Energy | ICSE Class 6 Physics Notes

This note covers energy and work, the six simple machines, the parts and orders of levers, load and effort, mechanical advantage, the lever balance rule, simple calculations and observations using a model lever.

What are energy, work and simple machines?

Definition: Energy is the ability to do work. A force is a push or pull. Work is done by a force when it moves an object through a distance in the direction of that force.

A machine is a device that helps us do work. A machine need not be a large, complicated object. A bottle opener, a needle and a doorknob are machines. Some machines are more complex than others.

How can a machine make a task easier?

A simple machine changes the direction or the magnitude of an applied force. Magnitude means the size of the force. Changing its direction can make a task more convenient; changing its magnitude can reduce the force a person must apply.

The force applied to a machine is called the effort. The force that must be overcome is called the load. These terms describe forces, even when we also use the word load informally for the object being lifted. An object’s weight is the gravitational force pulling it towards Earth.

Machines do not create energy. Ignoring friction, the force that opposes relative motion between surfaces in contact, the work put into a machine equals the useful work done on its load. A smaller effort can act through a greater distance.

Note: Easier work does not mean that a machine supplies energy by itself. It changes how a force is applied. A machine can be useful through a change of direction even when it does not multiply force.

Which are the six simple machines?

The six simple machines are the lever, wheel and axle, pulley, inclined plane, wedge and screw. Their shapes and arrangements differ, but each helps us apply a force to carry out a task.

A lever turns about a support. A wheel and axle turns as a connected arrangement. A pulley guides a rope around a wheel. An inclined plane provides a sloping surface. A wedge has sloping faces, while a screw has a winding inclined surface.

How can simple machines occur together?

Many machines used in daily life contain two or more simple machines. Identifying a machine therefore involves looking at its working parts. The name of the whole device is less useful than noticing what turns, where force is applied and what moves.

A bottle opener provides a lever example, a needle illustrates a wedge, and a doorknob illustrates a wheel and axle. These familiar objects show why a machine is identified by the way it works, rather than by its size.

What are the parts of a lever?

A lever is a rigid bar that can rotate about a fixed point. Rigid means that the bar keeps its shape sufficiently well while being used. The fixed turning point is the fulcrum, also called the pivot.

A lever has three main parts to identify: the fulcrum, the load and the effort. The load is the force to be overcome. The effort is the force applied. The fulcrum supports the turning action that connects the effects of these forces.

What are the load arm and effort arm?

The load arm is the distance from the fulcrum to the point where the load acts. The effort arm is the distance from the fulcrum to the point where the effort acts. These descriptions apply to the simple lever arrangements considered here.

Both arms are measured from the fulcrum. An arm is not automatically the entire length of the bar. Before measuring or calculating, locate the turning point and the two points where the forces act.

A slanting bar rests on a support near a rock. The drawing labels the load near the rock, the effort near the raised end, the fulcrum, the load arm and the effort arm.

See Fig. 7.32 in your NCERT textbook

In everyday life, levers are often used to lift heavy objects. The positions of the forces matter as well as their sizes. A long effort arm can allow a smaller effort to overcome a larger load placed closer to the fulcrum.

To read a lever diagram, first mark the fulcrum. Then identify the applied effort and the load being overcome. Finally, trace each arm back to the same fulcrum. This avoids confusing an arm with the gap between load and effort.

How are the three orders of levers different?

Levers may be classified into three orders, also called classes, according to the relative positions of the fulcrum, load and effort. The decisive question is which one lies between the other two. Turning a drawing around does not change that relationship.

What lies in the middle?

In a first-order lever, the fulcrum separates the load and effort. A seesaw illustrates this arrangement. The fulcrum need not be exactly halfway between the forces: its position between them is what determines the order.

In a second-order lever, the load lies between the fulcrum and effort. A bottle opener is an example. Locate the support point, the load being acted on and the point where effort is applied before assigning its order.

In a third-order lever, the effort lies between the fulcrum and load. Tweezers provide an example. Here the word “third” describes the arrangement, rather than the number of parts or the number of forces used.

How should an unfamiliar lever be classified?

