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DYNAMICS · CONCURRENT FORCES IN TWO DIMENSIONS

Forces and Newton's Second Law

Combine forces of arbitrary magnitude and direction. Observe the net force, equilibrium conditions and motion of a particle with constant acceleration.

Physical Parameters

kg
m/s²

Applied Forces

Angles are measured counterclockwise from +x: 0° right, 90° up, 180° left, −90° down. All forces act on the same point.

Enter 1–8 applied forces, plus optional weight.

Initial Conditions

m
m
m/s
m/s
s

Ranges: m 0.01–1000 kg, g 0–30 m/s², force magnitude 0–5000 N, angle −360°…360°, position −10,000…10,000 m, velocity −200…200 m/s, duration 0.5–60 s. Use a decimal point.

Controls

Examples: Horizontal Acceleration · Force Equilibrium · Oblique Net Force · Weight and Applied Force · Opposing Forces and Uniform Motion · Reversal of Motion

Force Vectors and Motion

True-Scale Directions 1:1: Horizontal and vertical components use the same scale in both diagrams. Force arrows use a scale in newtons, separate from the trajectory scale in meters.

Concurrent Forces Applied at One Point

Particle Trajectory

Position (x, y)—
Velocity (vₓ, vᵧ)—
Acceleration (aₓ, aᵧ)—
Speed |v|—

The particle does not collide with walls or floors: normal reaction, friction and bouncing are not introduced automatically. Forces remain constant throughout the experiment. On phones, scroll the diagrams horizontally without changing vector angles.

Net Force, Equilibrium and Newton's Second Law

Net Force Fₓ—
Net Force Fᵧ—
Magnitude |F|—
Net Force Direction—
Acceleration aₓ—
Acceleration aᵧ—
Magnitude |a|—
Force Condition—

Synchronized Graphs

The x and y components are shown separately. To choose a time, click a graph, use the arrow keys, or enter an exact time.

Selected Time: 0.00 sThe two components use different colors.

Position x(t) and y(t)

Velocity vₓ(t) and vᵧ(t)

Acceleration aₓ(t) and aᵧ(t)

Net Force Fₓ(t) and Fᵧ(t)

x Component y Component (dashed)

Values Table

t (s)x (m)y (m)vₓ (m/s)vᵧ (m/s)aₓ (m/s²)aᵧ (m/s²)

SI units; comma-separated values and decimal point.

Physical Model

A free particle in two dimensions is subject to constant, concurrent forces. The net-force components are the algebraic sums of all individual force components, including weight if enabled.

Apply Newton's second law component by component: Fₓ = maₓ and Fᵧ = maᵧ. If the net force is zero, acceleration is zero, but the particle may keep moving at constant velocity: force equilibrium does not necessarily mean rest.

Velocity may change direction over time. Under constant acceleration, x(t) and y(t) are quadratic functions of time, while velocity components are linear.

Assumptions: inertial reference frame, constant mass, constant forces acting on one point, no implicit torque, rotation, constraints, drag or collisions. Mass is both inertial and gravitational for optional weight. No surfaces constrain the trajectory.

FROM FORCES TO MOTION

Step-by-Step Calculations

Vector resolution, component sums and equations of motion with SI units at every step.

Results are computed without intermediate rounding; values are rounded only for display. The absence of constraints or impacts is part of the model.

Other Experiments: Inclined Plane · Motion in a Straight Line · Projectile Motion · Back to Physics Lab

by Andrea Minini