D. Structures and Mechanisms · Machines and Mechanisms

Pulley Systems: Changing Direction and Force

D2.2 D2.4 D2.5 A1.2 A1.4About 45 minutes

Learning goals

I can name the parts of a pulley system and describe the purpose of each part.
I can explain that a fixed pulley changes the direction of a force.
I can count the ropes holding up a load to predict how much a pulley system reduces the force needed.
I can explain the trade-off: less force means pulling more rope.
I can test a pulley system fairly and safely.

Words to know

pulley
A wheel with a groove around its edge for a rope, cord, cable or belt.

fixed pulley
A pulley fastened in one place. It changes the direction of the pull.

movable pulley
A pulley attached to the load. It moves with the load and reduces the force needed.

pulley system
Two or more pulleys working together, like a block and tackle.

block and tackle
A pulley system with several pulleys and one rope, used to lift very heavy loads.

effort
The force you use to work a machine.

load
The object the machine moves or lifts.

newton (N)
The unit scientists use to measure force. A small apple pulls down on your hand with a force of about 1 newton.

fair test
A test where you change only one thing and keep everything else the same.

Remember from Grade 2

A pulley is a wheel with a groove that a rope runs over. A fixed pulley changes the direction of your pull: pull down, the load goes up. A movable pulley moves with the load and lets you lift with less force. In Grade 4 you will find out how much less force, and what the trade-off is.

A heavy bucket at the cottage

Noah's family is fixing the roof of their cottage. They need to lift a bucket of shingles from the ground to the roof. The bucket is heavy. Lifting it straight up takes a force of 40 newtons (40 N). (A newton is the unit for force. A small apple pulls down on your hand with about 1 newton.)

Can pulleys help? Let's find out.

A metal bucket of roof shingles hangs from a rope that runs over a pulley fixed to a wooden beam on a cabin. — This is a fixed pulley like the one Noah's family could use. Pulling down on the free end of the rope lifts the bucket up, so the pulley changes the direction of the pull. AI-generated image

The parts of a pulley system

Pulley wheel: turns as the rope moves over it. The groove keeps the rope from slipping off.
Axle: the pin the wheel turns on.
Block (frame): holds the axle and wheel and has a hook.
Rope (or cord or cable): carries the pull.
Hook or anchor: fastens a fixed pulley to something strong, or joins a movable pulley to the load.
Load: the thing being lifted. Effort: your pull.

Left: a fixed pulley. One rope holds the load, and pulling down makes the load go up. Right: a movable pulley. Two ropes hold the load up, so each rope holds about half.

Count the ropes!

Here is a trick engineers use. Count the rope sections that hold up the load (the ropes going to the pulley that moves with the load).

Fixed pulley: 1 rope section holds the load. You pull with about the same force as the load. It only changes the direction.
Movable pulley: 2 rope sections hold the load. Each one holds half. You pull with about half the force.
Block and tackle with 4 rope sections: you pull with about one quarter of the force.

We say about because real pulleys have friction (rubbing) and the movable pulley has its own weight, so you always need a little more.

The trade-off

A machine can't give you something for nothing! When a pulley system cuts the force you need, you must pull more rope.

2 rope sections: about half the force, but pull 2 times as much rope.
4 rope sections: about one quarter of the force, but pull 4 times as much rope.

Less force, more distance.

Worked example

Let's work out the shingle bucket

The bucket of shingles needs 40 N to lift straight up. It must go up 3 metres to the roof. Compare three ways to lift it.

Fixed pulley (1 rope section): pull down with about 40 N. Pull about 3 m of rope. Easier to pull down than to lift up, but no less force.
Movable pulley plus a fixed pulley (2 rope sections hold the movable pulley): about 40 ÷ 2 = 20 N. But pull 2 × 3 = 6 m of rope.
Block and tackle (4 rope sections): about 40 ÷ 4 = 10 N. But pull 4 × 3 = 12 m of rope.
Each answer is "about", because friction adds a little extra force.

More rope sections holding the load means less force but more rope to pull. Noah's family could use the block and tackle to lift the heavy bucket with about 10 N.

Pulley system	Rope sections holding the load	Force needed (load 40 N)	Rope pulled to lift 1 m
no pulley (lift by hand)	—	40 N	1 m
fixed pulley	1	about 40 N	1 m
movable pulley	2	about 20 N	2 m
block and tackle	4	about 10 N	4 m

Comparing pulley systems

The table as two bar graphs. As the force bars get shorter, the rope bars get longer. That is the pulley trade-off: less force, more distance.

Pulley systems in daily life

Flagpoles and window blinds use fixed pulleys to change direction.
Cranes at building sites use block and tackle systems with strong steel cables to lift steel beams.
Sailboats use pulley blocks so sailors can pull ropes to raise sails.
Tow trucks have a winch and pulleys to pull cars.
Exercise machines at a gym use pulleys and cables to change the direction of your pull.

Just for fun

What did the bucket of shingles say to the pulley?

"Thanks for the lift!"

Worked example

Let's plan a fair test

Maya wants to test: "Does a movable pulley really need less force?" How should she test fairly?