1. Find the fixed point about which the bar turns.
2. Locate the load, meaning the force that must be overcome.
3. Locate the effort, meaning the force applied to operate the lever.
4. Identify the middle part and match it to the correct order.

Remember the three middle parts in order: fulcrum, load, effort. Use this rule with the arrangement shown, rather than trying to recognise a lever solely from its appearance or from which way its handle points.

What does mechanical advantage tell us?

Mechanical advantage is the factor by which a machine multiplies the applied force. It compares the load with the effort. A ratio is a comparison made by division, so the mechanical advantage is the ratio of load to effort.

Use MA as the abbreviation for mechanical advantage. In the following formula, “Load” and “Effort” mean the magnitudes of the two forces. The division sign, ÷, means “divided by”.

MA = Load ÷ Effort

The load belongs above the effort in a fraction, or before it in a division. Reversing this order answers a different question. Mechanical advantage asks how large the load is compared with the effort supplied to the machine.

Does mechanical advantage have a unit?

Express both forces in the same unit before dividing. The newton, written N, is the SI unit of force. SI means International System of Units. Because the same force unit occurs in both parts of the ratio, mechanical advantage has no unit.

A machine with mechanical advantage equal to one can still be useful. A fixed pulley makes lifting more convenient by changing the direction of the effort. Mechanical advantage describes a force comparison; it does not describe every benefit of a machine.

When a numerical answer has been obtained, explain its meaning in words. A value above one indicates a larger load than effort. This interpretation is an essential check that the ratio has been written in the correct order.

How does the lever balance rule work?

For a lever in balance, meaning that its turning effects oppose and balance one another, the load and effort must be considered together with their arms. A larger force can be balanced by a smaller force acting farther from the fulcrum.

Use the simple model in which the bar's own weight and friction at the fulcrum can be ignored, and the applied forces act at right angles to the bar. A right angle is the angle of a square corner. Under these conditions:

Load × Load arm = Effort × Effort arm

The multiplication sign, ×, means “multiplied by”; the equals sign, =, means that the quantities on its two sides have the same value. Write the load and effort in matching force units and the arms in matching length units.

Derivation: How does the lever rule give mechanical advantage?

Let $Q$ be the load and $E$ the effort, both in newtons. Let $a$ be the load arm and $b$ the effort arm, both in metres. Use the balanced lever model and conditions stated above.

1. The opposing turning effects balance: $Qa = Eb$.
2. Divide both sides by $Ea$, with non-zero effort and load arm: $\frac{Qa}{Ea} = \frac{Eb}{Ea}$.
3. Cancel the common factors: $\frac{Q}{E} = \frac{b}{a}$. The force ratio is the mechanical advantage.

$\mathrm{MA} = \frac{b}{a}$. Mechanical advantage equals effort arm divided by load arm; the matching length units cancel.

The effort arm is now above the load arm. Notice the different order: load divided by effort for forces, but effort arm divided by load arm for distances. Both describe the same mechanical advantage under the stated conditions.

Keeping the load and load arm unchanged, increasing the effort arm reduces the effort needed for balance. With a lever, the effort required is generally smaller, but it has to move through a larger distance.

How can an unknown effort be found?

Rearrange the same balance rule, rather than treating each problem as a new rule:

Effort = Load × Load arm ÷ Effort arm

For an unknown load arm, divide effort multiplied by effort arm by the load. After solving, substitute the answer into the original balance rule. The products on the two sides should agree when calculated in matching units.

Note: Do not confuse the length of an arm with the distance its end moves. The arm is measured from the fulcrum; the end moves as the lever turns.

How does a pulley make lifting more convenient?

A pulley is a wheel with a groove that guides a rope. The groove is the channel around the edge of the wheel. When the rope moves, the wheel turns and the rope transmits the applied effort to the load.

A fixed pulley is supported at a fixed position. When a rope passes over it, pulling down on one end can raise the load attached to the other end. A flag or a load can be raised in this way.

What changes in a fixed pulley?

The important change is the direction of effort. Instead of applying an upward force directly to the load, a person pulls the rope downwards. This makes the task more convenient without multiplying the force in the simple frictionless model.

Drawing (a) shows a person raising a load directly, with the effort arrow pointing upwards. Drawing (b) adds an overhead pulley, and the effort arrow points downwards. Both drawings label the load and effort.

