Application of Forces and Energy Transfer - Study Notes

Key Concepts

Contact and Non-Contact Forces

A force is defined as a push or a pull. Forces can change an object in the following ways: (1) change its size or shape; (2) alter its direction of motion; (3) set a stationary object in motion; (4) increase or decrease the speed of a moving object; (5) stop a moving object that is already in motion. The SI unit of force is the Newton (N).

Contact Forces:

• Forces that act when objects are physically touching each other
• The force is transmitted through direct physical contact between surfaces
• Examples include:
  • Friction - resistance when surfaces slide against each other
  • Normal force - support force perpendicular to a surface
  • Tension - pulling force through a string, rope, or cable
  • Air resistance (drag) - friction from air molecules
  • Applied force - push or pull directly applied to an object

Non-Contact Forces:

• Forces that act at a distance without physical contact
• The force acts through a field (gravitational, magnetic, or electric)
• Examples include:
  • Gravitational force - attraction between masses (e.g., Earth pulling objects down)
  • Magnetic force - attraction or repulsion between magnets
  • Electrostatic force - attraction or repulsion between charged objects

Friction

• A contact force that opposes motion between two surfaces
• Always acts in the opposite direction to the motion (or intended motion)
• Caused by microscopic bumps and irregularities on surfaces that interlock
• Factors affecting friction:
  • Type of surfaces - rougher surfaces produce more friction
  • Normal force - greater force pressing surfaces together increases friction
  • Note: Friction does NOT depend on the surface area in contact
  • Note: Friction does NOT depend on speed

Types of Friction:

• Static friction - prevents stationary objects from starting to move
• Kinetic (sliding) friction - opposes objects already in motion
• Rolling friction - when objects roll (usually less than sliding friction)

Advantages of Friction:

• Allows us to walk without slipping
• Enables vehicles to grip the road and brake
• Allows us to hold objects
• Enables writing with pen on paper

Disadvantages of Friction:

• Causes wear and tear on moving parts
• Produces unwanted heat
• Wastes energy in machinery
• Slows down motion

Reducing Friction:

• Use lubricants (oil, grease) to separate surfaces
• Polish surfaces to make them smoother
• Use ball bearings to change sliding friction to rolling friction
• Use streamlined shapes to reduce air resistance
• Use wheels instead of dragging objects

Increasing Friction:

• Use rougher surfaces (e.g., treads on shoes)
• Increase the force pressing surfaces together
• Add materials with high friction (e.g., rubber)
• Remove lubricants

Pressure

• Pressure is the force acting per unit area
• Formula: Pressure = Force / Area or P = F / A
• SI Unit: Pascal (Pa) or Newton per square metre (N/m²)
• 1 Pa = 1 N/m²

Key Principles:

• For the same force, smaller area produces higher pressure
• For the same area, larger force produces higher pressure
• Pressure acts equally in all directions at a given point in a fluid

Applications of High Pressure:

• Sharp knife - small cutting edge area concentrates force
• Thumbtacks/drawing pins - pointed end has very small area
• Needles - fine point creates high pressure for piercing
• High-heeled shoes - small heel area creates high pressure on ground

Applications of Low Pressure:

• Wide tyres - large area spreads weight to prevent sinking
• Snowshoes - large area prevents sinking in snow
• Camel’s feet - wide feet spread weight on sand
• Wide straps - distribute force to reduce discomfort
• Foundations of buildings - wide base spreads weight

Pressure in Liquids:

• Increases with depth (more liquid above exerts more weight)
• Acts equally in all directions at the same depth
• Pressure at bottom = Pressure at surface + (density × gravity × depth)
• Dams are thicker at the bottom to withstand greater pressure

Speed and Velocity

Speed:

• How fast an object is moving
• A scalar quantity (has magnitude only, no direction)
• Formula: Speed = Distance / Time or v = d / t
• SI Unit: metres per second (m/s) or kilometres per hour (km/h)
• An object moving at constant speed travels the same distance in every equal unit of time — its speed does not change throughout the journey.

