Application of Forces and Energy Transfer - Study Notes

Key Concepts

Contact and Non-Contact Forces

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)

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

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:

A force must be applied
The object must move
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

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).

Diagrams and Structures

Diagram 1: Contact vs Non-Contact Forces

To draw:

Draw a table with two columns labeled “Contact Forces” and “Non-Contact Forces”
Under Contact Forces, draw:
- A hand pushing a box (label: Applied Force)
- Two surfaces with arrows pointing opposite to each other between them (label: Friction)
- A book on a table with upward arrow (label: Normal Force)
Under Non-Contact Forces, draw:
- Earth and a falling apple with downward arrow (label: Gravitational Force)
- Two magnets with arrows showing attraction or repulsion (label: Magnetic Force)
- Two charged spheres with arrows between them (label: Electrostatic Force)

Diagram 2: Friction on an Inclined Surface

To draw:

Draw a sloped surface (incline) at approximately 30°
Draw a rectangular block on the slope
Draw and label these arrows:
- Downward arrow from center of block (Weight/Gravitational Force)
- Arrow perpendicular to slope pointing away from surface (Normal Force)
- Arrow pointing up the slope (Friction Force)
- Arrow pointing down the slope (Component of weight causing motion)
Note: Friction always opposes the direction of motion or intended motion

Diagram 3: Pressure Applications

To draw:

High Pressure Example (Knife):
- Draw a knife blade cutting into a tomato
- Label the sharp edge as “Small area”
- Show arrow labeled “Force” pointing downward
- Write: “Small area → High pressure → Easy cutting”
Low Pressure Example (Snowshoe):
- Draw a foot wearing a wide snowshoe on snow surface
- Label the wide base as “Large area”
- Show arrow labeled “Weight” pointing downward
- Write: “Large area → Low pressure → Prevents sinking”

Diagram 4: Speed-Time Graph

To draw:

Draw x-axis labeled “Time (s)” and y-axis labeled “Speed (m/s)”
Mark a horizontal line showing constant speed
Mark a line with positive slope showing acceleration (increasing speed)
Mark a line with negative slope showing deceleration (decreasing speed)
Note: The distance travelled equals the area under the speed-time graph

Diagram 5: Energy Transfer in a Pendulum

To draw:

Draw a pendulum at five positions (swing left → bottom → swing right → bottom → swing left)
Label Position A (highest left): “Maximum GPE, Zero KE”
Label Position B (quarter down): “GPE decreasing, KE increasing”
Label Position C (bottom center): “Minimum GPE, Maximum KE”
Label Position D (quarter up right): “GPE increasing, KE decreasing”
Label Position E (highest right): “Maximum GPE, Zero KE”
Show arrows indicating energy conversion: GPE ⇄ KE
Note: Total energy (GPE + KE) remains constant throughout

Diagram 6: Energy Flow Diagram (Sankey Diagram)

To draw:

For a light bulb: Draw a wide arrow entering from left labeled “100 J Electrical Energy Input”
Split the arrow into two:
- Thinner arrow going straight: “10 J Light Energy (Useful)”
- Wider arrow going downward: “90 J Heat Energy (Wasted)”
Write: “Efficiency = (10/100) × 100% = 10%”
Note: Width of arrows represents amount of energy

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.

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 ✓

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

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.

Common Mistakes to Avoid

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

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:

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

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

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”

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