See Fig. 7.24 in your NCERT textbook

For the fixed pulley considered here, ignoring friction, the effort and load have equal magnitudes. Dividing the load by the equal effort gives mechanical advantage equal to 1. No particular numerical force is needed to establish this comparison.

A movable pulley moves with its attached load. Movable pulleys or systems of pulleys can have a mechanical advantage greater than one. Pulleys are used in elevators and cranes because of the convenience they provide.

Distinguish the pulley arrangements before making a statement about force. “A fixed pulley changes the direction of effort” is more precise than saying that every pulley reduces effort. The result depends on which arrangement is being considered.

How do a wheel and axle work together?

A wheel and axle consists of a larger wheel connected to a smaller central shaft called the axle. They turn together. A shaft is a rod that carries or transmits a turning motion. The connection between the wheel and axle is essential.

When effort turns the larger wheel, it also turns the axle. Applying effort farther from the central turning line can provide a stronger turning effect than applying the same force close to it. This helps explain why the larger part can make turning convenient.

How does a doorknob illustrate this machine?

In a doorknob, the knob acts as the wheel and its connected central shaft acts as the axle. Turning the knob turns the shaft. Identify the two connected parts, rather than looking for the large open wheel of a vehicle.

The wheel and axle and the pulley both involve wheels, but their arrangements differ. In a wheel and axle, the larger and smaller connected parts turn together. In a pulley, the groove guides a rope used to apply effort and move a load.

For identification, look for the connected turning parts and explain what the effort makes them do. A complete description should name both the wheel and axle. Simply writing “it is round” does not explain the mechanism or distinguish it from a pulley.

How does an inclined plane help move a load?

An inclined plane is a sloping surface that helps move a load to a higher or lower level. A ramp is an inclined plane. A smooth plank placed against a platform lets a box be pushed up the slope instead of lifted straight upwards.

The sloping route is longer than the vertical rise. Under the simple conditions considered here, it allows a smaller force to act over a larger distance. The machine changes how the work is performed; it does not create energy.

What happens when the slope becomes gentler?

For the same height, making the plank less steep means using a longer sloping path. The force required to pull a cart up a smooth plank decreases as the plank becomes less steep. The effort must then act through a greater distance.

A spring balance is a device that measures force using the stretching of a spring. Attaching one to a cart makes it possible to compare the force needed for direct lifting with the force needed to pull along a plank.

Two photographs show a cart on a plank supported by books, pulled with a spring balance. Photograph (a) labels the cart, plank and spring balance. Photograph (b) shows a longer, less steep plank reaching the books.

See Fig. 7.27 in your NCERT textbook

To make the comparison meaningful, use the same cart and final height. Pull slowly and steadily and compare the spring balance readings. Changing the load at the same time would no longer isolate the effect of changing the slope.

The useful comparison is between force and distance. The gentler slope requires less force over a longer path. Describing both changes gives a fuller explanation than saying merely that the ramp makes a box easier to move.

How are wedges and screws related to sloping surfaces?

A wedge has sloping surfaces that meet at a thin edge or point. When it is pushed into material, its sloping faces help separate the material. Wedges can be used to cut, split or pierce.

A needle illustrates the piercing action of a wedge. Its pointed end enters material when effort is applied. The example shows how a small object can act as a simple machine through the shape of its working end.

What is the difference between a wedge and a ramp?

With a ramp, the load moves along the sloping surface. A wedge itself is pushed into the material on which it acts. Both involve slopes, but the movement of the machine relative to the material is different.

A screw has an inclined surface wound around a cylinder. A cylinder is a solid with circular ends and a curved side. The winding ridge is called a thread. Turning a screw makes it advance along its length through a matching material or opening.

What should be identified on a screw?

Look for the winding thread and the turning action. A fastening screw holds parts together by being turned into material. Its shape connects the idea of an inclined plane with an action that combines turning and forward movement.

These descriptions help distinguish the six simple machines by their working arrangements. Naming an object is useful, but identifying its point, thread, rope, pivot or connected shaft explains why it belongs to a particular type.

How can a seesaw problem be solved using the lever rule?

