Simple machines - Practice

What you will learn

the six simple machines and how each alters force,
the lever rule $F_1 d_1 = F_2 d_2$ and the three classes of lever,
why a pulley can halve the effort needed to lift a load,
how an inclined plane trades distance for a smaller force,
mechanical advantage and why no simple machine is $100\%$ efficient.

Worked example 0 Real-world example: a crowbar lifting a heavy crate

A crate weighs $600$ N. You use a $2.0$ m crowbar and place the pivot (fulcrum) $0.20$ m from the crate. How much force do you need at the far end?

The lever rule: load arm × load force = effort arm × effort force. $F_L \, d_L = F_E \, d_E$ .
Load arm $d_L = 0.20$ m. Effort arm $d_E = 2.0 - 0.20 = 1.80$ m.
$600 \times 0.20 = F_E \times 1.80$ .
$F_E = \dfrac{120}{1.80} = 66.7$ N.

You only need about $67$ N — roughly the weight of a $7$ kg bag — to lift a $60$ kg crate.

Key idea: the longer the effort arm compared to the load arm, the smaller the effort force needed. But you have to move the effort end further.

1. The six simple machines

Lever — a rigid bar that pivots around a fulcrum.
Inclined plane — a ramp; a flat surface tilted at an angle.
Wedge — a double-inclined plane that splits or separates things (axe, knife).
Screw — an inclined plane wrapped around a cylinder.
Pulley — a wheel with a grooved rim carrying a rope.
Wheel and axle — a large wheel attached to a small axle.

Every complicated machine (a bicycle, a crane, a piano) is built from combinations of these.

2. Levers and the lever rule

A first-class lever. Load and effort are on opposite sides of the fulcrum.

Lever rule

Balance condition

F_L \, d_L = F_E \, d_E

$F_L$ = load force, $d_L$ = distance from load to fulcrum, $F_E$ = effort force, $d_E$ = distance from effort to fulcrum.

Three classes of lever:

Class 1 — fulcrum in the middle. Examples: see-saw, crowbar, scissors.
Class 2 — load in the middle. Examples: wheelbarrow, bottle-opener.
Class 3 — effort in the middle. Examples: tweezers, fishing rod, human forearm.

Worked example 1 Balancing a see-saw

A $40$ kg child sits $2$ m from the fulcrum. Where should a $60$ kg child sit to balance?

Weights: $40 \times 10 = 400$ N and $60 \times 10 = 600$ N.
Balance: $400 \times 2 = 600 \times d$ .
$d = 800/600 = 1.33$ m.

The heavier child must sit closer to the fulcrum.

3. Mechanical advantage

Mechanical advantage (MA) measures how many times a machine multiplies your effort.

Mechanical advantage

\text{MA} = \dfrac{\text{load force}}{\text{effort force}} = \dfrac{F_L}{F_E}

An MA of $4$ means you can lift a $400$ N load with only $100$ N of effort.

Worked example 2 Mechanical advantage of a crowbar

In the crowbar worked example above, load was $600$ N and effort was about $67$ N.

\text{MA} = \dfrac{600}{67} \approx 9.

The crowbar multiplied the effort by about $9$ times.

4. Inclined planes and wedges

A ramp lets you trade force for distance. A $3$ m ramp rising $1$ m in height moves $3$ m of distance for every $1$ m of lift — and needs about a third of the vertical lifting force.

Worked example 3 Pushing a barrel up a ramp

A $300$ N barrel must be lifted onto a truck $1.0$ m high. A ramp of length $3.0$ m is used.

Work done lifting straight up: $300 \text{ N} \times 1.0 \text{ m} = 300$ J.
Pushing along the ramp, same work done over $3.0$ m (in an ideal ramp): force $= 300/3.0 = 100$ N.
MA $= 300/100 = 3$ .

You push with one-third of the direct force, but move three times the distance.

Key idea: a machine never reduces the work required (in the ideal case). It only changes the balance between force and distance.

A wedge is a moving inclined plane — axes and knives use wedges to split wood or food.

5. Pulleys

A single fixed pulley changes the direction of a force but not the size. Using two ropes to support a load (a movable pulley system) halves the effort force — but you must pull twice as much rope.

Worked example 4 Pulley to lift a bucket

A single fixed pulley is used to lift a $200$ N bucket from a well. You pull down on the rope.

Effort needed: $200$ N (same as the weight).
Direction: you pull downward; the bucket goes upward.

Now with two ropes supporting the bucket (block and tackle):

Each rope supports half the weight, so effort $= 100$ N.
You must pull $2$ m of rope for every $1$ m the bucket rises.
MA $= 2$ .

Key idea: pulleys can change direction, size, or both — depending on how the ropes are configured.

6. Wheel and axle; screws

A wheel and axle (e.g. a tap or a doorknob) uses a large wheel turned by a small force to turn a small axle with a larger force. The larger the wheel vs the axle, the bigger the mechanical advantage.

A screw is an inclined plane wrapped around a cylinder. Turning the screw converts a rotation (a small force over many turns) into a powerful forward push through wood or metal.

Practice: Year 7

Fluency

Tier 1: recall and identify

Name the six simple machines.
State the lever rule in symbols.
For a wheelbarrow, identify: fulcrum, effort, load. Which class of lever is it?
What is mechanical advantage?
A force of $50$ N lifts a $200$ N load. Find the MA.
A lever has load $300$ N at $0.5$ m from the fulcrum, effort applied at $1.5$ m. Find the effort force.
A ramp $4$ m long is used to lift a $100$ N box $1$ m high. What force is needed, ideally?
Give an everyday example of a class-3 lever.
What does a single fixed pulley change: direction, size, or both?
A screw is equivalent to what other simple machine wrapped around a cylinder?

Reasoning

Tier 2: explain and reason

Explain why pushing a $100$ kg piano up a ramp is easier than lifting it straight up.
Why must the effort arm of a lever be longer than the load arm to give MA greater than $1$ ?
A pulley system has MA $= 3$ . Explain what that means for the effort force and the length of rope pulled.
Two people sit on a see-saw. Explain why the heavier person moves closer to the fulcrum to balance.
Why is no simple machine $100\%$ efficient in the real world?
A carpenter uses the claw end of a hammer to pull out a nail. Explain how this works as a lever.

Problem solving

Tier 3: apply to a novel context

A $60$ kg child sits at one end of a $4$ m see-saw with the fulcrum in the middle. Where should a $40$ kg child sit to balance?
A ramp is used to roll a $500$ N barrel into a truck $1.2$ m high. If the effort needed is $150$ N (ideal), how long is the ramp?
A block and tackle has MA $= 4$ and is used to lift a $600$ N load $2$ m. What force is needed? How much rope is pulled?
A nutcracker has its hinge at one end, nut in the middle, and hands at the other end. Which class of lever is it? Explain.

Challenge

Reasoning

Harder reasoning

A bicycle uses gears — a variable wheel-and-axle system. Explain why a low gear is chosen for climbing a hill and a high gear for flat roads, using the idea of trading force for distance.
A $2$ m lever with fulcrum in the middle balances a $50$ N weight on one end with a $50$ N weight on the other. A student slides both weights to within $0.2$ m of the fulcrum (on opposite sides). Does the lever still balance? Justify.
A real ramp has friction that absorbs $20\%$ of the work. A $400$ N box is lifted $1$ m using a $4$ m ramp. Calculate the ideal effort, the actual effort, and the efficiency.
Pulleys used in construction can have MA of $8$ or more. Explain why workers do not simply use a crane (lever system) instead, and what trade-offs matter on a real building site.