Phys: Forces

What is the fundamental difference between vector and scalar quantities, and what are three examples of each?

Vector quantities have both magnitude and direction (e.g., force, velocity, displacement, acceleration, momentum); scalar quantities have magnitude only with no direction (e.g., speed, distance, mass, temperature, time).

How do contact and non-contact forces differ, and what are examples of each type?

Contact forces require objects to be touching to act (e.g., friction, air resistance, tension, normal contact force); non-contact forces act without objects needing to touch (e.g., gravitational force, electrostatic force, magnetic force).

What is an interaction pair, and how does it relate to Newton's Third Law?

An interaction pair consists of two equal and opposite forces that act on two interacting objects, where each object exerts an identical magnitude of force in opposite directions on the other.

What is the difference between mass and weight, and how is weight measured?

Mass is the amount of matter in an object and remains constant everywhere (measured in $\text{kg}$ with a mass balance); weight is the force acting on an object due to gravity, which changes with gravitational field strength (measured in $\text{N}$ using a calibrated spring balance or newtonmeter).

What is the center of mass of an object, and where is it located for a uniform object?

The center of mass is the single point from which the entire weight of an object can be considered to act; for a uniform object of regular shape and density, it is located at the geometric center.

What formula links weight ($W$), mass ($m$), and gravitational field strength ($g$)?

$W = m g$, where weight is in newtons ($\text{N}$), mass is in kilograms ($\text{kg}$), and gravitational field strength is in newtons per kilogram ($\text{N/kg}$).

What is a free body diagram, and how do its arrows represent forces?

A free body diagram illustrates all the forces acting on an isolated object or system; the direction of each arrow shows the direction of the force, and the length of each arrow represents its relative magnitude.

What is a resultant force, and how is it calculated for forces acting along the same straight line?

A resultant force is a single overall force that replaces a number of forces acting at a single point, having the same effect as all original forces combined; it is calculated by adding parallel forces in the same direction and subtracting forces acting in opposite directions.

What does it mean when a force does work on an object, and what equation is used to calculate work done?

Work is done when a force causes an object to move through a distance, transferring energy between stores; calculated using $W = F s$, where work done ($W$) is in joules ($\text{J}$), force ($F$) is in newtons ($\text{N}$), and distance ($s$) along the line of action is in metres ($\text{m}$).

How much work is done when a force of $1\text{ N}$ moves an object a distance of $1\text{ m}$?

$1\text{ joule}$ of work is done ($1\text{ J} = 1\text{ N m}$).

How do you use a scale drawing to find the magnitude and direction of a resultant force?

Draw all forces acting on an object to scale tip-to-tail, draw a straight line from the start of the first force to the end of the last force, then measure its length for magnitude and use a protractor to find its angle/bearing.

What condition must be met for an object to be in equilibrium, and how is this shown on a scale diagram?

All forces acting on the object must combine to give a resultant force of zero; on a scale diagram, the forces will form a closed shape where the tip of the last force meets the tail of the first force (e.g., a closed triangle for three forces).

How can an angled force be resolved into components on a scale grid?

Draw the force vector to scale on a grid, then draw perpendicular horizontal and vertical component vectors along the grid lines that meet the original vector's tip and measure their lengths.

Why must more than one force act on an object to stretch, compress, or bend it?

If only a single force acts on an object, it will simply accelerate or move in the direction of the applied force rather than changing shape.

What is the difference between elastic deformation and inelastically (plastic) deformation?

An object is elastically deformed if it returns to its original shape and length after the forces are removed; it is inelastically deformed if it does not return to its original shape and length.

What equation links force ($F$), spring constant ($k$), and extension ($e$) for an elastically stretched spring?

$F = k e$, where force is in newtons ($\text{N}$), spring constant is in newtons per metre ($\text{N/m}$), and extension (or compression) is in metres ($\text{m}$).

What does the spring constant ($k$) represent, and how does its value relate to spring stiffness?