A seesaw is a first-order lever because its fulcrum lies between the forces on its two sides. When two children balance it, their positions matter as well as their weights. The heavier child can balance closer to the fulcrum.

Mass is the amount of matter in an object. The kilogram, written kg, is a unit of mass. The metre, written m, is a unit of length. At the same place, the children's weights are proportional to their masses, meaning that their weight ratio equals their mass ratio.

Where should the children sit?

Worked example 1. A seesaw has seats labelled A, B, D and E, and a fulcrum labelled C. Seats A and B are on one side of C; seats D and E are on the other. A and E are each 2 m from C; B and D are each 1 m from C.

A child of mass 15 kg sits at A. Where should a child of mass 30 kg sit to balance the seesaw? Ignore the seesaw's own turning effect and friction. Both children experience the same gravitational conditions.

Answer: Let x be the distance in metres of the 30 kg child from C. Because the weights are proportional to the masses, the common weight-per-kilogram factor cancels from the balance equation.

Formula: $ma = Mx$, so $x = \frac{ma}{M}$, where $m$ is the smaller mass, $M$ the larger mass and $a$ the smaller child's distance from C.

Substitute: $15\,\mathrm{kg}\times2\,\mathrm{m} = 30\,\mathrm{kg}\times x$.

Therefore, $x = \frac{15\times2}{30}\,\mathrm{m} = 1\,\mathrm{m}$. The 30 kg child should sit at D, on the opposite side of C from A.

The calculation uses masses only because the same conversion from mass to weight applies to both children and cancels. Kilograms are not force units. In a problem that gives forces directly, use those forces in the lever balance rule.

What is the mechanical advantage of this arrangement?

Worked example 2. For the balanced seesaw above, take the force of the 15 kg child at A as the effort and the force of the 30 kg child at D as the load. The effort arm is 2 m and the load arm is 1 m. Find the mechanical advantage.

Answer: MA = effort arm ÷ load arm = 2 m ÷ 1 m = 2. The load force is twice the effort force. Mechanical advantage has no unit because the matching length units cancel.

Check the first calculation by comparing 15 × 2 with 30 × 1. Both products are equal. Check the second by noticing that the heavier child's weight is twice the lighter child's weight, consistent with the arm ratio.

How can a model lever demonstrate balance?

A model lever makes the positions of fulcrum, load and effort visible. A long ruler, string, paper cups and identical coins can form a beam balance, a device comparing weights on opposite sides of a supported bar. Identical coins allow the forces on the two sides to be compared by counting coins.

How is the beam arranged?

1. Tie string around the midpoint of a long ruler and hang it from a stand or hook so that it can swing freely.
2. Hang a paper cup near each end using thread. These cups act as the two pans of the balance.
3. Check that the empty arrangement is level. Adjust the hanging points until the two sides balance.
4. Place one coin in each pan and observe the level beam. Call the force on one side the effort and the force on the other the load.

The ruler acts as the lever and the central suspension provides the fulcrum. Each arm is the distance from that suspension point to the corresponding pan. The number of identical coins provides a way to compare the added weights.

What happens when the load increases?

Add another identical coin to the load pan so that it contains two coins. The beam tilts. Move the heavier pan closer to the centre until balance is restored, then measure its distance from the centre.

Repeat with four coins and then eight coins in the load pan. Record the number of coins and the measured arm length each time. Do not assume an unmeasured distance: the observations are used to investigate the balance rule.

The expected relationship is that a greater load can balance with a shorter load arm when the effort and effort arm stay unchanged. The comparison depends on considering the forces and their distances together, rather than comparing the forces alone.

Compare the products of coin count and arm length on the two sides. This models the relationship between effort multiplied by effort arm and load multiplied by load arm. Actual readings come from the arrangement being observed.

How can work and ramp calculations be checked?

A machine changes the force and distance needed for a task. Calculating work helps explain this trade-off. For a constant force, multiply the force by the displacement in its direction: $W = Fs$. Here $W$ is work, $F$ is force and $s$ is displacement along the force.

Which units should be used?

The SI unit of work is the joule (J). The SI unit of displacement is the metre (m). Use newtons for force and metres for displacement to obtain work in joules.

$1 J = 1 N \times 1 m$. One joule of work is done when a constant force of one newton displaces an object by one metre in the direction of that force.

