Physics Mechanics

Classical Mechanics Problem-Solving Workflow

Classical mechanics covers the physics of objects in motion, and most problems follow a clear sequence: identify the forces acting, apply Newton's laws to find acceleration, then use kinematics or energy methods to find the final state. The Force Calculator handles Newton's second law (F = ma) directly — for a 5 kg object accelerating at 3 m/s², F = 15 N. Once you have the force, use it to find work and energy.

Force, Mass, and Acceleration

Newton's second law (F = ma) is the engine of classical mechanics. For a 1,500 kg car accelerating from 0 to 60 mph (26.8 m/s) in 8 seconds, the average acceleration is 3.35 m/s² and the force required is 5,025 N (about 1,130 lbf). The Acceleration Calculator handles all kinematic relationships including a = (v - u) / t and a = 2s / t².

Kinetic and Potential Energy

Kinetic energy is KE = ½mv². A 1,500 kg car traveling at 60 mph (26.8 m/s) has KE = ½ × 1,500 × 26.8² = 538,920 J ≈ 540 kJ. Gravitational potential energy is PE = mgh. The same car parked on a 10-meter hill has PE = 1,500 × 9.81 × 10 = 147,150 J. The Kinetic Energy Calculator and Potential Energy Calculator solve these directly.

Projectile Motion

For a projectile launched at angle θ with initial velocity v₀, the horizontal range is R = (v₀² × sin 2θ) / g. Maximum range occurs at 45 degrees. A ball thrown at 20 m/s at 45° has a range of 20² × sin(90°) / 9.81 = 400 / 9.81 ≈ 40.8 m. The Projectile Motion Calculator handles all launch angle, range, and time-of-flight calculations.

Pendulum Period and Oscillation

The period of a simple pendulum is T = 2π × √(L/g), where L is the length in meters and g = 9.81 m/s². A 1-meter pendulum has T = 2π × √(1/9.81) ≈ 2.006 seconds. Doubling the length increases the period by √2 ≈ 1.41 times (not doubled). The Pendulum Calculator solves for period, frequency, or length given the other variables.

Density, Buoyancy, and Momentum

Density is ρ = m/V. The Density Calculator handles all material density problems. For buoyancy, Archimedes' principle states that the buoyant force equals the weight of fluid displaced: F_b = ρ_fluid × V_submerged × g. An object floats when its average density is less than the fluid. The Buoyancy Calculator determines whether an object sinks or floats and calculates the net force. The Momentum Calculator computes p = mv and handles conservation of momentum in collisions. The Speed, Distance and Time Calculator rounds out the kinematics toolkit for basic motion problems.