D. Structures and Mechanisms · Machines and Mechanisms

How Machines Change Forces

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

Learning goals

I can explain the ways machines change forces: making them smaller, bigger, or changing their direction.
I can explain the trade-off between force and distance.
I can compare the force needed with and without a machine using a simple measuring tool.
I can explain how a lever, a wheel and axle, a pulley, a ramp and gears each change a force.

Words to know

force
A push or a pull.

effort force
The force you put into a machine.

output force
The force the machine puts on the load.

trade-off
Getting more of one thing by giving up some of another. Machines trade force for distance.

mechanical advantage
How many times a machine multiplies your force. If a machine lets you lift a 30 N load with 10 N, its mechanical advantage is about 3.

fulcrum
The point a lever turns on.

Remember from Grade 3

In Grade 3 you learned that a force is a push or a pull, that forces can start, stop, speed up, slow down or change the direction of an object, and that a bigger force makes a bigger change. Now let's find out how machines change the forces we use.

Opening a stuck paint can

Grandpa's paint can lid is stuck tight. He can't pull it off with his fingers. He slides the tip of a flat screwdriver under the lid's edge, rests the screwdriver on the rim, and pushes down gently on the handle. Pop! The lid lifts off.

His small push on the long handle became a big force on the lid. The screwdriver was used as a lever.

A screwdriver tip pushed under the lid of a metal paint can, lifting the lid on a workbench. — Used this way, the screwdriver is a lever. The rim of the can is the fulcrum, and a small push down on the long handle makes a big upward force on the lid. AI-generated image

Grandpa's screwdriver as a lever. The rim of the can is the fulcrum. A small push on the long handle makes a big upward force on the lid, because the handle end is much farther from the fulcrum.

Three ways machines change forces

Make the force bigger (you push with a small force and the machine pushes with a big force). Example: a lever lifting a paint can lid; a movable pulley; a ramp.
Change the direction of the force. Example: a fixed pulley (pull down, load goes up); a seesaw (push one end down, the other end goes up).
Make the output faster or travel farther by using a bigger force. Example: a hockey stick. Your hands move a little; the blade moves a lot, and fast.

Many machines do more than one of these at the same time.

You can't get something for nothing

When a machine makes your force bigger, you must move farther.

A ramp: less force, but a longer path than lifting straight up.
A movable pulley: half the force, but twice the rope.
A long lever: less force, but your end moves farther than the load.

When a machine gives more speed or distance, you must use more force.

How each machine changes force

Lever: the farther your push is from the fulcrum, the less force you need to lift the load near the fulcrum.
Wheel and axle: turning the big wheel a long way gives a strong turn on the small axle. A doorknob, a screwdriver handle and a steering wheel work this way.
Pulley system: more rope sections holding the load means less force.
Inclined plane (ramp): a long, gentle ramp needs less force than a short, steep one, but you go farther.
Gears: a small gear turning a big gear gives a stronger turning force but a slower turn.

Wheel and axle. Your hand moves the big wheel a long way with a small force. The small axle turns a short way with a strong force. That's why a doorknob is wider than the rod inside it.

Worked example

Let's measure the force a ramp saves

Sam pulls a toy truck full of blocks up onto a stack of books 15 cm high. He measures the pull with a rubber band and a ruler (a longer stretch means a bigger force).

Lift straight up: the rubber band stretches 12 cm.
Long gentle ramp (60 cm long): the stretch is 4 cm.
Short steep ramp (30 cm long): the stretch is 7 cm.
Compare: the long ramp needs the least force (4 cm compared to 12 cm). But the truck must travel 60 cm instead of 15 cm.
Mechanical advantage of the long ramp: about 12 ÷ 4 = 3. The ramp makes the pull about 3 times smaller.

The long ramp needs the least force but the longest distance. That's the trade-off.

Worked example

Let's find the mechanical advantage

A lever lets Ayesha lift a 60 N rock with a push of 20 N. What is the mechanical advantage? What is the trade-off?

Mechanical advantage = load force ÷ effort force.
60 ÷ 20 = 3.
Trade-off: her end of the lever moves about 3 times farther than the rock rises.

Mechanical advantage about 3. Small push, longer distance.

Just for fun

The ancient Greek thinker Archimedes is said to have joked: "Give me a place to stand and a lever long enough, and I will move the world!" He would need a VERY long lever, and somewhere to stand in space.

