

Force Direction for Sliding Boxes

Kinetic friction acts in the opposite direction to the sliding motion, regardless of the applied force direction.

Inequality of Static Friction

Static friction can be written as |F{f,s}| ≤ μs |F_N|, showing that it adjusts to maintain equilibrium.