Forces

Question 1

Average Speed

Answer 1

Distance over time for the entire region of interest.

Question 2

Free-Fall

Answer 2

the only force acting on the object is the force of gravity.

Question 3

Projectile Motion

Answer 3

Projectile Motion:

• Motion of an object fired from a point with only gravity acting on it.
• Key Concepts:
  • Time of flight: How long the projectile is in the air.
  • Maximum height: Height where the projectile is momentarily at rest.
  • Range: Horizontal distance travelled.
• Horizontal Motion:
  
  • Constant velocity (no acceleration).
• Vertical Motion:
  
  • Constant acceleration due to gravity.

Types of Projection:

1. Vertical projection: Straight up or down.
2. Horizontal projection: Fired horizontally.
3. Projection at an angle: Fired at an angle to the horizontal.

Problem-Solving Tips:

• Split motion into horizontal and vertical components. (Suvat both)
• Analyse each component separately.

Effect of Air Resistance on Projectiles:

• Air resistance decreases the horizontal component of a projectile’s velocity.
• This reduces:
  
  • The range (horizontal distance travelled).
  • The maximum height reached.
• Compared to a scenario with no air resistance, both range and height are reduced.

Question 4

Instantaneous Speed

Answer 4

The exact speed of an object at a specific given point.
(Draw tangent)

Question 5

Reaction Time

Answer 5

The time taken to process a stimulus and trigger a response to it.
It is affected by alcohol, drugs and tiredness.

Question 6

Archimedes’ Principle

Answer 6

• The upwards force acting on an object submerged in a fluid, is equal to the weight of the fluid it displaces.
• (Upthrust = 𝜌_liquid 𝑉_object 𝑔)
• (Upthrust = (h₂ - h₁)𝜌gA)

Question 7

Centre of Mass

Answer 7

Centre of Gravity (Mass):

• The single point where an object’s mass can be considered to act.
• An object will topple if its centre of mass moves past its pivot (direction of moment changes).

Stability:

• Stability depends on the position of the centre of mass:
  
  • An object is stable if its centre of mass lies above its base.
  • An object topples if its centre of mass moves outside its base.
• Wider base and lower centre of mass increase stability.
• Narrower base and higher centre of mass make an object more likely to topple.

Centre of Mass Properties:

• Does not depend on the gravitational field.
• Can lie inside or outside the body.
• Can shift depending on the shape of the body.

Question 8

Couple

Answer 8

• A couple consists of a pair of equal and opposite coplanar forces that act to produce rotation only.
• A couple has the following characteristics:
  
  • Equal in magnitude
  • Opposite in direction
  • Perpendicular to the distance between them
  • Zero acceleration (resultant force)

Question 9

Drag

Answer 9

Drag Forces:
- Forces that oppose motion of an object moving through a fluid (gas or liquid).

• Characteristics:
  
  • Act in the opposite direction to motion.
  • Slow down objects or keep them moving at a constant speed.
  • Convert kinetic energy into heat and sound.

Factors of drag
- Cross-sectional area in contact with fluid
- Density of the fluid.
- Speed of the object (d∝v²)

(Factors for air resistance)
- Altitude.
- Temperature.
- Humidity.

Question 10

Equilibrium

Answer 10

Equilibrium:

• For an object to be in equilibrium:
  
  • The resultant force must be zero.
  • The resultant moment must be zero.
• An object in equilibrium will:
  
  • Remain at rest or move at a constant velocity.
  • Not rotate.

Coplanar Forces in Equilibrium:

• Coplanar forces can be represented by closed vector triangles.
• When vectors are joined, they form a closed path.
• In exam questions, diagrams are often drawn to scale – use a ruler for accuracy.

Question 11

Free-Body Diagram

Answer 11

Free Body Diagrams:

• Used to model forces acting on an object.
• Each force is represented as a vector arrow:
  
  • Scaled to the magnitude of the force.
  • Points in the direction the force acts.
  • Labelled with the force’s name.

Uses of Free Body Diagrams:

• Identify which forces act in which plane.
• Resolve the net force in a specific direction.

Calculating Net Force:

• Use labelled angles and magnitudes.
• Resolve each force into horizontal and vertical components.

Question 12

Moment of Force

Answer 12

Moments:
- A moment is the turning effect of a force, causing objects to rotate about a pivot.