Average Speed:

• Total distance travelled divided by total time taken
• Formula: Average speed = Total distance / Total time
• Used when speed varies during a journey

Velocity:

• Speed in a specific direction
• A vector quantity (has both magnitude and direction)
• Formula: Velocity = Displacement / Time
• SI Unit: metres per second (m/s) in a specified direction
• Two objects can have the same speed but different velocities if moving in different directions

Displacement vs Distance:

• Distance - total length of path travelled (scalar)
• Displacement - straight-line distance from start to end point with direction (vector)

Conversion:

• To convert km/h to m/s: divide by 3.6
• To convert m/s to km/h: multiply by 3.6
• Example: 36 km/h = 36 ÷ 3.6 = 10 m/s

Speed of Sound

Not in Sec 2 2026: The speed of sound and its dependence on medium and temperature are not part of the 2026 Sec 2 syllabus. Sound and wave properties (including speed of sound) are covered in Sec 3/4 Physics. This section is retained here for general interest but will not be assessed at Sec 2.

The speed of sound depends on the medium it travels through:

• Sound travels faster in denser mediums (e.g. seawater) than in less dense mediums (e.g. air) because molecules are packed more closely, allowing energy to be transferred more rapidly through collisions.
• Higher temperatures increase the speed of sound because particles have greater kinetic energy, vibrate more rapidly, and collide more frequently, transferring energy faster.
• Example: Sound travels at approximately 343 m/s in air at 20 °C but about 1500 m/s in seawater.

Distance-Time and Speed-Time Graphs

Distance-Time Graph:

• y-axis = distance, x-axis = time

• Horizontal line = stationary (object is not moving)

• Straight line with positive gradient = constant speed

• Steeper gradient = faster speed

• Gradient of a distance-time graph = speed

  $$\text{Speed} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in distance}}{\text{change in time}}$$

Speed-Time Graph:

• y-axis = speed, x-axis = time

• Horizontal line = constant speed (no acceleration)

• Straight line going up = constant acceleration

• Straight line going down = constant deceleration

• Area under a speed-time graph = distance travelled

  $$\text{Distance} = \text{Area under speed-time graph}$$

Worked example — area under speed-time graph:

• A car travels at 20 m/s for 5 seconds. Find the distance travelled.
• Area under graph = 20 × 5 = 100 m

Work Done and Energy Transfer

Work Done:

• Work is done when a force moves an object in the direction of the force
• It is a measure of energy transferred
• Formula: Work done = Force × Distance moved in direction of force
• W = F × d
• SI Unit: Joule (J)
• 1 Joule = 1 Newton × 1 metre (1 J = 1 N⋅m)

Conditions for Work to be Done:

1. A force must be applied
2. The object must move
3. Movement must be in the direction of the force (or have a component in that direction)

No Work Done When:

• Force is applied but object doesn’t move (pushing a wall)
• Object moves but no force acts in direction of motion (object sliding on frictionless surface after push ends)
• Force is perpendicular to motion (carrying bag while walking horizontally - no vertical motion)

Energy:

• The ability to do work
• Measured in Joules (J)
• Energy exists in many forms
• Can be transferred from one form to another
• Can be transferred from one object to another

Forms of Energy:

• Kinetic energy - energy of moving objects
• Gravitational potential energy - energy due to position in a gravitational field
• Elastic potential energy - energy stored in stretched or compressed objects
• Chemical energy - energy stored in chemical bonds (food, fuels, batteries)
• Thermal (heat) energy - energy due to temperature; kinetic energy of particles
• Light energy - energy carried by light waves
• Sound energy - energy carried by sound waves
• Electrical energy - energy carried by moving electric charges
• Nuclear energy - energy stored in atomic nuclei

Energy Transfers:

