lilernoEngineeringOpening Lilerno
Chapter 04 · Guided self-study
Intro + external course studyDraw a physical model before choosing a formula.
Build the idea
An original introduction, worked example and practice, followed by a curated reading sequence. The external courses supply deeper teaching and problem sets.
This guide is an orientation, not a complete university module. Practical work needs suitable facilities, safety review and supervision.
Start with these prerequisites
Shared science foundations
A physical model starts by choosing what belongs inside the system and what acts on it from outside. A good free-body diagram is often more valuable than memorizing another formula.
Module lens
The free-body diagram makes the selected body, external forces and sign convention visible before calculation.
Velocity describes how position changes with time. Acceleration describes how velocity changes. A body can move at constant velocity while its acceleration is zero; zero net force does not imply zero velocity.
For constant mass in an inertial frame, sum external force vectors before using Fnet = ma. Weight and mass are different: near Earth's surface weight is approximately mg. Opposing forces subtract when you use a signed axis.
Work transfers energy through a force acting over displacement. A constant force parallel to motion does work Fd. Momentum is mv; impulse changes momentum. These are complementary models with different assumptions, not interchangeable names for force.
See the relationship
Change one quantity, watch the graph respond, then explain the result in your own words.
Predict → change → explain
Keep the force fixed. What happens to acceleration when mass doubles?
Axes: Time (s) → Position (m). Bounds may rescale when inputs change.
a = F/m = 3 m/s². Negative force gives negative displacement from rest.
Constant horizontal net force; initial position and velocity zero. Other horizontal forces are omitted. The graph shows position, not force.
Original Lilerno illustration. Inputs are illustrative; this is not experimental evidence or a design rating.
| Series | Time (s) | Position (m) |
|---|---|---|
| Cart position | 0 | 0 |
| Cart position | 0.05 | 0.00375 |
| Cart position | 0.1 | 0.015 |
| Cart position | 0.15 | 0.03375 |
| Cart position | 0.2 | 0.06 |
| Cart position | 0.25 | 0.09375 |
| Cart position | 0.3 | 0.135 |
| Cart position | 0.35 | 0.1837 |
| Cart position | 0.4 | 0.24 |
| Cart position | 0.45 | 0.3038 |
| Cart position | 0.5 | 0.375 |
| Cart position | 0.55 | 0.4538 |
| Cart position | 0.6 | 0.54 |
| Cart position | 0.65 | 0.6338 |
| Cart position | 0.7 | 0.735 |
| Cart position | 0.75 | 0.8438 |
| Cart position | 0.8 | 0.96 |
| Cart position | 0.85 | 1.084 |
| Cart position | 0.9 | 1.215 |
| Cart position | 0.95 | 1.354 |
| Cart position | 1 | 1.5 |
| Cart position | 1.05 | 1.654 |
| Cart position | 1.1 | 1.815 |
| Cart position | 1.15 | 1.984 |
| Cart position | 1.2 | 2.16 |
| Cart position | 1.25 | 2.344 |
| Cart position | 1.3 | 2.535 |
| Cart position | 1.35 | 2.734 |
| Cart position | 1.4 | 2.94 |
| Cart position | 1.45 | 3.154 |
| Cart position | 1.5 | 3.375 |
| Cart position | 1.55 | 3.604 |
| Cart position | 1.6 | 3.84 |
| Cart position | 1.65 | 4.084 |
| Cart position | 1.7 | 4.335 |
| Cart position | 1.75 | 4.594 |
| Cart position | 1.8 | 4.86 |
| Cart position | 1.85 | 5.134 |
| Cart position | 1.9 | 5.415 |
| Cart position | 1.95 | 5.704 |
| Cart position | 2 | 6 |
| Cart position | 2.05 | 6.304 |
| Cart position | 2.1 | 6.615 |
| Cart position | 2.15 | 6.934 |
| Cart position | 2.2 | 7.26 |
| Cart position | 2.25 | 7.594 |
| Cart position | 2.3 | 7.935 |
| Cart position | 2.35 | 8.284 |
| Cart position | 2.4 | 8.64 |
| Cart position | 2.45 | 9.004 |
| Cart position | 2.5 | 9.375 |
| Cart position | 2.55 | 9.754 |
| Cart position | 2.6 | 10.14 |
| Cart position | 2.65 | 10.53 |
| Cart position | 2.7 | 10.94 |
| Cart position | 2.75 | 11.34 |
| Cart position | 2.8 | 11.76 |
| Cart position | 2.85 | 12.18 |
| Cart position | 2.9 | 12.61 |
| Cart position | 2.95 | 13.05 |
| Cart position | 3 | 13.5 |
| Cart position | 3.05 | 13.95 |
| Cart position | 3.1 | 14.42 |
| Cart position | 3.15 | 14.88 |
| Cart position | 3.2 | 15.36 |
| Cart position | 3.25 | 15.84 |
| Cart position | 3.3 | 16.33 |
| Cart position | 3.35 | 16.83 |
| Cart position | 3.4 | 17.34 |
| Cart position | 3.45 | 17.85 |
| Cart position | 3.5 | 18.38 |
| Cart position | 3.55 | 18.9 |
| Cart position | 3.6 | 19.44 |
| Cart position | 3.65 | 19.98 |
| Cart position | 3.7 | 20.54 |
| Cart position | 3.75 | 21.09 |
| Cart position | 3.8 | 21.66 |
| Cart position | 3.85 | 22.23 |
| Cart position | 3.9 | 22.81 |
| Cart position | 3.95 | 23.4 |
| Cart position | 4 | 24 |
Save your place when you finish reading.
Original Lilerno example
An ideal 2 kg cart experiences 8 N right and 2 N left. Find its acceleration.
Choose right as positive.
Sum forces: 8 − 2 = 6 N.
Divide net force by mass: 6/2 = 3 m/s².
State that other horizontal forces are neglected.
Test the model
Open learning, traceable sources
Work in this order. These links open the publisher’s material; free access does not always permit republication.
OpenStax
Start with: College Physics 2e, section 4.3
Distinguish mass, weight and net force; draw the chosen system for each example.
MIT OpenCourseWare
Start with: Newton's Laws, Vectors, and Reference Frames
Study the first module and attempt its problems before moving to rotation.
Recall, then record
Close the explanation and answer these in your own words. Return tomorrow, then again later in the week.
Can a moving object have zero net force?
What is inside your system?
How do work and force differ?
Sketch an object at rest and one moving steadily. Label all external forces and explain why both can have zero net force.
Self-reported tasks, not an assessment of mastery or university credit. Reading a page does not complete a chapter.
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Open learning, traceable sources
Original Lilerno lessons and diagrams, supported by these references. Free access does not always permit republication. Links open the publisher’s material.
Net force, mass, acceleration and the choice of a physical system.
External reading only; no textbook text or figures redistributed. Verify current book and asset terms before reuse.
Open source ↗Rights / publisher record ↗Newton's laws, reference frames, torque, rigid bodies and mechanical vibration; includes problem-solving videos and exams.
CC BY-NC-SA 4.0 except separately credited material. Linked for external study, not reproduced. Some assigned textbooks/software require separate access.
Open source ↗Rights / publisher record ↗