• Formula:
  
  • Moment (N m) = Force (N) × Perpendicular distance from the pivot (m).
• SI Unit: Newton metres (N m) to the pivot.**

Key Points:
- The pivot is the point about which an object rotates.
- Anything can act as a pivot (and create simultaneous equations)
- Perpendicular distance is crucial: only the component of force perpendicular to the pivot creates a moment.
- Drawing forces on a diagram helps identify which forces contribute to the turning effect.
- Choosing a pivot can simplify calculations by eliminating the reaction force at that point.

Question 13

Newton’s Second Law

Answer 13

• The resultant force equals the rate of change of momentum.
• The change in momentum is in the same direction as the resultant force.

Effects of Resultant Force:

1. Along the direction of motion:
   
   • Speeds up (accelerates) or slows down (decelerates) the body.
2. At an angle to the motion:
   
   • Changes the direction of the body.

Question 14

Principle of Moments

Answer 14

• For an object to be in equilibrium, the sum of the clockwise moments about a point must equal the sum of the anticlockwise moments about the same point.
• Note: The object can be spinning while in equilibrium.

Question 15

Terminal Velocity

Answer 15

Terminal Velocity:

• Occurs when the resistive force (drag) equals the driving force (weight).
• Initially: Only weight (W = mg) acts, causing acceleration.
• As velocity increases, drag force increases, reducing resultant force and acceleration.
• When drag force = weight,
  resultant force = 0,
  and acceleration stops
  – object reaches terminal velocity.

• Velocity-time graph:
  • Acceleration (gradient) decreases until it reaches zero at terminal velocity.
• Parachute deployment:
  
  • Causes deceleration to a lower terminal velocity, reducing landing impact.
• Misconception: Skydivers do not move upwards when parachutes deploy – they simply decelerate.

Question 16

Conservation of Energy

Answer 16

Principle of Conservation of Energy:

• Energy cannot be created or destroyed, only transferred between forms.
• The total energy in a closed system remains constant.

Energy Dissipation:

• Wasted energy is lost to the surroundings, often as heat, light, or sound.
• Energy not transferred to useful stores is considered wasted.

Energy Transfers and Stores:

• Examples:
  
  • Gravitational potential energy → kinetic energy (falling object).
  • Chemical energy → electrical and light energy (battery).
  • Elastic potential energy → kinetic energy (spring).
• Work done against resistive forces (e.g., friction) also dissipates energy.

Question 17

Elastic Potential Energy

Answer 17

Work and Elastic Potential Energy:

• Work is done to stretch a material.
• Before the elastic limit, all work done is stored as elastic potential energy (while obeying Hooke’s Law).
• Beyond the elastic limit, calculate the area under the graph by splitting it into segments and summing the areas.

Elastic Potential Energy (EPE):

• Energy stored in a material (e.g., spring) when stretched or compressed.
• Calculated from the area under the force-extension graph (within the limit of proportionality).

Danger of Breaking Wire:

• If a wire under stress breaks, its elastic potential energy converts to kinetic energy:
  
  • EPE = KE → ½ kx² = ½ mv².
  • Speed (v) is proportional to extension (x): greater extension = greater speed on breaking.

Question 18

Hooke’s Law

Answer 18

Hooke’s Law:

• The extension of an elastic object is directly proportional to the force applied, up to the limit of proportionality.

Key Points:

• Force constant (k): Measures stiffness; larger k = stiffer material.
• Applies to both extensions (increase in length) and compressions (decrease in length).
• (1/K _total for springs in series)
• Force-extension graph:
  
  • Gradient = force constant (k) if force is on the y-axis and extension on the x-axis.
  • If axes are swapped, gradient = 1/k.

Question 19

Types of deformation

Answer 19

Deformation:

• Forces can change the motion, size, or shape of a body.
• Tensile forces: Stretch a body (e.g., pulling a spring).
• Compressive forces: Compress a body (e.g., pushing a spring).

Example:

• A spring extends under tensile force and compresses under compressive force.

Question 20

Tensile Stress and Tensile Strain

Answer 20

Tensile Stress:

• Defined as force per unit cross-sectional area:
  
  • Stress = Force / Area.
• Units: Pascals (Pa), same as pressure.
• Ultimate Tensile Stress:
  
  • The maximum stress a material can handle before fracturing.

Tensile Strain:

• Defined as extension per unit length:
  
  • Strain = Extension / Original Length.
• Dimensionless (ratio of lengths).
• Can be expressed as a percentage.