The spring constant represents how stiff a spring or material is; a higher spring constant means a stiffer spring that requires more force to extend or compress.

What is the limit of proportionality on a force-extension graph?

The point (often labeled $P$) beyond which extension is no longer directly proportional to the applied force, causing the linear graph line to curve.

How do you set up and carry out a practical investigation to determine the relationship between force and extension for a spring?

Measure the natural length of a clamped spring at eye level with a millimetre ruler using a marker; add masses one by one, allow the spring to come to rest, record the new length, calculate extension ($\text{new length} - \text{natural length}$), repeat for at least 6 masses, and plot a force-extension graph.

What is the purpose of conducting a quick pilot experiment before carrying out a spring extension investigation?

To load an identical spring with up to 5 masses to check that the chosen masses are suitable and do not exceed the spring's limit of proportionality (indicated by a sudden larger increase in extension).

What does the straight line portion of a force-extension graph indicate, and how is the spring constant determined from it?

A straight line shows a linear relationship where force and extension are directly proportional ($F = k e$); the gradient of this straight line section equals the spring constant ($k$).

What equation calculates the energy stored in a spring's elastic potential energy store, and how can it be found from a graph?

$E_e = \frac{1}{2} k e^2$ (where $E_e$ is elastic potential energy in $\text{J}$, $k$ is spring constant in $\text{N/m}$, and $e$ is extension in $\text{m}$), provided the spring is not stretched past its limit of proportionality; this energy also equals the area under the force-extension graph.

What is a moment, and what equation is used to calculate it?

A moment is the turning effect of a force; calculated using $M = F d$, where moment ($M$) is in newton-metres ($\text{N m}$), force ($F$) is in newtons ($\text{N}$), and distance ($d$) is the perpendicular distance from the pivot to the line of action of the force in metres ($\text{m}$).

How can you maximize the moment (turning effect) applied to an object, such as when using a spanner?

Apply a larger force, push at a greater perpendicular distance from the pivot, and exert the force at right angles ($90^\circ$) to the pivot.

What condition must be met for a balanced object to remain stationary around a pivot according to the principle of moments?

The total anticlockwise moment about the pivot must equal the total clockwise moment about the pivot.

How do levers make work easier when lifting loads or turning objects?

Levers increase the distance ($d$) from the pivot at which an input force is applied, meaning a smaller force is required to produce the same required moment ($M = F d$).

How do interlocked gears transmit turning forces, and how do gear sizes affect moment and rotation speed?

Interlocked gear teeth cause adjacent gears to turn in opposite directions; a force transmitted to a larger gear produces a bigger moment (due to a greater distance to the pivot) but causes the larger gear to turn slower than a smaller gear.

What is a fluid, and how do fluid particles exert pressure on a surface?

A fluid is a liquid or gas whose particles are free to move and collide with surfaces; pressure is exerted at right angles (normal) to any surface in contact with the fluid.

What equation links pressure ($p$), force ($F$), and surface area ($A$)?

$p = \frac{F}{A}$, where pressure is in pascals ($\text{Pa}$), force is in newtons ($\text{N}$), and area is in square metres ($\text{m}^2$).

Why does pressure in a liquid increase with both liquid density and depth?

A denser liquid has more particles per unit volume to collide with a surface, and increasing depth adds a greater weight of liquid particles above that point, increasing the total downward force.

What equation is used to calculate the pressure ($p$) exerted by a column of liquid at a specific depth?

$p = h \rho g$, where $p$ is pressure in pascals ($\text{Pa}$), $h$ is height/depth of the liquid column in metres ($\text{m}$), $\rho$ is liquid density in $\text{kg/m}^3$, and $g$ is gravitational field strength ($\text{N/kg}$).

What causes upthrust on an object submerged in a fluid, and how is its magnitude determined?

Since pressure increases with depth, the pressure on the bottom of a submerged object is greater than on the top, causing a resultant upward force (upthrust); this upthrust equals the weight of fluid displaced by the object.

Under what condition will an object float, and why does relative density determine floating or sinking?