The SI unit of energy is also the joule (J). Work transfers energy. If displacement is opposite to the applied force, the work done by that force is negative. Identify the force doing the work before assigning the sign.

How are force and displacement used?

Worked example 3. A constant force of 10 N moves an object through 1 m in the direction of the force. Calculate the work done.

Answer: Formula: $W = Fs$. Substitute: $W = 10\,\mathrm{N}\times1\,\mathrm{m} = 10\,\mathrm{J}$. The work done is 10 J, positive because force and displacement have the same direction.

Worked example 4. A goalkeeper applies a force of 200 N to stop a ball. Her hand moves back by 15 cm as the ball stops. Calculate the work done by the goalkeeper on the ball.

Answer: The applied force opposes the ball's displacement, so the displacement along the force is negative. Convert the distance: $15\,\mathrm{cm} = 0.15\,\mathrm{m}$, giving $s = -0.15\,\mathrm{m}$.

Formula: $W = Fs$. Substitute: $W = 200\,\mathrm{N}\times(-0.15\,\mathrm{m}) = -30\,\mathrm{J}$. The work done is −30 J. The negative sign describes the opposing directions.

Derivation: Why does a longer smooth ramp reduce effort?

Move a load slowly at constant speed up a ramp, ignoring friction. Let $Q$ be the load and $E$ the effort along the ramp, both in newtons. Let $h$ be the vertical height and $L$ the sloping length, both in metres.

1. Lifting the load vertically through height $h$ requires work $W = Qh$.
2. Moving it up the ramp requires work $W = EL$. The same load reaches the same height without a change in speed, so $EL = Qh$.
3. Divide by $Eh$, with non-zero effort and height: $\frac{Q}{E} = \frac{L}{h}$. Since mechanical advantage is load divided by effort, it equals sloping length divided by vertical height.

$\mathrm{MA} = \frac{L}{h}$. Increasing the sloping length for the same height increases mechanical advantage and reduces the effort. The smaller force acts through a greater distance, while the work remains the same.

How is the sloping length used in examples?

Worked example 5. A ramp raises an object over a step 30 cm high and has a horizontal width of 40 cm. Find its mechanical advantage, ignoring friction and moving the object at constant speed.

Answer: Let $h$ be the height, $b$ the horizontal width, $L$ the sloping length and $A$ the mechanical advantage. Formula: $L = \sqrt{h^2+b^2}$ for the right-angled triangle; $A = \frac{L}{h}$.

Substitute: $L = \sqrt{30^2+40^2}\,\mathrm{cm} = \sqrt{2500}\,\mathrm{cm} = 50\,\mathrm{cm}$. The sloping length is 50 cm.

Then $\mathrm{MA} = \frac{50}{30} = \frac{5}{3} \approx 1.67$. The centimetre units cancel. Mechanical advantage is about 1.67, with no unit.

Worked example 6. A cart is pulled slowly and steadily up a smooth plank about 1.5 m long to a height of about 0.5 m. Calculate the expected mechanical advantage using these approximate dimensions and ignoring friction.

Answer: The sloping length is 1.5 m and the vertical height is 0.5 m. Formula: $\mathrm{MA} = \frac{L}{h}$. Substitute: $\mathrm{MA} = \frac{1.5}{0.5} = 3$.

The expected mechanical advantage is about 3, with no unit. The load is about three times the effort in this model. This is a calculated prediction; spring balance readings provide the experimental comparison.

Glossary

• Energy — The ability to do work, allowing a force to bring about movement.
• Work — Work is done when a force moves an object in the direction of that force.
• Simple machine — A device that makes a task easier by changing the magnitude or direction of applied force.
• Effort — The force applied to a machine to act on its load.
• Load — The force that must be overcome by the operation of a machine.
• Fulcrum — The fixed point about which the bar of a lever turns.
• Lever — A rigid bar that can rotate about a fixed point called the fulcrum.
• Load arm — The distance from the fulcrum to where the load acts in the simple lever arrangement.
• Effort arm — The distance from the fulcrum to where the effort acts in the simple lever arrangement.
• Mechanical advantage — The ratio of load to effort, expressing how a machine changes the applied force.
• Pulley — A wheel with a groove that guides a rope used to move a load.
• Wheel and axle — A larger wheel connected to a smaller central shaft so that they turn together.
• Inclined plane — A sloping surface used to move a load between different levels.
• Wedge — A simple machine with sloping faces meeting at a thin edge or point.
• Screw — A simple machine with a winding inclined surface that advances when turned.