Key Point:

• For strain, extension and original length can be in any units, as long as they are the same.

Question 21

Young Modulus

Answer 21

Young Modulus:

• Measures a material’s stiffness (ability to withstand changes in length under load).
• Calculated as the ratio of stress to strain:
  
  • Young Modulus = Stress / Strain.
• Units: Pascals (Pa) (since strain is dimensionless).

Stress-Strain Graph:

• For materials exhibiting elastic behaviour, stress and strain are directly proportional (linear relationship passing through zero).
• The gradient of the linear part of the graph equals the Young Modulus.

Question 22

Conservation of Momentum

Answer 22

• The total momentum before a collision equals the total momentum after a collision, provided no external force acts.
• Formula:
  
  • Momentum before = Momentum after.
• (kgms-¹) Or (Ns)

Question 23

Types of Energy Transfer in Collisions

Answer 23

Types of Collisions:

1. Elastic Collision:
   
   • Kinetic energy is conserved.
   • Objects do not stick together and may move in opposite directions.
2. Inelastic Collision:
   
   • Kinetic energy is not conserved.
   • Objects stick together after the collision.

Determining Collision Type:

• Compare kinetic energy before and after the collision.

Question 24

Impulse

Answer 24

Impulse:

• Defined as the change in momentum when a force acts on an object.
• Formula: Impulse = F × Δt, where:
• Unit: N s (Newton-seconds).

Key Points:

• A small force acting over a long time can have the same effect as a large force acting over a short time.
• On a force-time graph, impulse is the area under the curve:
  
  • For a curve, count the squares underneath.
  • For straight lines, split the graph into sections and sum the areas.

Question 25

Newton’s First Law

Answer 25

• A body will remain at rest or move with constant velocity unless acted on by a resultant force
• For an object to accelerate, it requires a resultant force.

Newton

• The force that will give a mass of 1 kg an acceleration of 1 m s–2
• The SI unit for force is kg m s–2

Question 26

Newton’s Third Law

Answer 26

Newton’s Third Law:

• If Body A exerts a force on Body B, then Body B exerts a force of equal magnitude and opposite direction on Body A.

Key Points:

• Force pairs act on two different objects.
• Force pairs must be of the same type (e.g., gravitational, frictional).

Question 27

Car safety

Answer 27

Car Safety Features:

1. Airbags and Seatbelts:
   • Increase the time (𝑡) for deceleration, reducing the force (𝐹) on the driver.
   • Formula: 𝐹 = (𝑚𝑣 - 𝑚𝑢) / 𝑡
2. Crumple Zones:
   • Absorb energy by deforming, further reducing the force on the driver.

Question 28

Pressure in a liquid

Answer 28

Pressure in a Fluid Column:

• An object in a fluid feels pressure from the weight of the fluid above it.
• Pressure at the base of the fluid is the same in all directions.

Equations:

1. Weight of the column:
   
   • W = m × g = ρ × A × h × g.
2. Pressure at the base:
   
   • P = W / A = ρ × h × g.
3. Hydrostatic pressure change:
   
   • ΔP = ρ × g × Δh.

Key Points:

• Pressure increases with depth because of the weight of the fluid above.
• Atmospheric pressure might need to be added in some cases.
• Volume divided by cross-sectional area equals height (h).

Question 29

Time graph

Answer 29

Displacement-Time Graph:

• Gradient (slope) = Velocity
• Y-intercept = Initial Displacement
• Straight Diagonal Line = Constant Velocity
• Curved Line = Acceleration
• Horizontal Line (Zero Slope) = Object at Rest

Velocity-Time Graph:

• Slope = Acceleration
• Y-intercept = Initial Velocity
• Straight Line = Uniform Acceleration
• Curved Line = Non-Uniform Acceleration
• Horizontal Line (Zero Slope) = Constant Velocity
• Area Under the Curve = Displacement or Distance Travelled

Acceleration-Time Graph:

• Y-intercept = Initial Acceleration
• Horizontal Line (Zero Slope) = Constant Acceleration
• Area Under the Curve = Change in Velocity

Question 30

Change in Momentum if it rebounds (hits a wall)

Answer 30

• Change in momentum is only due to horizontal velocities
• ∆p = m(v_f - v_i)

Question 31

Torque

Answer 31

• The size of a turning effect
• τ = Fd

Where:

τ= torque (N m)

F= one of the forces (N)

d= perpendicular distance between the forces (m)

Question 32

Mass on a slope

Answer 32

Forces on an Object on a Slope

• Weight (mg): Acts vertically downward.
• Reaction Force (Fr): Acts perpendicular to the slope, preventing the object from sinking into the surface.
• Parallel Component (mgsinθ): The force pulling the object down the slope.
• Perpendicular Component (mgcosθ): Contributes to the normal force and affects friction.

