Intuition The ONE core ideaA pulley lets you share a heavy load across several rope-strands , so each strand — and your hand — carries only a fraction of the weight. Because nature never gives energy for free, the price of pulling easier is pulling farther : force down by some factor means distance up by the same factor.
This page builds every symbol the parent note Pulley Systems — Mechanical Advantage uses, starting from absolutely nothing. Nothing below assumes you have seen force, tension, or an arrow-diagram before. Read top to bottom; each idea is a brick for the next.
A force is simply a push or a pull. We write it F newtons , short symbol N
The picture: a force is drawn as an arrow . The arrow's length tells you how strong the push is; the arrow's direction (where it points) tells you which way it pushes.
Intuition Why we need arrows, not just numbersA number alone (5 N both a size and a direction is called a vector , and an arrow is the natural picture of a vector. Every force in pulley problems is a vector, so we always draw it.
Weight W straight down . It is a force, so it is measured in newtons and drawn as a downward arrow.
To turn a mass into a weight we multiply by g
50 kg W = 50 × 9.8 = 490 N 490
Why the topic needs it: the whole point of a pulley is to lift a weight, so W
Imagine a taut rope. Grab it anywhere and it pulls back on your hand. That inward pull the rope carries along its own length is called tension .
Tension T along a stretched rope or string. At any point, the rope pulls on whatever is attached to it, aimed away from that point, along the rope .
Intuition Why one rope has ONE tension everywhereCut out a tiny piece of an ideal rope (see §6 for "ideal"). It has no weight of its own. Whatever pulls it from the left must exactly balance whatever pulls it from the right — otherwise a massless piece would feel infinite acceleration. So the pull is the same size at both ends of the piece, and stringing all pieces together, the same T
Why the topic needs it: the magic sentence of the whole chapter is "one ideal rope → one tension T Without understanding tension you cannot count how the load is shared. See Tension in strings .
Definition The summation symbol∑ ∑ "add up all of these." So ∑ F up
An object is in equilibrium when it is not speeding up or slowing down — it is still, or moving steadily. For this to happen, the arrows pulling it up must exactly cancel the arrows pulling it down:
∑ F up = ∑ F down
The picture: think of a tug-of-war that isn't moving. Both teams pull equally hard; the flag stays put. A hanging load held steady by rope-strands is the same idea, vertically.
Why the topic needs it: to find mechanical advantage of a static (still) pulley, we set the load in equilibrium: the strands' upward tensions must add up to the weight. That single balance line, n T = W n
Equilibrium is the "not moving" case. When forces don't cancel, the object accelerates.
Definition Net force and acceleration
Net force F n e t Acceleration a m/s 2
Intuition Equilibrium is just the special casea = 0 a = 0 F n e t = 0 Newton's Second Law and Atwood machine .
Why the topic needs it: every free-body diagram in the chapter writes F n e t = ma
The chapter keeps saying ideal rope and ideal pulley. These are simplifying assumptions:
Definition Ideal pulley/rope
Massless : the rope and pulley weigh nothing, so their own weight never enters the sums.Frictionless : nothing rubs, so a pulley can turn the rope's direction without eating any of its tension.
Intuition Why "ideal" makes the algebra cleanMassless ⇒ tension is uniform (§3). Frictionless ⇒ a pulley only bends the rope's direction, never shrinks T T Friction ; that loss is measured by efficiency , next.
Now we can read the parent's headline formulas as plain fractions.
Definition A ratio, in picturesA ratio B A "how many times bigger is A B If A = 40 B = 10 4 A B
The word "work" here is a precise physics quantity, not the everyday meaning.
Work = force × in the force's direction .
Work = F × d joules , J
Intuition Why work is the key to the "no free lunch" ruleA pulley can shrink the force you apply, but it can never shrink the work . So if force drops by a factor n n F × d W in = n W × ( n h ) = W h = W o u t Work–Energy Theorem .
Common mistake Confusing weight-W W W both weight (force) and work (energy). They are different! Weight is in newtons; work is in joules. Tell them apart by context: W W in , W o u t
An inextensible rope cannot stretch — its total length is fixed. That single fact links how the pieces move.
Definition Inextensible & constraintInextensible = "cannot be stretched." If one part of a fixed-length rope shortens, another part must lengthen by the same amount. A rule forced on us this way is a constraint .
Why the topic needs it: it is the missing equation that lets you solve moving-pulley systems — never guess accelerations, derive them from constant length.
Force F = push or pull arrow
Newtons Second Law Fnet = ma
Ideal massless frictionless
Work = force times distance
Inextensible string constraint
Each foundation on the left feeds into Mechanical Advantage on the right. If any left-hand box is shaky, the MA box will wobble.
Test yourself — cover the right side and answer:
What is a force, and how do we draw it? A push or pull, measured in newtons N
What is weight W W = m g g ≈ 9.8 N/kg
What is tension T The pulling force carried along a stretched rope, aimed away along the rope at every point.
Why does an ideal rope have one uniform tension? It is massless, so each tiny piece has F n e t = ma = 0 T
What does ∑ F up = ∑ F down Equilibrium — all upward arrows cancel all downward arrows, so the object does not accelerate.
State Newton's Second Law and its still-case. F n e t = ma a = 0 F n e t = 0
What do "massless" and "frictionless" buy us? Uniform tension (massless) and direction-only pulleys (frictionless): the clean "one rope, one T
Define mechanical advantage as a ratio. MA = F load / F effort
Define work and its unit. Work = F × d J
Why can a pulley reduce force but not work? Energy conservation: W in = ( W / n ) ( nh ) = W h = W o u t
What is an inextensible-string constraint? Fixed total rope length ties the accelerations together; e.g. a 1 + a 2 = 2 a pulley
Parent: Pulley Systems — Mechanical Advantage — this page is its zero-level foundation.Newton's Second Law — the F n e t = ma Tension in strings — the uniform-tension idea developed here.Work–Energy Theorem — the W in = W o u t Constraint relations — inextensible-rope acceleration links.Atwood machine — first moving-pulley application.Friction — where real efficiency η < 1 Inclined plane mechanical advantage — same force-for-distance trade in another machine. 