• When work is done, energy is transferred
• Energy can change from one form to another
• Examples of energy transfers:
  • Falling object: gravitational potential → kinetic
  • Electric motor: electrical → kinetic
  • Light bulb: electrical → light + thermal
  • Photosynthesis: light → chemical
  • Battery in circuit: chemical → electrical
  • Friction: kinetic → thermal

Conservation of Energy

Principle of Conservation of Energy:

• Energy cannot be created or destroyed
• Energy can only be converted from one form to another
• Energy can be transferred from one object to another
• The total amount of energy in a closed system remains constant

Useful and Wasted Energy:

• Not all energy is converted to the desired form
• Useful energy - converted to the intended form (e.g., kinetic energy from a car engine)
• Wasted energy - converted to unwanted forms, usually heat and sound
• Total energy input = Useful energy output + Wasted energy output

Energy Efficiency:

• Measures how much input energy is converted to useful output energy
• Formula: Efficiency = (Useful energy output / Total energy input) × 100%
• Can also be expressed as: Efficiency = (Useful power output / Total power input) × 100%
• Efficiency is expressed as a percentage (%) or as a decimal between 0 and 1
• No machine is 100% efficient (some energy always wasted as heat/sound due to friction)

Examples of Energy Conservation:

• Pendulum: potential energy ⇄ kinetic energy (back and forth)
• Roller coaster: gravitational potential energy → kinetic energy → potential energy
• Stretched spring released: elastic potential → kinetic
• At the highest point of a swing: maximum potential, zero kinetic
• At the lowest point of a swing: maximum kinetic, minimum potential

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Important Definitions

Contact Force: A force that acts only when two objects are physically touching each other.

Non-Contact Force: A force that acts at a distance without the objects needing to touch.

Friction: A force that opposes motion between two surfaces that are in contact with each other.

Pressure: The force acting per unit area; calculated as P = F/A, measured in Pascals (Pa) or N/m².

Speed: The distance travelled per unit time; a scalar quantity measured in m/s or km/h.

Average Speed: The total distance travelled divided by the total time taken.

Velocity: The rate of change of displacement; speed in a specific direction; a vector quantity measured in m/s.

Displacement: The straight-line distance from the starting point to the ending point, measured in a specific direction.

Work Done: The product of force and the distance moved in the direction of the force; measured in Joules (J); W = F × d.

Energy: The ability or capacity to do work; measured in Joules (J).

Kinetic Energy: The energy possessed by an object due to its motion.

Gravitational Potential Energy: The energy possessed by an object due to its position in a gravitational field (its height above the ground).

Conservation of Energy: The principle that energy cannot be created or destroyed, only converted from one form to another or transferred from one object to another.

Efficiency: The ratio of useful energy output to total energy input, expressed as a percentage.

Scalar Quantity: A quantity that has magnitude (size) only, with no direction (e.g., speed, distance, energy, mass, temperature).

Vector Quantity: A quantity that has both magnitude and direction (e.g., velocity, displacement, force, acceleration).

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Worked Examples

Example 1: Calculating Pressure

Question: A brick has dimensions 20 cm × 10 cm × 5 cm and weighs 30 N. Calculate the pressure exerted when: (a) The brick rests on its largest face (b) The brick rests on its smallest face

Solution:

(a) Largest face:

Step 1: Identify the largest face area

• Largest face = 20 cm × 10 cm = 200 cm²

Step 2: Convert area to m²

• 200 cm² = 200 ÷ 10,000 = 0.02 m²
• (Remember: 1 m² = 10,000 cm²)

Step 3: Apply pressure formula

• Pressure = Force / Area
• P = 30 N / 0.02 m²
• P = 1,500 Pa or 1,500 N/m²

(b) Smallest face:

Step 1: Identify the smallest face area

• Smallest face = 10 cm × 5 cm = 50 cm²

Step 2: Convert area to m²

• 50 cm² = 50 ÷ 10,000 = 0.005 m²

Step 3: Apply pressure formula

• Pressure = Force / Area
• P = 30 N / 0.005 m²
• P = 6,000 Pa or 6,000 N/m²

Conclusion: The pressure is 4 times greater when resting on the smallest face because the area is 4 times smaller.