Object’s Motion

• Stationary/Constant Speed:
  
  • An equal and opposite force (e.g., friction) balances the force pulling it down the slope.
• Moving Down the Slope:
  
  • No Friction: Gravitational Potential Energy (GPE) converts entirely into Kinetic Energy (KE).
  • With Friction: Some GPE is converted into work against friction, reducing the KE at the bottom.

Question 33

Time graph of a bouncing ball

Answer 33

1. Upwards Motion:
   
   • Positive velocity decreases (decelerates) until reaching the highest point.
2. At Point A (Highest Point):
   
   • Maximum displacement.
   • Velocity = 0 (momentarily).
   • Velocity changes from positive to negative (direction change).
   • Acceleration (g) remains constant and downward.
3. At Point B (Lowest Point):
   
   • Minimum displacement (ball on the ground).
   • Velocity changes from negative to positive (instantaneous direction change).
   • Speed (magnitude) remains the same.
   • Momentary acceleration due to change in velocity.

Question 34

Stopping distance

Answer 34

Stopping Distance:

• Stopping distance = Thinking distance + Braking distance.
• Increases considerably with speed:
  
  • Thinking distance increases proportionally with speed.
  • Braking distance increases proportionally to the square of speed (u²).

===

Thinking Distance:

• Distance travelled before brakes are applied.
• Formula:
  
  • Thinking distance = Initial speed (u) × Reaction time.
• Factors affecting thinking distance:
  
  • Initial speed.
  • Intoxication (alcohol/drugs).
  • Distractions (e.g., mobile phones).
  • Tiredness (slower reaction times).

===

Braking Distance:

• Distance travelled after brakes are applied.
• Formula:
  
  • Work done by brakes = Braking force × Braking distance = ½ mv².
• Factors affecting braking distance:
  
  • Initial speed.
  • Mass of the vehicle.
  • Poor road conditions (e.g., icy, wet).
  • Car conditions (e.g., worn brakes).

Question 35

Tension, Upthrust, Friction, Normal Contact Force, Lift

Answer 35

Tension (T):
- The force experienced by a cable, rope, or string when:
- Pulled, hung, rotated, or supported.

Normal Contact Force (N or R):
- The force arising when an object rests against another object.
- Acts perpendicular (90°) to the plane of contact.
- Also called the reaction force (from Newton’s Third Law).

Upthrust:
- The upward buoyancy force acting on an object in a fluid (liquid or gas).
- Always acts upwards.

Friction (F or Fr):
- The force arising when two surfaces are in contact.
- Always opposes motion.
- Acts at the point of contact and in the opposite direction to motion.

Lift
- An upwards force on an object moving through a fluid.
- Acts perpendicular to fluid flow.
- Example: Aeroplane wings push air down, creating an equal and opposite reaction (lift) due to Newton’s Third Law.

Question 36

Work Done

Answer 36

Work Done:

• Energy transferred when a force moves an object over a distance.
• If the force acts in the direction of motion, the object gains energy.
• If the force acts opposite to the motion, the object loses energy.

The Joule (J):

• Unit of energy or work.
• SI unit: kg m² s⁻².
• Definition: Energy transferred when a 1 N force moves an object 1 m parallel to its motion.

Calculating Work Done:

• General formula: W = Fx cos θ
  
  • θ = angle between force and displacement.
• For vertical motion, use sin θ
• Always use the component of force parallel to the displacement.

Common Exam Mistake:

• Choosing the incorrect force (not parallel to motion).
• Resolve the force vector to find the parallel component.

Question 37

Derivation of Kinetic Energy

Answer 37

1. Mass at rest accelerates to speed v over distance d.
2. Work done: W = F × d.
3. Force: F = ma (Newton’s Second Law).
4. SUVAT equation: v² = u² + 2as.
   
