mechanics, materials, electricity Flashcards
Current
- Movement of charge carriers
- The rate of flow of charge carriers in a circuit
The greater the Current…
- The more carriers that flow
- The quicker the charge carriers flow
What is EMF?
The energy supplied by the power source to each unit of charge (1C)
- 1C = 1As
- EMF = P.D + Lost Volts
- lost volts = energy lost due to resistance.
What are lost volts?
Energy dissipated per unit charge
What is potential difference?
The energy transferred from the charge to the output of the electrical circuit is the P.D..
/
ability for the charge carriers to do work
Kirchoff’s 1st Law
Law 1: charge is conserved in an electrical circuit
- The sum of current into a junction = sum of current out of
a junction
- at a junction current splits in inverse to total resistance of
each path (e.g. see example below)
- Current entering a component is the same as current
leaving a component.
- The current passing through two or more components in series is the same through each.
Kirchoff’s 2nd Law
Law 2: energy is conserved in an electrical circuit.
- loop law/closed circuit law
- the algebraic sum of P.D.s in any loop must equal zero
- can find P.D. at component using the Directly Proportional relationship of P.D. and Resistance.
- Potential difference across components in parallel are the same (each loop is considered a closed system)
- For any complete loop of a circuit, the sum of the EMF is equal to the sum of the potential drop around the loop.
Principle of Moments
Anti-Clockwise Moments = Clockwise Moments
Magnitude of Moments
The moment is dependent on
- the magnitude of the force ( larger force, greater moment)
- perpendicular distance ( greater distance, greater moment)
M=fd
NM = N x m
Couples
A couple is a pair of forces acting on a body that are of equal magnitude and opposite direction, acting parallel to one another, but not along the same line
thus the resultant force is zero but the resultant moment is a non-zero value
A couple causes a turning effect but not by accelerating, instead by changing direction.
Centre of Mass & Weight
The point at which all the mass of an object is concentrated
The point at which all the weight of an object is concentrated
CM —> M
CM^2 —-> M^2
CM^3 —> M^2
%\x1000
%\x 10,000
%\x 1,000,000
Hooke’s Law
The force needed to stretch or compress a material is directly proportional to the extension or compression of the material from its natural length provided the limit of proportionality hasn’t need exceeded.
What is the UTS?
The ultimate tensile stress of a material is the greatest stress a material can handle.
_ for materials with high UTS’ we consider them to be stronger materials.
Brittle
A material that fractures without significant plastic deformation.
Ductile
The degree to which a material can withstand plastic deformation without fracturing.
Newton’s 1st Law
Object remains at rest or at constant velocity unless a resultant force is enacted upon it.
Inertia
- The tendency for an object to resist changes in velocity.
- ## Objects of greater mass have a greater inertia
Newton’s 2nd Law
The resultant force is directly proportional to the product of an object’s mass and acceleration
Why may an object moving upwards but slowing down experience a force downwards/ feel lighter?
Because an object decelerating is the same as on object accelerating downwards, thus the resultant force is downwards.
Newton’s Third law
If object A exerts a force on object B, then object B exerts an equal and opposite force of the same type on object A.
- The action and reaction forces must be the same and equal.
How does newton’s third law explain the motion of a vehicle?
The frictional force of the tire on the ground pushes it back whilst the frictional force of the ground on the tire pushes it forwards.
Conservation of Momentum
the momentum before = momentum after
given a CLOSED SYSTEM with NO external forces
Circuits in Parallel
- For components in parallel the potential difference is the same
- The total current in to a junction must equal the total current out of the junction
- Most of the current flows through the route with the smallest resistance.
- adding resistors in parallel decreases TOTAL resistance by providing an additional path for the current to flow through.
the definition of potential difference/ voltage
the work done per unit charge across a component
Circuits in series
- for components in series the current flowing is the same (current in = current out)
- the potential difference is shared in the same ratio as resistance
- adding resistors in series increases TOTAL resistance and therefore DECREASES current
What effect does adding a component to a circuit have if it’s in:
Series
Parallel
SERIES <—
- total resistance will increase because current will have to flow through all components/resistors
- this decreases current flow because V=IR (for a given p.d.)
PARALLEL <—
- total resistance will decrease because the current now has additional paths to flow through
- increases the current that can flow for a given pd
Ohm’s Law
The potential difference across a metallic conductor is directly proportional to the current through it, provided the physical conditions do not change.