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Example 2: Speed and Average Speed Calculation

Question: A car travels from Town A to Town B, a distance of 120 km, in 2 hours. It then travels from Town B to Town C, a distance of 80 km, in 1 hour. Calculate: (a) The speed for each part of the journey (b) The average speed for the entire journey

Solution:

(a) Speed for each part:

For A to B:

• Speed = Distance / Time
• Speed = 120 km / 2 h
• Speed = 60 km/h

For B to C:

• Speed = Distance / Time
• Speed = 80 km / 1 h
• Speed = 80 km/h

(b) Average speed for entire journey:

Step 1: Calculate total distance

• Total distance = 120 km + 80 km = 200 km

Step 2: Calculate total time

• Total time = 2 h + 1 h = 3 h

Step 3: Calculate average speed

• Average speed = Total distance / Total time
• Average speed = 200 km / 3 h
• Average speed = 66.7 km/h (or 66⅔ km/h)

Important note: Average speed ≠ average of the two speeds!

• (60 + 80) / 2 = 70 km/h ✗ (This is WRONG)
• Must use total distance / total time ✓

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Example 3: Work Done and Energy Transfer

Question: A student pushes a trolley with a force of 50 N for a distance of 12 m along a horizontal corridor. (a) Calculate the work done by the student. (b) If the trolley has a mass of 20 kg and starts from rest, explain the energy transfers that occur. © If only 400 J of energy is converted to kinetic energy of the trolley, calculate the efficiency of the energy transfer.

Solution:

(a) Work done:

Step 1: Write the formula

• Work done = Force × Distance
• W = F × d

Step 2: Substitute values

• W = 50 N × 12 m
• W = 600 J

Answer: The student does 600 J of work on the trolley.

(b) Energy transfers:

• The student’s muscles contain chemical energy (from food)
• Chemical energy is converted to kinetic energy as the student pushes
• This kinetic energy is transferred to the trolley through the applied force
• The trolley gains kinetic energy and moves
• Some energy is converted to thermal (heat) energy due to friction between the trolley wheels and floor
• Some energy may be converted to sound energy

© Efficiency:

Step 1: Identify useful and total energy

• Useful energy output = 400 J (kinetic energy of trolley)
• Total energy input = 600 J (work done by student)

Step 2: Apply efficiency formula

• Efficiency = (Useful energy output / Total energy input) × 100%
• Efficiency = (400 J / 600 J) × 100%
• Efficiency = 0.667 × 100%
• Efficiency = 66.7% or 67% (to 2 significant figures)

Step 3: Account for wasted energy

• Wasted energy = 600 J - 400 J = 200 J
• This 200 J is converted to heat (due to friction) and sound

Answer: The efficiency of the energy transfer is 67%. 33% of the energy is wasted as heat and sound.

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Common Mistakes to Avoid

1. Confusing contact and non-contact forces:

   • ✗ Thinking gravity only acts when objects touch the ground
   • ✓ Gravity acts on all objects with mass, whether touching ground or not

2. Misunderstanding friction:

   • ✗ Thinking friction depends on surface area in contact
   • ✓ Friction depends on the types of surfaces and the normal force only
   • ✗ Thinking friction always acts downward or in one direction
   • ✓ Friction always acts opposite to the direction of motion (or intended motion)

3. Pressure calculations:

   • ✗ Forgetting to convert cm² to m² (must divide by 10,000)
   • ✗ Using diameter instead of area
   • ✗ Confusing force with pressure
   • ✓ Always use P = F/A with SI units (N and m²)

4. Speed vs. Velocity:

   • ✗ Using the terms interchangeably
   • ✓ Speed is scalar (no direction), velocity is vector (includes direction)
   • ✗ Thinking an object moving in a circle at constant speed has constant velocity
   • ✓ Velocity changes when direction changes, even if speed is constant