An object floats when its weight equals upthrust; an object less dense than the fluid displaces a volume of fluid equal to its own weight before full submersion, whereas a denser object cannot displace enough fluid weight to match its weight and sinks.

How do submarines adjust their buoyancy to submerge or rise in water?

To sink, large ballast tanks fill with water so total submarine weight exceeds upthrust; to rise, tanks are emptied using compressed air, reducing weight below upthrust.

Why does atmospheric pressure decrease as altitude above the Earth increases?

At higher altitudes, the atmosphere becomes less dense with fewer air molecules to collide with a surface, and the weight of the air column above the surface decreases.

What is the difference between distance and displacement?

Distance is a scalar quantity measuring how far an object has moved without regard to direction; displacement is a vector quantity measuring distance and direction in a straight line from starting to finishing point.

How do speed and velocity differ, and how can an object move at a constant speed while changing velocity?

Speed is a scalar quantity showing how fast an object moves, whereas velocity is a vector specifying speed in a given direction; an object moving in a circle at constant speed constantly changes velocity because its direction is continually changing.

What equation links distance travelled ($s$), speed ($v$), and time ($t$)?

$s = v t$, where distance ($s$) is in metres ($\text{m}$), speed ($v$) is in metres per second ($\text{m/s}$), and time ($t$) is in seconds ($\text{s}$).

What are the typical everyday speeds for walking, running, cycling, a car, a train, and a plane?

Walking: $\approx 1.5\text{ m/s}$; Running: $\approx 3\text{ m/s}$; Cycling: $\approx 6\text{ m/s}$; Car: $\approx 25\text{ m/s}$; Train: $\approx 30\text{ m/s}$; Plane: $\approx 250\text{ m/s}$.

What is the typical speed of sound in air, and what factors affect wind speed?

The typical speed of sound in air is $330\text{ m/s}$; wind speed is affected by temperature, atmospheric pressure, and nearby structures or terrain like forests.

What is acceleration, and what equation calculates average acceleration ($a$)?

Acceleration is the rate of change of velocity in a given time; calculated using $a = \frac{\Delta v}{t}$, where acceleration ($a$) is in metres per second squared ($\text{m/s}^2$), change in velocity ($\Delta v$) is in $\text{m/s}$, and time ($t$) is in $\text{s}$.

What is deceleration, and how is it represented in acceleration calculations?

Deceleration is negative acceleration occurring when an object slows down, represented by a negative value for acceleration.

What is uniform acceleration, and what value is used for free-fall acceleration near Earth's surface?

Uniform acceleration is constant acceleration; objects in free fall near Earth's surface accelerate uniformly due to gravity at approximately $9.8\text{ m/s}^2$.

What equation links final velocity ($v$), initial velocity ($u$), acceleration ($a$), and distance ($s$) for uniform acceleration?

$v^2 - u^2 = 2 a s$, where final velocity ($v$) and initial velocity ($u$) are in $\text{m/s}$, acceleration ($a$) is in $\text{m/s}^2$, and distance ($s$) is in $\text{m}$.

What features on a distance-time graph represent speed, stationary motion, and changing speed?

The gradient represents speed (steeper means faster); flat horizontal sections mean stationary; straight uphill sections mean steady speed; curves represent acceleration (steepening) or deceleration (levelling off).

How do you find the instantaneous speed of an accelerating object from a curved distance-time graph?

Draw a tangent to the curve at that specific point and calculate the gradient of the tangent line.

What features on a velocity-time graph represent acceleration, steady speed, and distance travelled?

The gradient represents acceleration or deceleration (steeper means greater acceleration); flat horizontal sections represent steady speed; the area under the graph equals distance travelled.

How can you estimate the distance travelled on a velocity-time graph with an irregular curve?

Count the grid squares under the curve and multiply the total count by the distance value represented by one square.

What is drag, and how can it be reduced for moving objects?

Drag is the resistive force experienced by an object moving through a fluid (gas or liquid), such as air resistance; it is reduced by keeping the object streamlined to allow fluid to flow easily past it.