Machine	How it changes force	What you trade
long lever (crowbar)	makes force bigger	your end moves farther
fixed pulley	changes direction	nothing much (a little extra force for friction)
block and tackle	makes force bigger	you pull much more rope
ramp	makes force bigger (less needed)	you move the load a longer distance
doorknob (wheel and axle)	makes turning force bigger	your hand moves around a bigger circle
small gear turning big gear	makes turning force bigger	the big gear turns slower
hockey stick or broom	gives more speed and distance at the end	you need more force

How machines change forces

Hands-on activity

Rubber band force meter

You need: a rubber band, a paper clip, a ruler, a small bag with a load (like 4 juice boxes or a few cans), a stack of books, a board or stiff piece of cardboard for a ramp, a long ruler or wooden spoon (for a lever), and a pencil (as a fulcrum).

Make your meter: hook the paper clip through the rubber band. Hook the clip onto the bag's handle. Pull on the other end of the rubber band and measure how long it stretches (the length of the band while you lift).
Test 1, lift straight up: lift the bag 10 cm. Measure the stretch.
Test 2, ramp: pull the bag up a board ramp to the top of the book stack. Measure the stretch. Try a longer and a shorter ramp.
Test 3, lever: put the pencil under a long ruler. Put a lighter load (a juice box) on one end of the ruler, with the pencil close to that end. Hook the rubber band over the other end and pull down until the load lifts. Move the pencil closer to or farther from the load and compare.
Record each result in a table. Keep the same load and the same rubber band for every test to keep it fair.
Conclude: which machine needed the least force? What did you trade?

What to look for: ramps and long lever arms need less stretch than lifting straight up, but the load or your hand moves farther. Safety: keep loads light, stretch the rubber band gently, point it away from faces, and don't let it snap.

Your turn

Name three ways machines can change a force.

A ramp needs less force than lifting straight up. What is the trade-off?

Why is a doorknob wider than the rod inside it?

A lever lets you lift a 40 N load with 10 N. What is the mechanical advantage?

Which changes only the direction of a force: a fixed pulley or a movable pulley?

A hockey stick makes the blade move farther and faster than your hands. What do you trade?

In a rubber band force meter, what does a longer stretch mean?

More practice: warm-up

What is a force?

What is the point a lever turns on called?

Which needs less force, a long gentle ramp or a short steep ramp?

What is the force you put into a machine called?

Name a wheel and axle in your home.

More practice: on your own

Sam's results: lift straight up, 12 cm stretch; long ramp, 4 cm; short ramp, 7 cm. Order the ways from most force to least force.

A screwdriver with a fat handle is easier to turn a stuck screw with than one with a skinny handle. Explain.

A crane's block and tackle has a mechanical advantage of 5. The motor pulls with 2000 N. About how heavy a load can it lift?

Lucy tested a ramp with a heavy load, then a different ramp with a light load. Why is that not a fair test?

Why does a broom sweep far with each stroke even though your top hand barely moves?

Challenge

A lever has a mechanical advantage of 4. To lift a rock 10 cm, about how far must you push your end down? Explain.

A wheelchair ramp at a library must be long and gentle, not short and steep. Use what you know about forces to explain why.

Design a test to find out whether a fat-handled or a thin-handled screwdriver needs less force to turn a screw. What will you change, keep the same and measure?

Check your understanding

Quiz

A machine that makes your force bigger makes you...

A fixed pulley...

A lever lifts a 50 N load with a 10 N push. The mechanical advantage is...

Which needs the least force to get a load to the same height?

Why is it easy to turn a doorknob?

A hockey stick gives more speed at the blade. What do you trade?

In a fair test of ramps, you should keep the same...

For parents and teachers

Big idea (D2.5): Machines change forces: they make a force bigger (and the distance longer), change its direction, or give more speed and distance (and need more force). Mechanical advantage = load force ÷ effort force. The rubber-band meter supports a fair test (A1.2); safe use of tools and elastics is A1.4.

Remember from earlier grades: Grade 2 measured force with a rubber band; Grade 3 studied forces. Grade 4 explains the force-distance trade-off and introduces mechanical advantage informally.

Common difficulties:

Thinking machines reduce the work. They reduce the force but increase the distance.
Thinking all machines make force bigger. Some (hockey sticks, brooms, fishing rods) trade force for speed.
Safety: rubber bands can snap. Stretch gently and keep them away from eyes.