5. Average speed calculations:

   • ✗ Taking the average of two different speeds: (v₁ + v₂)/2
   • ✓ Must use: Average speed = Total distance / Total time

6. Work done misconceptions:

   • ✗ Thinking work is done when holding a heavy object still
   • ✓ Work requires movement in the direction of the force
   • ✗ Thinking work is done when carrying a bag horizontally at constant height
   • ✓ No work done in direction of force (vertical) because no vertical movement

7. Unit conversions:

   • ✗ Forgetting to convert km/h to m/s (must divide by 3.6)
   • ✗ Mixing units in calculations (e.g., using km and seconds together)
   • ✓ Always convert to SI units before calculating

8. Energy conservation:

   • ✗ Thinking energy can be lost or disappear
   • ✓ Energy is always conserved; it just changes form
   • ✗ Forgetting to account for “wasted” energy (heat, sound)
   • ✓ Total input energy = useful output + wasted energy (always)

9. Efficiency calculations:

   • ✗ Using total output instead of useful output
   • ✗ Calculating efficiency greater than 100%
   • ✓ Efficiency can never exceed 100% (and is usually much less)
   • ✗ Forgetting to multiply by 100 to convert to percentage

10. Direction of forces:

    • ✗ Drawing friction arrows in the direction of motion
    • ✓ Friction always opposes motion
    • ✗ Confusing weight (always downward) with normal force (perpendicular to surface)

11. Rounding errors:

• ✗ Giving an answer with too many or too few significant figures (e.g. writing 5.188 m/s)
• ✓ Unless instructed otherwise, round final answers to 3 significant figures (e.g. 5190 m/s)

12. Omitting units from final answers:

• ✗ Writing a bare number such as “1500” with no unit
• ✓ Every calculated answer must include the correct SI unit (e.g. 1500 m/s, 200 Pa)

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Exam Tips

Keywords and Phrases to Use for Full Marks:

For Forces:

• “The force acts in the direction of…” or “opposite to…”
• “Contact force requires physical touch between surfaces”
• “Non-contact force acts at a distance through a field”
• “Friction opposes motion” or “acts in the opposite direction to motion”
• Always specify the direction when describing forces

For Pressure:

• “Pressure is force per unit area” or “force acting per unit area”
• “Pressure = Force / Area”
• “Small area produces high pressure” (explain why using the formula)
• “Large area produces low pressure” (explain why using the formula)
• Always include units (Pa or N/m²)

For Speed/Velocity:

• “Speed is the distance travelled per unit time”
• “Velocity is speed in a specific direction”
• “Average speed = Total distance / Total time”
• Always state direction when discussing velocity
• Include units (m/s or km/h)

For Work Done:

• “Work is done when a force moves an object in the direction of the force”
• “Work done = Force × Distance moved in direction of force”
• “No work is done if there is no movement” or “if force is perpendicular to motion”
• Include units (Joules, J)

For Energy:

• Name the specific forms of energy (kinetic, gravitational potential, chemical, etc.)
• “Energy is transferred from… to…”
• “Energy is converted from [form 1] to [form 2]”
• “According to the principle of conservation of energy…”
• “Useful energy output + Wasted energy = Total energy input”

For Efficiency:

• “Efficiency = (Useful energy output / Total energy input) × 100%”
• “No machine is 100% efficient because…”
• “Energy is wasted as heat (due to friction) and sound”
• Express as a percentage with % symbol

Answering Strategies:

1. Define before explaining: If asked to explain a concept, start with a definition
2. Show all working: Even if you can do mental math, write all steps for partial credit
3. Include units: Every numerical answer must have the correct unit
4. Use formulas: Write the formula first, then substitute values, then calculate
5. Draw diagrams when appropriate: Especially for forces (arrows showing direction and magnitude)
6. Be specific: Instead of “it moves faster,” say “the speed increases from X m/s to Y m/s”
7. Compare using numbers: When comparing, use actual calculated values
8. For energy transfers: Always mention both the form converted FROM and the form converted TO
9. Circle or underline final answers: Makes them easy for examiners to find
10. Check reasonableness: Does your answer make sense? (e.g., efficiency > 100% is impossible)
11. Significant figures: Unless the question states otherwise, give all calculated answers to 3 significant figures. Check by counting from the first non-zero digit.