Negative Temperature Coefficient Thermistor
- A thermistor where when the temperature goes up the resistance goes down
superconductor
A material which has zero resistivity at or below a critical temperature
applications:
strong electormagnets
to produce large currents
transmission cables
difficulty of superconductors
- the conductor will need to be cooled below a critical temperature which can be very low and may require liquid nitrogen or helium
internal resistance definition
the lost volts
the work done per unit charge across the internal resistance of the circuit.
Emf definition
The energy supplied per unit charge by the power source
terminal voltage
the work done per unit charge across the load.
Explain why the terminal voltage decreases as current increases on a terminal voltage-current graph
- As current increases, more energy lost inside the cell due to internal resistance increases.
- Since the lost p.d. larger and the terminal voltage decreases
or
- To increase the current the load’s resistance must be decreased. Internal resistance is unchanged.
When is power at a maximum in a circuit?
power delivered to the load is maximum when the resistance of the load = internal resistance of the power supply.
Displacement definition
Displacement is the shortest distance from the initial position to the final position of an object in motion.
/ a change in position
Angular displacement, angular velocity & centripetal acceleration
A change in position of an object taking a circular path defined by its change in angle.
- Δθ
The rate of change of angular displacement
the rate of change of angular velocity directed to the centre of an objects circular path caused by a centripetal force
( TIF: do you remember how we derive linear displacement, acceleration and velocity from khan academy?)
Why can we ignore the internal composition of an object when looking at the external forces applied on it?
Due to the force pairs ( ie the electromagnetic forces between the particles of the object holding it together) that naturally arise due to the nature of forces arising from the interaction of two objects.
According to Newton 3 those force pairs are equal in magnitude and opposite in direction so they cancel each other out overall in the system so it doesn’t impact the macroscopic motion of an object.
Why can a system not exert a net force on itself?
Each intern push or pull force on one part of a system is countered by an opposite push or pull force on another part of the system.
Explain why this is an incorrect free-body diagram for the forces acting on a bucket of balls being lifted at a constant velocity
- The force of one bucket on the ball and the balls on the bucket are valid newton 3 pairs but their interactions are internal to the system
- free body diagrams only model external forces
Explain why this free-body diagram that models the forces applied to a bucket full of tennis balls is incorrect
- It’s true that there are newton 3 pairs for the hand and system + the system and earth
- HOWEVER, only the forces in each pair that acts on the system should be modeled on the system’s free-body diagram.
- the other force in each pair acts on a different object
Law of Inertia
If the net force acting on a system is zero, the velocity of the system will remain constant.
Where Inertia - the tendency of objects to maintain their present state of motion (ie their present velocity)
Newton’s 2nd Law
F = ma
Force is proportional to acceleration- the greater the net force the more
rapidly the system’s velocity changes
Acceleration is inversely proportional to mass - the more massive an object/system is, the more inertia and thus resistance to change in velocity it has.
Thus the greater the mass the lower the acceleration
Why may an elevator still be moving upwards if it’s experiencing a resultant force and an acceleration downwards?
- The net force of an object does not affect the direction of motion (velocity£ on an object, it only dictates the direction of acceleration.
- a negative acceleration with a positive velocity means an object/system is slowing down
- thus the elevator is slowing down.
How does work done relate to the kinetic energy of an object in motion.
the net work done on an object during a displacement is equal to the change in the object’s kinetic energy during that displacement:
NET Work Done
The net work done on an object during a displacement is the sum of the work done by all individual forces acting on the object. (This is equivalent to first finding the net force, and then finding the work done by the net force.)
What is Kinetic Friction?
Kinetic friction refers to the force that acts on an object in motion, opposing its movement.
Kinetic friction is always present between two surfaces that slide against each other
Ff = coefficient of friction x normal force
Mechanical Energy
E(mech) = KE(tot) + PE(tot)
where E(mech) arises from a conservative force
- when the objects in a system only interact via conservative forces, and there are NO unbalanced external forces doing work on the system, the system’s mechanical energy is conserved.
therefore the ΔE(mech) = 0
because the system’s total KE and PE energies will not change over time
when a system has non-conservative forces ( e.g. friction and air resistance ) these forces do not have associated potential energies, when they do negative work on an object, the KE transferred is instead dissipated as thermal or sound energy.
therefore the work done by a nonconservative force is lost from a systems mechanical energy
(beyond A-level) Path-independency of conservative forces
work is independent of the path taken from the initial to final configuration
Carbon Dating
- plants and trees contain a small percentage of radioactive isotope, carbon-14
- due to carbon being taken in by living plants due to photosynthesis a small percentage of the carbon content of any plant is carbon-14.