How does the speed of an object affect the drag force acting on it?

Drag increases as speed increases, meaning a vehicle's engine must work much harder at higher speeds to maintain a steady speed against frictional forces.

How does a falling object reach terminal velocity in terms of forces and acceleration?

Initially, weight is much greater than drag, causing rapid acceleration; as speed increases, drag builds up, reducing acceleration until drag equals weight, making resultant force zero and locking the object at a steady maximum speed.

Why do all objects fall at the same rate on the Moon, but fall at different terminal velocities on Earth?

On the Moon, there is no air resistance so gravity accelerates all objects equally; on Earth, air resistance acts against motion, making terminal velocity depend on an object's shape, surface area, and weight.

How does opening a parachute drastically lower a skydiver's terminal velocity?

Opening a parachute greatly increases surface area, increasing air resistance at any given speed; since weight remains constant, the forces balance at a much lower speed (around $15\text{ mph}$ instead of $120\text{ mph}$).

What is Newton's First Law of Motion?

Newton's First Law states that if the resultant force on a stationary object is zero, the object will remain stationary; if the resultant force on a moving object is zero, it will continue moving at the same velocity (same speed and direction).

What five forms can acceleration take when a non-zero resultant force acts on an object?

Starting, stopping, speeding up, slowing down, and changing direction.

How does acceleration depend on resultant force and mass according to Newton's Second Law?

Acceleration is directly proportional to the resultant force ($F \propto a$) and inversely proportional to the mass of the object.

What equation represents Newton's Second Law of Motion?

$F = m a$, where resultant force ($F$) is in newtons ($\text{N}$), mass ($m$) is in kilograms ($\text{kg}$), and acceleration ($a$) is in metres per second squared ($\text{m/s}^2$).

What is inertia, and how is inertial mass defined?

Inertia is the tendency of objects to continue in their existing state of motion (at rest or at constant velocity); inertial mass measures how difficult it is to change an object's velocity and is calculated as the ratio of force over acceleration ($m = \frac{F}{a}$).

What is Newton's Third Law of Motion?

Newton's Third Law states that when two objects interact, the forces they exert on each other are equal in magnitude and opposite in direction.

Why does an object accelerate when pushed, even though Newton's Third Law states forces are equal and opposite?

The equal and opposite forces act on two different objects, so each individual object experiences a non-zero resultant force.

Why is a book resting on a table in equilibrium NOT an example of Newton's Third Law?

The downward weight and upward normal contact force acting on the book are two different types of forces both acting on the same object, whereas Newton's Third Law forces are identical types of forces acting on two different interacting objects.

How is a light gate and card interrupt used to measure the acceleration of a trolley in an experiment?

A piece of card with a gap in the middle is fixed to the trolley to interrupt the light gate signal twice; inputting card bit lengths into data logging software allows the gate to calculate velocity for each section and derive acceleration.

How do you investigate the effect of varying mass on acceleration while keeping force constant?

Add masses directly onto the trolley to increase total system mass, keep the mass on the hook unchanged so accelerating force stays constant, release the trolley from a fixed starting line, and record acceleration using a light gate.

How do you investigate the effect of varying force on acceleration while keeping total mass constant?

Start with all extra masses on the trolley and transfer them one at a time to the hanging hook, which increases accelerating force while keeping overall system mass constant, then record acceleration for each force value.

What equation defines total stopping distance, and what are its two components?

$\text{Stopping Distance} = \text{Thinking Distance} + \text{Braking Distance}$; thinking distance is distance travelled during driver reaction time, and braking distance is distance travelled while braking force is applied.

What factors directly affect a vehicle's thinking distance?

Vehicle speed (faster speed means greater distance covered during reaction time) and driver reaction time (longer reaction time increases thinking distance).

What factors directly affect a vehicle's braking distance?

Vehicle speed, weather or road surface conditions (wet/icy roads reduce friction), tyre condition (bald tyres cannot clear water, causing skidding), and brake condition (worn/faulty brakes apply less force).