For Calculation Questions:

• Write: Formula → Substitution → Answer with unit
• Example format:

  Speed = Distance / Time
        = 100 m / 5 s
        = 20 m/s
  

For Explanation Questions:

• Use structured points (not continuous prose)
• Include scientific reasoning, not just observations
• Link cause and effect clearly

For Sound Speed Questions:

Not in Sec 2 2026: Speed of sound questions are not assessed at Sec 2. This exam tip applies to Sec 3/4 Physics only.

When asked to explain why sound travels faster or slower in a given medium:

• State whether the medium is denser or less dense (or hotter/cooler).
• Link density to molecular spacing: denser → molecules closer together.
• Link molecular spacing to energy transfer: closer molecules → more frequent collisions → faster transfer of sound energy.
• Conclude: therefore sound travels faster. Example answer: “Seawater is denser than air; its molecules are closer together. Sound energy is transferred through molecular collisions, so more frequent collisions in seawater result in a higher speed of sound.”

Common Mark-Earning Phrases:

• “Due to conservation of energy…”
• “Energy is transferred from [form] to [form]…”
• “Friction converts kinetic energy to thermal energy…”
• “As pressure increases, [state effect]…”
• “For the same force, reducing area increases pressure because…”
• “Work is done because a force causes the object to move in the direction of the force”

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Quick Summary

Contact vs Non-Contact Forces:

• ✓ Contact forces require touching; friction, tension, normal force, air resistance
• ✓ Non-contact forces act at a distance; gravitational, magnetic, electrostatic

Friction:

• ✓ Opposes motion between surfaces; depends on surface type and normal force, NOT area
• ✓ Can be reduced (lubricants, smooth surfaces, ball bearings) or increased (rough surfaces, increased force)

Pressure:

• ✓ P = F/A measured in Pa or N/m²; force per unit area
• ✓ Small area = high pressure; large area = low pressure (for same force)
• ✓ Convert cm² to m² by dividing by 10,000

Speed and Velocity:

• ✓ Speed = Distance/Time (scalar, no direction); Velocity = speed with direction (vector)
• ✓ Average speed = Total distance / Total time (NOT the average of speeds)
• ✓ Convert km/h to m/s: divide by 3.6; m/s to km/h: multiply by 3.6

Work Done:

• ✓ Work = Force × Distance (in direction of force), measured in Joules (J)
• ✓ No work done if: no movement, force perpendicular to motion, or no force applied
• ✓ Work done = Energy transferred

Energy Forms and Transfers:

• ✓ Main forms: kinetic, gravitational potential, elastic potential, chemical, thermal, light, sound, electrical, nuclear
• ✓ Energy is transferred when work is done; converted from one form to another
• ✓ Energy diagrams show conversions using arrows (→)

Conservation of Energy:

• ✓ Energy cannot be created or destroyed, only converted or transferred
• ✓ Total energy in a closed system remains constant
• ✓ Total input = Useful output + Wasted output (usually as heat and sound)

Efficiency:

• ✓ Efficiency = (Useful energy output / Total energy input) × 100%
• ✓ Always less than 100%; some energy always wasted as heat due to friction
• ✓ Higher efficiency means less energy wasted

Key Formulas to Memorize:

• ✓ Pressure: P = F/A
• ✓ Speed: v = d/t
• ✓ Work: W = F × d
• ✓ Efficiency: η = (Useful output / Total input) × 100%

Units to Remember:

• ✓ Pressure: Pa or N/m²; Speed/Velocity: m/s or km/h; Work/Energy: J; Force: N; Distance: m; Time: s

Always Remember:

• ✓ State direction for velocity and forces
• ✓ Show all working with units
• ✓ Account for wasted energy in all real processes