- the isotope has a half-life of 5570 years ( thus there is negligible decay during the lifetime of a plant)
- after a tree is dead the proportion of carbon-14 decreases due to nuclei decay.
- by measuring the activity of the dead sample its age can be calculated
( carbon-14 is formed in the atmosphere as a result of comics rays knocking out neutrons from nuclei )
Why does a person experience a greater pain when catching a heavier ball than a lighter ball provided both are travelling at the same velocity?
- Due to the larger ball being more massive the momentum of the ball is greater than the smaller ball at the same velocity.
- when caught both of the momentum’s of the ball reduce to zero
- the larger ball will thus have a greater change in momentum over time than the smaller ball
- Fnet = Δp/t so the larger ball will apply a greater force on the hand of catcher.
How does pulling a hand back or downwards when catching an object reduce the amount of force experienced?
- increased time over which momentum is reduced to zero ( change in momentum)
- Fnet = Δp/t
- therefore there is a reduction in the rate of change of momentum
- causing a reduced force on impact
Two Cars, A and B beginning from rest start their vehicles. Car A’s engine applies a thrust force of 25,000N in 0.1s, Car B’s engine applies a thrust force of 50N for over a minute, which vehicle will have the greatest velocity upon starting?
Impulse = change in momentum
F*t = Δp
F = 25000N t = 0.1s IMP = 2500Ns
F = 50N t = 60s IMP = 3600Ns
both vehicles started from rest, therefore car B has a greater velocity.
An egg dropped from the same height on to a stone breaks, but on to a pillow it doesn’t, why?
- The egg will have the same change in momentum in both scenarios
- ∴ The impulse for both scenarios of the egg also remain the same
- however, the pillow is able to deform when egg makes contact, meaning the egg is falling/in motion for a greater time period
- for impulse to remain the same in both scenarios the force on the egg from the pillows upon impact must be smaller
- causing the egg to not crack
- F*Δt = impulse
What is the purpose of a crumple zone on a vehicle? FINISH
Elastic vs Inelastic collisions
Elastic: Total kinetic energy is conserved (of a macroscopic object)
Inelastic: Total kinetic energy is NOT conserved
A perfectly elastic collision has 0 transfer of KE to waste so the two interacting objects would definitely rebound
A perfectly inelastic collision will cause the two objects to stick together and move off as a single unit.
regardless of whether a collision is elastic or plastic, momentum WILL be conserved.
Why is kinetic energy not conserved in a collision but momentum is?
Kinetic energy is a scalar quantity so when kinetic energy is lost it is not cancelled out due to direction
momentum is a vector quantity so any momentum in one direction will be cancelled to zero by momentum in the opposing direction, therefore momentum is always conserved in a collision
What is a Moment?
- The moment of a force about any point is defined as the product of the force and the perpendicular distance from the line of action of the force at a point
Define Centre of Mass
- the centre of mass of a body is the point through which a single force on the body has no turning effect
Calculating the weight of a ruler (make this a Q)
What is a Couple?
- A couple is a pair of trial and opposite forces acting on a body, but not along the same line
Why does an object in stable equilibrium return to equilibrium when it is displaced then released?
- Ths centred of mass of the object is directly below the point of support when the object is at rest
- This allows the weight of the object to towards its centre
- when displaced after its release the line of action of the force no longer acts through its centre so the weight acts a restorative force to bring the object back to equilibrium.
For example, in the case of a plank on a ball, Why do objects within unstable equilibrium topple easily?
- The centre of mass of the object will be directly above above the point of support when equilibrium
- If the the object is displaced slightly, the centre of mass is no longer above the point of support
- The weight therefore acts to turn the plank further from the equilibrium position
What is the Toppling of an object being tilted dependent on? Why?
- The position of it’s centre of mass (how far above the surface is it)
- The size of its base
- When a base is larger the line of action of the weight will pass through the pivot after a much larger tilt than had it been a smaller base
- the higher placed the centre of mass of an object allows for the line of action of the weight to escape past the pivot at shorter distances
In the case of objects on a slope of what causes them to topple over?
- If an object is an a slope that is too steep
- the line of action of the force will sit outside of the objects base, this will cause the object to topple
How does centre of mass effect stability?
- The lower the centre of mass of an object, the more stable it is
- Conditions for a body to be in equilibrium
- the resultant force must be zero
- the principle of moments must apply (i.e. the moments of the forces about the same point must balance out
What causes the tension in the back of the man and the reaction force at his hip?