Change only one thing: the way of lifting (straight up, with a fixed pulley, with a movable pulley).
Keep the same: the same load (a bag with 6 juice boxes), the same rubber band to measure the pull, the same height lifted.
Measure: how long the rubber band stretches (a longer stretch means a bigger force), and how much string she pulls.
Repeat each test 3 times to make sure her results are reliable.
Her results: straight up, 9 cm stretch; fixed pulley, 10 cm; movable pulley, 5 cm. String pulled to lift the bag 20 cm: 20 cm, 20 cm and 40 cm.

Her test was fair. The movable pulley needed about half the force but twice the string. The fixed pulley needed a little more force than lifting (friction) but changed the direction.

Hands-on activity

Build and test a pulley system

You need: 2 empty thread spools (or 2 round plastic lids with a hole in the middle), 2 pencils or chopsticks, string (about 3 metres), a small cloth bag or a plastic cup with a string handle, a load (a few juice boxes or toys), a rubber band, a ruler, tape, and two chairs.

Fixed pulley: Put one spool on a pencil. Tape the pencil ends across the backs of two chairs placed side by side (a grown-up helps). Tie the bag to the string and lay the string over the spool.
Measure the load: Loop the rubber band on the end of the string. Lift the bag straight up, no pulley, holding the rubber band. Measure the stretch with the ruler.
Test the fixed pulley: Pull down through the rubber band. Measure the stretch.
Movable pulley: Push the second pencil through the second spool and hang the bag from both ends of the pencil with a loop of string. Tie one end of the long string to the chair bar. Run it down and under the movable spool, up and over the fixed spool, and down to your rubber band. Pull and measure.
Measure the rope: Mark the string with a piece of tape. Lift the bag 10 cm with each set-up. How far did the tape mark move?
Record your results in a table and describe the pattern.

What to look for: with the movable pulley, the stretch should be close to half, and you pull about 20 cm of string to lift 10 cm. Safety: keep string away from necks, don't stand under the load, use light loads only, and keep chairs steady.

Your turn

What is the purpose of the groove in a pulley wheel?

What does a fixed pulley change?

A movable pulley has 2 rope sections holding the load. About how much force do you need compared to lifting the load by hand?

A load needs 60 N to lift straight up. About how much force with a movable pulley (2 rope sections)?

What is the trade-off when you use a movable pulley?

A block and tackle has 4 rope sections holding the load. To lift the load 2 m, about how much rope do you pull?

Why do we say "about" half the force?

More practice: warm-up

What is a pulley?

Which pulley is attached to the load and moves with it?

What unit do scientists use to measure force?

Name a machine that uses a block and tackle.

In a fair test, how many things do you change?

More practice: on your own

A box needs 80 N to lift straight up. Find about how much force is needed with: a fixed pulley; a movable pulley (2 sections); a block and tackle (4 sections).

Why would a person choose a fixed pulley if it does not reduce the force?

In Maya's test, the fixed pulley needed a 10 cm stretch but lifting by hand needed 9 cm. Why was the fixed pulley a little harder?

A sailor pulls 6 m of rope to raise a sail 2 m. How many rope sections hold up the sail's pulley?

Maya used a different load for each pulley test. Was her test fair? Explain.

Challenge

A crane lifts a 6000 N steel beam with a block and tackle that has 6 rope sections holding the load. About how much force must the crane's motor pull with? About how much cable is pulled to lift the beam 10 m?

Your friend says, "If I add more and more pulleys, I can lift a car with my little finger, and it will be fast!" What is right and what is wrong about this idea?

Design a pulley system to lift a bucket of firewood (about 50 N) to a second-floor deck using a pull of about 25 N or less. Describe it.

Check your understanding

Quiz

What does a single fixed pulley do?

A movable pulley with 2 rope sections lifts a 50 N load. About how much force do you need?

When a pulley system lets you use less force, you must...

A block and tackle has 4 rope sections holding the load. To lift the load 1 m, about how much rope do you pull?

Why do you need a little more force than the math says?

Which unit measures force?

In a fair test of pulleys, you should...

For parents and teachers

Big idea (D2.2, D2.4, D2.5): Pulley systems change the direction of a force (fixed pulley) and can reduce the force needed (movable pulleys, block and tackle) at the cost of pulling more rope. Counting the rope sections that hold the moving pulley predicts the force: 2 sections, about half; 4 sections, about a quarter. The fair test is A1.2; safe handling is A1.4.

Science accuracy note: The "divide by the number of rope sections" rule gives the ideal force. Real pulleys need a bit more because of friction and the weight of the movable pulley, so your child's rubber-band results won't be exact. That is a great discussion point, not a failed experiment.

Newtons: Your child does not need to measure newtons exactly. The rubber band stretch is a fine way to compare forces. A small apple weighs about 1 N.

Common difficulties:

Counting the rope you pull as a supporting section in a fixed pulley. Only count ropes going to the pulley that moves with the load.
Thinking pulleys make work free. Less force always means more rope pulled.
Safety: no string near necks, light loads only, nothing hanging over heads.