   • Initial speed u = 0, distance s = d.
   • Equation simplifies to: v² = 2ad.
5. Rearrange for acceleration: a = v² / 2d.
6. Substitute a into F = ma: F = mv² / 2d.
7. Substitute F into work done: W = (mv² / 2d) × d = ½mv².
8. Kinetic energy due to speed: KE = ½mv².

Question 38

Derivation of P = F × v

Answer 38

1. Power is the rate of change of work:
   P = W / t.
2. Work done: W = F × d.
3. At constant velocity, distance d = v × t.
   
   • Therefore, W = F × v × t.
4. Substitute W into the power equation:
   P = (F × v × t) / t.
5. Cancel t:
   P = F × v.

Question 39

Force-Extension Graph

Answer 39

Force-Extension Graph:

• Hooke’s Law is obeyed up to the limit of proportionality, shown by a straight line through the origin.
• Beyond this point, the graph curves, and Hooke’s Law no longer applies.

Key Features:

1. Limit of Proportionality:
   
   • Point where extension is no longer proportional to the applied force.
   • Identified where the graph starts to curve (flatten out).
2. Force Constant (k):
   
   • Gradient of the straight part of the graph (linear region).
   • Represents stiffness of the material.
3. Elastic Limit:
   
   • Maximum stretch where the material can still return to its original length.
   • Always after the limit of proportionality.

Exam Tip:
- k is the gradient only in the linear region and must pass through zero where Hooke’s Law is obeyed.

Question 40

Type of materials

Answer 40

Brittle Materials:

• Definition: Fracture before plastic deformation.
• Behaviour:
  
  • Elastic until the breakpoint, where the material snaps.
  • No plastic deformation; loading and unloading curves are the same.
• Examples: Glass, ceramic.

Ductile Materials:

• Definition: Can withstand large plastic deformation without breaking.
• Behaviour:
  
  • Elastic deformation up to the elastic limit.
  • Plastic deformation until reaching ultimate tensile stress and breakpoint.
  • Can be hammered into thin sheets or drawn into long wires.
• Examples: Copper.

Polymeric Materials:

• Definition: Made of long, repeating chains of molecules.
• Behaviour:
  
  • Can endure high tensile stress before breaking.
  • No plastic deformation, but unloading curve differs from loading curve due to energy loss as thermal energy.
• Examples: Rubber, polythene.

Rubber:

• Does not obey Hooke’s Law and does not experience plastic deformation.
• Hysteresis Loop: The area between the loading and unloading curves.
  
  • Represents work done in stretching the material.
  • Energy is transferred to thermal energy when the force is removed.
  • Unloading curve is always below the loading curve.
  • Area between loading and unloading = Net work done (thermal energy dissipated).
  • Area under loading to the x axis = Minimum energy required to stretch the material to extension e.

Question 41

Stress-Strain Graph

Answer 41

1. Elastic Strain Energy per Unit Volume:
   
   • Equal to the area under the Hooke’s Law region (straight line).
2. Yield Stress:
   
   • The stress at which the material begins to deform plastically with a small increase in stress.
3. Breaking Point:
   
   • The maximum stress a material can withstand before fracturing.
4. Elastic Region:
   
   • Region up to the elastic limit.
   • Material returns to its original shape when the force is removed.
5. Plastic Region:
   
   • Region beyond the elastic limit.
   • Material permanently deforms and does not return to its original shape.

Question 42

Collisions

Answer 42

One-Dimensional Momentum Problems:

• Momentum (p) = m × v.
• Collisions occur in one direction (either x or y).
• Use conservation of linear momentum to find missing velocities or masses.

Two-Dimensional Momentum Problems:

• Momentum is a vector, so it can be split into x and y components.
• Collisions occur in both x and y directions.
• Use conservation of linear momentum and vector resolution to solve.

Key Points:

• If an object is stationary, its velocity = 0, so momentum = 0 and kinetic energy = 0.
• If two objects stick together after a collision, treat them as a single object with a mass equal to the sum of their masses.

Question 43

Total pressure

Answer 43

Total Pressure:

• Total pressure = Hydrostatic pressure + Atmospheric pressure.
• Atmospheric pressure (barometric pressure) = 101,325 Pa.

Key Points:

• Pressure values can vary widely and use metric prefixes (e.g., kPa, MPa).
• Ensure all pressures are in the same units (e.g., convert everything to Pascals (Pa)) to avoid errors.