- The vertical components of the weight of the man and the object cause a turning effect at the pivot of the man
- The man is in equilibrium so the sum of moments = 0 ∴ there is a tension in the back an it’s vertical component applies an anticlockwise moment about the pivot = in magnitude to the moment caused by the two objects
- The Tension in the back and the Weight of the man and object all have components parallel to his spine
- The reaction force opposes these forces
- it is larger than all of the forces involved and begins form the hip pivot (hence why it is not included in moment calculation)
- these forces act to compress the spine
Explain why when the person is not leaning to lift the suitcase, the compressive force in the spine is considerably less than if the person had leaned forward to lift the suitcase
- When the man is leaning over less/not at all there is a smaller parallel components of the weights of himself, the suitcase and the tension in the back
- This means the reaction force that opposes these forces reduces overall
Current Rules
- At any junction in a circuit, the total current leaving the junction is equal to the total current entering the junction
- The junction rule holds because the rates or charge flowing into
and out of a junction are always equal.
- The junction rule holds because the rates or charge flowing into
Components in Series
- The current entering a component is the same as the current leaving the component.
- The current passing through two or more components
in series is the same through each component.- because the rate of flow of charge at any instant will always be the same
Insulators, Conductors, Semi-Conductors
Insulators -
- each electron is attached to an atom so cannot move
- when voltage is applied to an insulator, no current passes through the insulator
Metallic Conductors
- has delocalised electrons that act as the charge carriers
- when voltage is applied the conduction electrons are attached to the positive terminal of the metal
Semi-Conductors
- number of charge carries increases with an increase in temperature
- resistance of semiconductor decreases as its temperature is raised
Potential Dividers and their capabilities
A potential divider consists of two or more resistors in series with each other and with a source of fixed potential difference.
potential difference of the source is divided between the components
in the circuit, as they are in series with each other.
By making a suitable choice of components, a potential divider can be used:
• to supply a pd which is fixed at any value between zero and the source pd
• to supply a variable pd
• to supply a pd that varies with a physical condition such as
temperarure or pressure.
How do batteries supply energy to a circuit?
- A battery has the Potential to transfer energy from its chemical store
- When connected in a circuit each electron passing through a circuit component does work to pass through the components
- the energy the electrons lose = the work done
so the energy supplied to a circuit is the work done for every unit of charge
E =QV
where the initial energy per charge supplied = EMF and the energy is lost through the components and the internal resistance of the circuit
Where do you place ammeters and voltmeters in a circuit and why
- Ammeter
- in series
- so that both the ammeter and the components are experiencing the same current
- must have almost 0 resistance to not effect current in the wire
- Voltmeter
- in parallel
- so that both the resistor/component it is measuring voltage of and itself are receiving the same voltage
- must have a sufficiently high resistance so no/little current flows through it
Ohm’s Law?
- Ohm’s law states that the pd across a metallic conductor is
proportional to the current through it, provided the physical
conditions do not change.
How to measure the resistivity of a wire
To determine the resistivity of a wire
• Measure the diameter of the wire d using a micrometer at several
different points along the wire, to give a mean value for d to calculate its cross-sectional area A.
• Measure the resistance R of different lengths L of wire to plot a
graph of R against L
The resistivity of the wire is given by the graph gradient
p = RA/L
Superconductors
A Superconductor is a wire or a device made of a material that has zero resistivity at and below a critical temperature that depends on the material
- when the wire/device has zero resistance, when current passes through it there is no P.D. across it because its resistance is 0, so current has no heating effect.
uses:
- making strong magnetic fields for stuff like MRI or particle accelerators
- research in use for power cables so we can zero energy loss in them, making them more efficient and for electric motors
Two methods of Investigating the relationship of current and Potential Difference
To measure the variation of current with pd for a component, use either
• a potential divider to vary the pd from zero, or
• a variable resistor to vary the current to a minimum.
The advantage of using a potential divider is that the current through
the component and the pd across it can be reduced to zero. This is not
possible with a variable resistor circuit.
Investigating Diodes
- A diode allows current to flow in one direction only
- one set of measurements are made for a diode in the forward direction
- another in the reverse direction
- The current is very small when the diode is in reverse and has to me recorded using milliamps>
- there is only a clear conductance at around 0.6 (for a silicon diode)
Positive and Negative Temperature Coefficient
- A metal is said to have a positive temperature coefficient because its resistance increases with increase of
temperature.
(The resistance of a metal increases with increase of temperature.