How does braking transfer energy, and what is the effect of large braking forces on the braking system?

Braking causes brake pads to press against wheels, doing work against friction to transfer kinetic energy from the wheels into the thermal energy stores of the brakes; very large braking forces cause severe deceleration and can overheat brakes or cause skidding.

What is a typical human reaction time range, and what factors can increase reaction time?

A typical human reaction time is between $0.2\text{ s}$ and $0.9\text{ s}$; it can be increased by tiredness, drugs, alcohol, or distractions.

How is the ruler drop test carried out to measure reaction time?

1) Rest arm on table edge; 2) Partner holds ruler vertically hanging between thumb and forefinger lined up with zero at eye level; 3) Drop ruler without warning; 4) Catch as quickly as possible; 5) Record distance dropped and calculate time using uniform acceleration ($v^2 - u^2 = 2as$ and $a = \frac{\Delta v}{t}$).

What experimental controls ensure the ruler drop test is fair and accurate?

Use the same ruler and same person dropping it, add modelling clay to the bottom so it falls straight down, and conduct multiple repeats to calculate a mean reaction time.

How are Highway Code stopping distances structured at $30\text{ mph}$, $50\text{ mph}$, and $70\text{ mph}$?

$30\text{ mph}$: $9\text{ m}$ thinking + $14\text{ m}$ braking ($23\text{ m}$ total / 6 car lengths); $50\text{ mph}$: $15\text{ m}$ thinking + $38\text{ m}$ braking ($53\text{ m}$ total / 13 car lengths); $70\text{ mph}$: $21\text{ m}$ thinking + $75\text{ m}$ braking ($96\text{ m}$ total / 24 car lengths).

How does speed affect thinking distance compared to braking distance?

Thinking distance increases proportionally with speed (linear relationship because reaction time is constant); braking distance increases with the square of speed ($v^2$) because work done to stop equals kinetic energy ($\frac{1}{2}m v^2$).

If speed doubles, how do kinetic energy, work done by brakes, and braking distance change?

Doubling speed increases kinetic energy $4$-fold ($2^2$), which requires $4$ times as much work done to stop, increasing braking distance $4$-fold (assuming constant braking force).

What is momentum, and what equation is used to calculate it?

Momentum is a vector property of all moving objects determined by mass and velocity; calculated using $p = m v$, where $p$ is momentum in kilogram metres per second ($\text{kg m/s}$), $m$ is mass in kilograms ($\text{kg}$), and $v$ is velocity in metres per second ($\text{m/s}$).

What is the principle of conservation of momentum?

In a closed system (where no external forces act), the total momentum before an event or collision is equal to the total momentum after the event.

How does the law of conservation of momentum apply to recoil events such as firing a gun or paintball marker?

Before firing, total momentum is zero; when fired, the forward momentum of the projectile is equal in magnitude and opposite in direction to the backward momentum of the recoil, ensuring the total momentum after remains zero.

What equation links force ($F$) to the rate of change of momentum?

$F = \frac{m \Delta v}{\Delta t}$, where force ($F$) is in newtons ($\text{N}$), change in momentum ($m \Delta v$) is in $\text{kg m/s}$, and time taken for the change ($\Delta t$) is in seconds ($\text{s}$).

Why are rapid changes in momentum dangerous during vehicle impacts?

A rapid change in momentum over a very short time interval produces a very large impact force on the body, which significantly increases the risk of severe injury.

How do vehicle safety features (crumple zones, seat belts, air bags) reduce impact forces during a crash?

They increase the time taken ($\Delta t$) for the occupants' momentum to change to zero; since $F = \frac{m \Delta v}{\Delta t}$, increasing impact duration reduces the overall force exerted on the body.

How do bike helmets, crash mats, and cushioned playground surfaces protect individuals from injury?

They contain crushable or compressible materials that lengthen the time taken to come to a complete stop, reducing the rate of change of momentum and minimizing the impact force.