Newton's Laws & Free-Body Diagrams
Why a moving object needs no force to keep moving, and how to draw what is actually acting.
Introduction
Push a cart along the floor and let go: it slows down and stops. Aristotle took that as proof that motion needs a force to keep it going.
A cord pulls a cart along a frictionless track, then releases. Just after the release, what is the horizontal force on the cart?
The first law and free-body diagrams
Newton saw it the other way: a force still acts after you let go, and it does the stopping.
First law. An object's velocity changes only when a net force acts on it. Constant velocity includes direction, so anything moving in a curve has a net force on it, even at constant speed.
The second law
With friction at zero, double the applied force and keep everything else the same. What doubles?
When the forces do not cancel, the net force sets the acceleration. That is the second law:
Add every force on the object as vectors, divide by its mass, and you have its acceleration. A force sets how fast the velocity changes, whichever way the object happens to be moving.
Friction
Friction is 0.02 and the mass is 1 kg. Double the pull from 0.4 N to 0.8 N. While the cord pulls, what happens to the cart's acceleration?
The third law
When the cord pulls the cart, the cart pulls back on the cord, just as hard. Forces come in pairs like this.
The cord is pulling the cart along a track with friction. Pair each force on the cart with its third-law partner.
Tap a force, then its partner. Tap again to change a pair.
Forces on the cart
Partners
The two forces of a pair act on different objects. That is why a pair never cancels: forces cancel only when they act on the same object.
A lamp hangs at rest from a cord fixed to the ceiling. Its weight is the Earth's pull on the lamp. What is the third-law partner of that weight?
Practice
A cart pulled by a hanging mass
A 1.0 kg cart on a frictionless track is tied by a cord, over a light pulley, to a 0.10 kg hanging mass. Find its acceleration and the cord's tension.
A pull against friction
A 2.0 kg cart is pulled along a track with a force of 2.5 N. The coefficient of friction is 0.10. What is its acceleration?
Each problem has its own numbers, and its answer comes from the simulation's model. Use m/s² throughout.
A cart of mass kg on a frictionless track is pulled with a steady N. What is its acceleration?
A kg cart is pulled with N along a track with a friction coefficient of . What is its acceleration while it slides?
A kg cart on a frictionless track is pulled with N for 1 s, then released. How fast is it moving 0.5 s after the release?
A kg cart starts from rest on a frictionless track. A cord pulls it with N for 1 s. How fast is it moving as the pull ends?
A kg cart starts from rest on a frictionless track. A cord pulls it with N for 1 s. How far has it moved as the pull ends?
A kg cart rests on a track with friction coefficient . A cord pulls it with N for 1 s. What is its speed as the pull ends?
A cart is launched along a level track at m/s and let go. The friction coefficient is . How far does it slide before it stops?
A kg cart rests on a track with friction coefficient , for static and sliding friction alike. A cord pulls it with N. What is its acceleration?
Check yourself
Five short questions on the whole lesson. Each wrong option is a belief many people hold before they study mechanics.
A curling stone slides across level ice after leaving the thrower's hand. Ignore friction. Which forces act on the stone while it slides?
A lift rises at a steady 2 m/s. How does the upward pull of its cable compare with the lift's weight?
A small car pushes a stalled van, and the two speed up together. How does the car's force on the van compare with the van's force on the car?
A ball is thrown straight up. At the very top, where it is at rest for an instant, what is the net force on it? Ignore air resistance.
A hovercraft glides over a frictionless floor, pushed by its fan with a constant force. The fan switches off. What happens next?
What comes next
You found the force that stops a cart, set a pull from , and paired each force with its partner. Next, friction in earnest: static friction turns out to be a force that adjusts itself to whatever is needed, up to a limit.
Ideas this lesson took on
Each of these is a common intuition the lesson put to the test. If one still feels right, the section that tests it is worth another look.
- “Motion requires a continuing force”
- “Force is proportional to velocity”
- “Action–reaction pairs cancel each other out”
- “An object at rest for an instant has no net force on it”
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Research behind this lesson
- Clement 1982: The belief that motion implies a force in the direction of motion survives a full mechanics course in a large fraction of students, including those who can state Newton's laws correctly.
- Halloun & Hestenes 1985: Students arrive with a coherent, stable, Aristotelian-flavoured theory of motion. Conventional instruction leaves much of it intact: the formalism is learned alongside the intuition rather than in place of it.
- Viennot 1979: Students spontaneously supply a force in the direction of motion and treat it as proportional to the speed: a pattern that appears across countries, languages and curricula.
- Rosengrant et al. 2009: Most students drew free-body diagrams even when nothing required one, but only correctly drawn diagrams predicted success, and the strongest students used the diagram twice, once to set up a solution and again to check it.
- Hestenes et al. 1992: A 29-item instrument, expanded to 30 in the 1995 revision, whose wrong answers are all documented student beliefs. It exposed how little conceptual understanding traditional courses were producing, and reoriented a generation of physics teaching.
- Sokoloff & Thornton 1997: A demonstration only teaches when students commit a written prediction, discuss it, watch the real event, and compare: a cycle that produced far larger gains on the Force and Motion Conceptual Evaluation than traditional lecture instruction.
- McDermott & Shaffer 2002: A research-validated elicit–confront–resolve sequence: surface the intuitive belief explicitly, put it in direct conflict with evidence, then help rebuild. Skipping the confrontation leaves the original belief intact alongside the new formalism.