- This is because the positive ions in the conductor vibrate more when its
temperature is increased.
- The charge carriers (conduction electrons) cannot pass through the metal as easily when a pd is applied
across the conductor.)
Negative temperature coefficient
- exists for thermistors made of intrinsic semiconductors
- The resistance of an intrinsic semiconductor decreases with
increase of temperature. - This is because the number of charge carriers (conduction electrons) increases when the temperature is increased.
- thus making them have a negative temperature coefficient
What makes Thermistors suitable to be temperature sensors?
- thermistors made of intrinsic semiconductors have the property of the negative temperature coefficient
- As temperature increase the resistance of the component calls due to the release of more charge carriers
- this makes them good for detecting temperature changes because they increase current in circuits when temperature changes
Kirchoff’s Laws
- At any junction in a circuit, the total current entering the junction is equal to the total current leaving the junction. (charge conservation)
- For any complete loop in a circuit, the sum of the emfs around the loop is equal to the sum of the potential drops around the loop
Potential Difference Rules
- if the charge carries lose energy then the p.d is a potential drop
- if the charge carries gain energy (at the battery) then the p.d is a potential gain
- For two or more components in series, the total pd across all the components is equal to the sum of the potential differences across each component.
- The pd across compo nents in parallel is the same.
- For any complete loop of a circuit, the sum of the emfs round the loop is equal to the sum of the potential drops around the loop.
Power in Resistance Heating
If the component is at constant temperature.
- heat transfer to the surroundings takes place at the same rate. -Therefore,the rate of heat transfer =I^2R
• If the component heats up, its temperature rise depends on the
power supplied to it (I^2R) and the rate of heat transfer to the
surroundings.
• The energy transferred to the object by the electric current
in time t =power x time =12 Rt.
• The energy transfer per second to the component (i.e., the power
supplied to it) does not depend on the direction of the current.
Terminal P.D.
• The pd across the terminals of the source is the electrical energy
per unir charge delivered by the source when ir is in a circuit. The
terminal pd is less than the emf whenever currem passes through the
The internal resistance of a source is the loss of potential
difference per unit current in the source when current passes
through the source.
Power in a Circuit with internal resistance
where ϵ = IR + Ir
power supplied by the cell, Iϵ = I^2R + I^2r
the power supplied by the cell is = the power delivered to R + the power wasted
the maximum power delivered to the load is when load resistance = internal resistance of the same source
R=r
Cells in Series
The same circuit rules apply in series but with cells
- however for cells, current through the cells is calculated by diving the net emf by the total resistance
Cells in Parallel
For a circuit with n identical cells in parallel, the current through each
cell = I/n, where I is the total current supplied by the cells .
Diodes in Circuits
In a circuit with one or more diodes:
• a pd of 0.6 V exists across a diode that is forward-biased and passing
a current
• a diode that is reverse-biased has infinite resistance.
If a diode is flipped in the reverse direction then the components after it will have 0 current and thus 0 P.D so the PD of the diode = PD of the circuit
Why are potential dividers able to supply a fixed P.D from 0 to the source P.D?
- in a series circuit voltage splits between resistors in series in proportion to their respective resistances
- to have a voltage of 0 a resistor must have an infinite resistance according to the ratios of the resistance and voltage
When measuring the effects of current on the brightness of a lamp should you use a variable resistor set up or a potential divider set up?
- Potential Divider Set up
- The potential divider enables the current through the light bulb to be reduced to zero
- If a variable resistor was used instead there would still be current through the bulb at maximum resistance
Sensor Circuits
- sensor circuits produce an output potential difference based upon a change of a physical variable such as temperature or light intensity
Temperature Sensors
- consists of a potential divider made using a thermistor and variable resistor
- the variable resistor allows us to set a p.d across the thermistor for a constant temperature
- a change in the resistance and thus the voltage of the thermistor will then be due to the change in temperature
e.g if temperature increases, resistance falls, so voltage will fall
Light Sensors
- potential divider using a Light-Dependent resistor and variable resistor
- the of across the LDR changes when incident light intensity on the LDR changes
e.g if light intensity increases, the resistance of the LDR falls and thus the P.D across it falls
Newton’s Laws
- Objects either stay at rest or moves with constant velocity
unless acted on by a force.
2.
What is Inertia ?
- an object’s resistance to a change in velocity/motion
measured in kg
What is drag force dependent on?
