Forces Flashcards
(44 cards)
1
Q
Average Speed
A
Distance over time for the entire region of interest.
2
Q
Free-Fall
A
the only force acting on the object is the force of gravity.
3
Q
Projectile Motion
A
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:
- Vertical projection: Straight up or down.
- Horizontal projection: Fired horizontally.
- 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.
4
Q
Instantaneous Speed
A
The exact speed of an object at a specific given point.
(Draw tangent)
5
Q
Reaction Time
A
The time taken to process a stimulus and trigger a response to it.
It is affected by alcohol, drugs and tiredness.
6
Q
Archimedes’ Principle
A
- The upwards force acting on an object submerged in a fluid, is equal to the weight of the fluid it displaces.
- (Upthrust = 𝜌liquid 𝑉object 𝑔)
- (Upthrust = (h2 - h1)𝜌gA)
7
Q
Centre of Mass
A
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.
8
Q
Couple
A
- 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)
9
Q
Drag
A
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.
10
Q
Equilibrium
A
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.
11
Q
Free-Body Diagram
A
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.
12
Q
Moment of Force
A
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.
13
Q
Newton’s Second Law
A
- 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:
-
Along the direction of motion:
- Speeds up (accelerates) or slows down (decelerates) the body.
-
At an angle to the motion:
- Changes the direction of the body.
14
Q
Principle of Moments
A
- 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.
15
Q
Terminal Velocity
A
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.
16
Q
Conservation of Energy
A
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.
17
Q
Elastic Potential Energy
A
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.
18
Q
Hooke’s Law
A
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.
19
Q
Types of deformation
A
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.
20
Q
Tensile Stress and Tensile Strain
A
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.
21
Q
Young Modulus
A
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.
22
Q
Conservation of Momentum
A
-
Definition:
The total momentum of a system before a collision equals the total momentum after a collision, when no external forces act. -
Key Principle:
Σp<sub>before</sub> = Σp<sub>after</sub>- p = mv (momentum = mass × velocity)
- Units: kg m s-1 or N s
-
Conditions:
- Only applies to closed systems (no external forces).
- Works for all collision types (elastic/inelastic).
-
Example Calculation:
Two cars collide and stick together:m<sub>1</sub>v<sub>1</sub> + m<sub>2</sub>v<sub>2</sub> = (m<sub>1</sub> + m<sub>2</sub>)v<sub>f</sub>
23
Q
Types of Energy Transfer in Collisions
A
Types of Collisions:
-
Elastic Collision:
- Kinetic energy is conserved.
- Objects do not stick together and may move in opposite directions.
-
Inelastic Collision:
- Kinetic energy is not conserved.
- Objects stick together after the collision.
Determining Collision Type:
- Compare kinetic energy before and after the collision.
24
Q
Impulse
A
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.
25
Newton’s First Law
- **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
26
Newton’s Third Law
**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).
27
Car safety
**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.
28
Pressure in a liquid
**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)**.
29
Time graph
**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**
30
Change in Momentum if it rebounds (hits a wall)
- Change in momentum is only due to horizontal velocities
- ∆p = m(vf - vi) = -2mv
**Key Points**:
- **Rebound effect**: Direction reversal **doubles** the momentum change.
- **Negative sign**: Indicates the **direction** of the momentum change (opposite to initial motion).
- **Assumption**: Perfectly elastic collision (no energy loss).
31
Torque
- **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)
**Key Points**:
- **Direction**: Torque is a **vector** (clockwise or anticlockwise).
- **Maximising Torque**:
- Increase **force** (F).
- Increase **perpendicular distance** (f) (e.g., using a longer spanner).
- **Units**: **N m**
32
Mass on a slope
**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.
33
Time graph of a bouncing ball
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.
34
Stopping distance
**Stopping Distance**:
- **Stopping distance** = **Thinking distance** + **Braking distance**.
- Increases **considerably with speed**:
- **Thinking distance** ∝ speed.
- **Braking distance** ∝ 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).
35
Tension, Upthrust, Friction, Normal Contact Force, Lift
**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**.
- = **weight** of fluid or air **displaced**
---
**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**.
36
Work Done
**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**.
37
Derivation of Kinetic Energy
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.
38
Derivation of P = F × v
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.
39
Force-Extension Graph
**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.
40
Type of materials
**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**.
41
Stress-Strain Graph
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.
42
Collisions
**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**.
43
Total pressure
**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.
- PSI (pound per square inch)
- turn pound into N
- turn square inch into square metre
44
Force on spring
1. **\( F = kx \)** can represent:
- The **applied force** needed to stretch/compress the spring (your effort).
- The **restoring force** the spring exerts (its reaction).
2. The **sign** depends on the reference frame:
- Applied force: \( +kx \) (in the direction of displacement).
- Restoring force: \( -kx \) (opposite to displacement).
