Grade 12 · Week 06 · Monday · Day 01

The Moving Cart Paradox

Learning objective: Explain why zero net force allows rest or constant velocity in an inertial frame.

45–60 min · Offline-capable · No physical apparatus required

Reading & explanation

Why moving does not always mean pushing

Imagine a cart moving on a nearly frictionless straight track. After a push ends, it can continue at constant velocity. Actual carts eventually slow because wheel and surface friction and air resistance still exert external forces. Newton's first law states that a body experiencing zero net external force retains its velocity in an inertial reference frame.

The important word is net

The vector sum of all external forces on a chosen object is the net force. A 6 N push right and a 6 N push left add to zero. Zero net force implies zero acceleration, not necessarily zero velocity. A cart already moving right at 3 m/s retains that velocity if the ideal force balance continues.

An object can be at rest too

The same balanced force diagram can represent a cart initially at rest. Initial velocity matters: zero initial velocity stays zero, while an initial velocity of 3 m/s stays 3 m/s. Distinguish a velocity arrow describing motion from force arrows describing interactions. Velocity is not an external force.

What a simulation leaves out

The Force Builder models a supported block with chosen constant external forces. It does not automatically compute rolling resistance, drag, collisions or a changing kinetic-friction direction. Real claims should state the chosen body, reference frame, initial velocity and forces rather than treating this model as a sensor measurement.

Vocabulary

inertia
Resistance to a change of velocity; closely related to mass.
net force
Vector sum of external forces on the selected body, measured in newtons.
inertial frame
Reference frame in which zero net force implies constant velocity.
external force
An interaction between the chosen body and something outside it.
constant velocity
Unchanging speed and direction, with acceleration zero.

Worked example

Mass 4 kg, forces +6 N and −6 N: ΣFx=0 N and ax=0 m/s². With initial velocity +3 m/s and constant forces over 2 s, ideal displacement is +6 m.

Show direction, units, body boundaries and your calculations.

Independent science journal

Compare balanced-at-rest and balanced-while-moving model presets; describe two identical force sums but different initial velocities.

Browser-local journal only. Export a backup for another device.

Daily · 4 Practice Questions

Public, open-book practice with feedback and an 80% correction target. It is not a supervised final.