- the shape of the object
- the speed of the object
- the viscosity of the fluid ( how easily a fluid flows over a surface)
- the faster an object travels in a fluid the greater the drag force on it
Motion of an object Falling in a Fluid
- The speed of an object increases as it falls
- the resultant force on the object is the difference of the force of gravity and the drag force acting on the object
- as the drag force increases the resultant force decreases
- so acceleration decreases to 0 as the object falls where W = D
- the object when acceleration = 0 has reached terminal velocity
and will remain at the constant speed for the rest of its motion
a = g - D/m
Motion of a powered Vehicle
- the top speed of a vehicle is dependent on its engine power and shape
- a vehicle with a more streamlined shape can reacher higher top speeds for the same engine than one that isn’t
the resultant force on a vehicle = F(e) - F(f) where Ff is the resistive force and Fe the driving force
- the drag force increases with speed so the max speed will be when Ff = Fe
Stopping Distance
Stopping Distance = Thinking Distance + Braking Distance
Thinking Distance
s = v t, where t is the reaction time of the driver
Braking Distance
v^2 = u^2 + 2as
where v is 0 and u is speed before breaks applied
thus, s = u^2/2a
Skidding
- Friction between the tyre and the road is what prevents wheel spin (slipping) so that the driving wheels can roll along the road
- If the driver accelerates to fast then the wheels skid, this is because there is an upper limit to the friction between the tyres and road
- breaks act to slow a vehicle down by increasing the friction between the tire and the road
- if the upper limit of friction reached then rather than slowing the breaks will lock, causing skidding/sliding of the vehicle
Vehicle Safety features
- ABS system
(anti-lock brake system)- to prevent skidding and sliding when break is applied at high speeds
- Seatbelts
- prevents crashing in to vehicle frame, force from belt is much lower than that of the force from the collision because it stops person much more gradually (higher impact time, lower force)
- Crumple Zone
- increases impact time so impact force is reduced
- Air bags
- reduced the force on individuals in vehicle by increasing impact time on person
- Vehicle Bumpers
- same as the crumple zone but lower effect
Why must Braking Distance increase when on greasy or icy roads?
- On a greasy or icy road, skidding is more likely because the limiting frictional force between the road and the tyres is reduced from its dry value.
- To stop a vehicle safely on a greasy or icy road, the brakes must be applied with less force than on a dry road otherwise skidding will
occur. - Therefore the braking distance is longer than on a dry road.
- (In fast-moving traffic, a driver must ensure there is a bigger gap to the car in front so as to be able to
slow down safely if the vehicle in front slows down.)
Advantages and Disadvantages of Potential Dividers vs Rheostats
potential dividers:
ADV - better control from 0 to maximum for current and voltage
DIS - power wasted because lower half of resistor always carries current
rheostat
ADV - easier to connect
DIS - minimum current through bulb is never 0
What is Superconductivity and what conditions are needed for a material to be superconducting?
- Superconductivity is a materials ability to have 0 resistance
- resistance decreases with a decrease in temperature
- For a material to become Superconducting they must be at or below the critical temperature
Why may a filament lamp most likely fail as it is switched on?
- Superconductivity is a materials ability to have 0 resistance
- resistance decreases with a decrease in temperature (for a metallic conductor)
- For a material to become Superconducting they must be at or below the critical temperature
How can Substances be identified using their Density?
- By finding the density of a material it can be compared to the density of known substances to identify them
How to find the Density of: A Liquid & An Irregular Solid
Liquid
- Measure the mass of an empty measuring cylinder.
- Pour some of the liquid into the measuring cylinder and measure the volume of the liquid directly.
- Use as much liquid as possible to reduce the percentage error in your measurement.
- Measure the mass of the cylinder and liquid to enable the mass of
the liquid to be calculated. - Calculate the density from mass/volume.
Irregular Solid
Measure the mass of the object.
• immerse the object on a thread in liquid in a measuring cylinder,
observe the increase in the liquid level. This is the volume of the object.
• Calculate the density of the object from its mass/volume
( or via eureka can method)
How to find the density of a regular solid
- take measurements of the lengths of the object using a micrometer or veneer callipers and find the volume doing cross section Area x height
- using a mass balance find the mass of the object
- density = mass/volume to fine the density
What does the stiffness of a metal wire depend on?
- Cross-Sectional Area
- The applied force will be spread out over this area (e.g in the same way it does for springs in parallel)
- thicker wire/large cross section = less force for given area = more stiff
- Length
- A longer wire will extend more (just like springs in series)
- The material it’s made out of
- the stiffness of the material itself (Young Modulus)