Common errors and misconceptions

• Misconception: A machine must be large and complicated. Correct: A machine is a device that helps us do work. A bottle opener, a needle and a doorknob are examples of small, familiar machines.
• Misconception: Every useful machine must reduce the size of the effort. Correct: Changing the direction of effort can also be useful. A fixed pulley allows a downward pull to raise a load.
• Misconception: The fulcrum must be exactly at the centre of a first-order lever. Correct: It must lie between the load and effort. Its position between them need not divide the bar into equal arms.
• Misconception: Mechanical advantage is effort divided by load. Correct: It is load divided by effort. For the simple balanced lever model, it also equals effort arm divided by load arm.
• Misconception: The load arm is the distance between load and effort. Correct: Each arm is measured from the fulcrum to the corresponding point where a force acts. Locate the fulcrum before measuring either arm.
• Misconception: Mechanical advantage should be written in newtons or metres. Correct: It has no unit. Express both quantities in the same units before forming either the force ratio or the arm ratio.
• Misconception: A lever creates energy when a smaller effort moves a larger load. Correct: Machines do not create energy. In the model that ignores friction, the useful work on the load equals the work supplied.
• Misconception: Kilograms measure force because masses appear in a seesaw calculation. Correct: Kilograms measure mass. Masses can replace the weights in this balance comparison because the same weight-per-kilogram factor cancels from both sides.

Exam-style questions with model answers

Q1. Define energy and a simple machine. [2 marks]

1. Energy is the ability to do work.
2. A simple machine is a device that makes a task easier by changing the magnitude or direction of the applied force.

Q2. A rigid bar turns about a fixed support to raise a load when effort is applied. Define the fulcrum, effort arm and load arm for this lever. [3 marks]

1. The fulcrum is the fixed point about which the rigid bar turns. In this arrangement, it is the point provided by the fixed support.
2. The effort arm is the distance from the fulcrum to the point on the bar where the effort acts.
3. The load arm is the distance from the fulcrum to the point on the bar where the load acts.

Q3. Classify three levers: the fulcrum is between load and effort in the first; the load is between fulcrum and effort in the second; the effort is between fulcrum and load in the third. Explain each classification. [3 marks]

1. The first lever is a first-order lever because its fulcrum lies between the load and effort. The middle part determines its order.
2. The second lever is a second-order lever because the load is the middle part, with fulcrum and effort on either side.
3. The third lever is a third-order lever because effort lies between fulcrum and load. Its classification follows the relative positions of these parts.

Q4. A rope passes over a fixed pulley. A person pulls one end downwards to raise a load on the other end. Ignoring friction, explain the change of direction, the force comparison, the mechanical advantage and the practical benefit. [4 marks]

1. The fixed pulley changes the direction of effort: pulling the free end of the rope downwards raises the load at the other end.
2. Ignoring friction, the effort and load have equal magnitudes, so this arrangement does not multiply the applied force.
3. Mechanical advantage is load divided by effort. Because the two forces are equal in magnitude, the mechanical advantage is one.
4. The practical benefit is convenience: the person can pull downwards rather than lift the load by applying an upward force directly.

Q5. Name the six simple machines and describe the basic structure of each. [6 marks]

1. A lever is a rigid bar that can turn about a fixed point. This turning point is called the fulcrum.
2. A wheel and axle has a larger wheel connected to a smaller central shaft. The connected parts turn together when operated.
3. A pulley is a wheel with a groove around its edge. The groove guides a rope used to move a load.
4. An inclined plane is a sloping surface between different levels. A load can move along it instead of being lifted vertically.
5. A wedge has sloping surfaces that meet at a thin edge or point. It is pushed into material to separate or pierce it.
6. A screw has an inclined surface wound around a cylinder. Its winding thread allows it to advance along its length when turned.

Q6. A seesaw has its fulcrum at C. Seats A and B are on one side, at 2 m and 1 m from C respectively. Seats D and E are on the other side, at 1 m and 2 m from C respectively. A 15 kg child sits at A. Where should a 30 kg child sit for balance? Ignore friction and the seesaw's own turning effect. Both children experience the same gravitational conditions. State the rule, explain the use of masses, form an equation, calculate the distance and name the seat. [5 marks]

1. The lever balance rule is load multiplied by load arm equals effort multiplied by effort arm. The two opposing turning effects must balance.
2. The children's weights are proportional to their masses under the same gravitational conditions. The common weight-per-kilogram factor therefore cancels from the two sides of the equation.
3. Let x be the distance of the 30 kg child from C. The balance equation becomes 15 kg × 2 m = 30 kg × x.
4. Dividing the product on the left by 30 kg gives x = (15 × 2 ÷ 30) m = 1 m.
5. The 30 kg child should sit at D, which is 1 m from C on the opposite side from A.

Q7. A balanced lever has an effort arm of 2 m and a load arm of 1 m. Ignore the bar's weight and friction, and assume that the forces act at right angles to the bar. State the formula for mechanical advantage, calculate it, explain its unit and interpret the result. [4 marks]

1. For this simple balanced lever, mechanical advantage equals effort arm divided by load arm. It also equals load divided by effort.
2. Substituting the given arm lengths gives mechanical advantage = 2 m ÷ 1 m = 2.
3. Mechanical advantage has no unit because the metre units used for the two arm lengths cancel when the lengths are divided.
4. The result means that the load force is twice the effort force. The longer effort arm allows the smaller effort to balance the larger load.

Q8. A cart is pulled slowly and steadily to the same height using smooth planks. A longer plank gives a less steep slope. Describe the machine, name a device for comparing the pulling forces, explain the changes in force and distance, and relate the result to work when friction is ignored. [5 marks]

1. The plank acts as an inclined plane, a sloping surface along which the cart can move to a higher level instead of being lifted vertically.
2. A spring balance attached to the cart can compare the pulling forces. Its reading indicates the force required during the slow, steady pull.
3. The force required decreases when the plank is made less steep, while the cart and the final height remain the same.
4. The longer plank gives a longer path to the same height. The smaller pulling force must therefore act through a greater distance.
5. Ignoring friction, the work required for the same lift remains the same. The inclined plane changes the combination of force and distance; it does not create energy.

Key takeaways

• Energy is the ability to do work; simple machines help by changing the magnitude or direction of applied force.
• The six simple machines are the lever, wheel and axle, pulley, inclined plane, wedge and screw.
• A lever turns about a fulcrum; its load arm and effort arm are measured from that turning point.
• The middle part identifies lever order: fulcrum for first order, load for second order and effort for third order.
• Mechanical advantage is load divided by effort and has no unit when matching force units are used.
• For the simple balanced lever model, load multiplied by load arm equals effort multiplied by effort arm.
• A fixed pulley changes effort direction; a smooth inclined plane allows a smaller force over a longer route.
• Machines do not create energy. Ignoring friction, useful work done on the load equals the work supplied to the machine.

Test yourself

What is the difference between effort and load?

Effort is the force applied to a machine. Load is the force that the machine must overcome.

From which point are both arms of a lever measured?

Both arms are measured from the fulcrum, the fixed point about which the lever turns.

A lever has the load between fulcrum and effort. What is its order?

It is a second-order lever because the load is the middle part.

Why can a fixed pulley be useful even with mechanical advantage equal to one?

It changes the direction of effort, allowing a downward pull to raise the load.

Why must the force units match when calculating mechanical advantage?

Matching units allow a valid force comparison and cancel in the ratio, leaving mechanical advantage without a unit.

What happens to the required effort when the effort arm increases while load and load arm stay unchanged?

The required effort decreases in the simple lever model because effort multiplied by effort arm must balance the unchanged load product.

What changes when a smooth ramp to the same height becomes longer and less steep?

The required force decreases, but it must act through a greater distance along the ramp.

Which parts distinguish a wheel and axle from a pulley?

A wheel and axle has connected parts that turn together. A pulley has a grooved wheel that guides a rope.