2nd: Dynamics; Forces, density & pressure; Work, energy & power Flashcards
centre of gravity
The point at which the weight of the object may be considered to act
where is CoG
-symmetrical objects with uniform density, the centre of gravity is located at the point of symmetry
-centre of gravity is roughly in the middle of the body behind the navel, and for a sphere, it is at the centre
stability
position of the centre of gravity of an object affects the object’s stability
An object is stable when its centre of gravity lies above its base
The wider the base of an object = lower its centre of gravity = more stable the object is
MOST STABLE have WIDE BASES AND LOW COG
The narrower the base of an object = higher its centre of gravity = less stable the object is
Centre of gravity versus centre of mass
in uniform gravitational field, the centre of gravity is identical to the centre of mass. Centre of mass does not depend on the gravitational field
+W = mg, the centre of gravity does depend on the gravitational field
++When an object is in space:
📍Its centre of gravity will be closer to object with larger gravitational field
📍Its centre of mass will be close to its geometric centre- CENTRE OF MASS IN MIDDLE
also: Since the centre of gravity is a hypothetical point, it can lie inside or outside of a body. Centre of gravity can also move, depending on the shape or the orientation of the object being considered. E.g, a human body’s centre of gravity is lower when leaning forwards than when standing upright.
moment = Fd
turning effect of a force (about a pivot)
-occurs when forces cause objects to rotate about a pivot
+The force may not always be applied perpendicularly to the pivot. But distance used in the equation must be the perpendicular distance from the pivot. In these cases, the component of the distance that is perpendicular to the pivot must be used
e.g in daily life
📍tip
opening a door
+door handle is placed on the opposite side of the door to the hinge (the hinge is the pivot)
+maximises the distance for a given force
-Which provides a greater moment (turning effect)
This makes it easier (requires less force) to push or pull the door open
📍📍
-only round your answer right at the end of your calculation. Always work with at least one, preferably two more significant figures than final answer requires.
-Sketching a quick diagram of all the forces acting on the object will help you visualise which forces are perpendicular to the distance from the pivot. Not all forces will provide a turning effect and it is common for questions to provide more forces than required to increase the level of difficulty of the question.
-DEFINITION - couple
-a couple consists of a pair of forces that are:
-couples produce…
-couples CANNOT…
📌 a pair of forces that acts to produce rotation only 📌
-a couple consists of a PAIR OF FORCES that are: EQUAL in magnitude ;; OPPOSITE in direction ;; PERPENDICULAR to the distance between them
-Couples produce a resultant force of zero
(so due to Newton’s 2nd law F=ma, object doesn’t accelerate)
-the forces that make up a couple cannot share the same line of action. The line of action is a line through the point at which the force is applied.
whats the difference between the moment of a single force and moment of a couple?
-moment of a single force depends on the perpendicular distance to the pivot
-However, the moment of a couple depends on the perpendicular distance 📌 BETWEEN 📌 the two forces
DEFINITION torque = Fd where d is perpendicular distance between the forces
moment of a couple =
moment of a pair of forces that acts to produce rotation only
[eg tau (torque) = 10 [FORCE OF COUPLE: opposite, perpendicular, equal] x 0.4 [length of steering wheel along the whole thing] = 4Nm.
4sin(30) [VERTICAL F] x 0.3 [RULER LENGTH] = 0.6Nm.]
DEFINITION! Principle of Moments
For a system to be in equilibrium, the sum of clockwise moments about a point must be equal to the sum of the anticlockwise moments (about the same point)
TIP
distances same units
know if forces CW or ACW
Make sure that all the distances are in the same units and you’re considering the correct forces as clockwise or anticlockwise, as seen in the diagram
force - up, right, CW & down left CW
up, left, ACW
down right ACW
DEFINITION - equilibrium
system is in equilibrium when all the forces are balanced
There is no resultant force and no resultant torque
so according to Newton’s 1st law -
an object in equilibrium will therefore remain at rest, or at a constant velocity, and will not rotate
so for moments, CW = ACW moments.
Coplanar forces in equilibrium
-Coplanar forces can be represented by vector triangles.
-Equilibrium, => coplanar forces are represented by closed vector triangles [forming closed path, keeping SAME LENGTH & DIRECTION - rearrange, connect tip to tail.]
-Forces are in equilibrium if an object is either: At rest, OR Moving at constant velocity
common F: weight, normal reaction force, normal contact force, tension (from cords & strings), friction
-USE RULER for exam
density = m/V
📍Gases are less dense than liquids, which are less dense than solids ;;; bc there are fewer particles, and therefore less mass, per unit volume
📍CALC VOLUME - sphere 4/3pir^3, cube d^3, cylinder pir^2xl
📍1000mm = 1m. IS smaller unit to larger (mm to cm), divide
pressure = F/A
📍DEFINE: force per unit area
📍 how concentrated a force is. SCALAR
📍If a force is spread over a large area it will result in a small pressure; spread over a small area = a large pressure
📍DEFINE - Hydrostatic pressure: the pressure at any given point within a fluid, that is exerted by the weight of the fluid above that point
📍if fluid is at rest, then all the points within the fluid are in equilibrium, so the pressure acts in all directions at each point
derivation of f ∆p = ρg∆h
Using W=mg, p=m/V, P=F/A
replace m and V in eqn.
- Rearrange to form m=pV, and V = Ah
- P = F/A = mg/A = pVg/A = pAhg/a = phg
- P = phg
Using the equation for hydrostatic pressure
📌📌 Total pressure = Hydrostatic pressure + Atmospheric pressure 📌📌
Atmospheric pressure (also known as barometric pressure) is 101 325 Pa 📌
📍When an object is immersed in a liquid, the liquid will exert a pressure which acts in all directions, squeezing the object
📍The size of this pressure depends upon: density, ρ, of the liquid;; depth, h, of the object;; gravitational field strength, g
📍The total pressure acting on the object considers both the weight of the fluid above the object, and the weight of the air above the object
When asked about the total pressure, the atmospheric pressure must also be included
📍 manometer: an instrument to measure pressure and density of two liquids
📍how it works: In Figure 1: The level of liquid is equal because the atmospheric pressure (Patm) is the same
In Figure 2: If the pressure on one side rises, the liquid will be forced down making the liquid in the other limb rise. The difference between the two levels gives the pressure difference between the two ends of the tube
In Figure 3: The U-tube now has two different liquids. The density of the blue one is greater than that of the orange one. The pressure at each point is due to the atmospheric pressure plus the weight of the liquid above it
e.g Atmospheric pressure at sea level has a value of 100 kPa. The density of sea water is 1020 kg m-3.
At what depth in the sea would the total pressure be 250 kPa?
D) 15m
h= (250,000 - 150,000) / (1020 x 9.81) = 15m.
REMEMBER:
-convert all the pressure values to SI units (Pa) before you begin the calculation
-kPa => Pa, x1000
-mPa => Pa, x 10⁶
upthrust
TIP: Since upthrust is a force, it is influenced by pressure, not by the density of the object
📍upthrust: a force which pushes upwards on an object submerged in a fluid (liquids and gases)
📍Also known as buoyancy force, upthrust is due to the difference in hydrostatic pressure at the top and bottom of the immersed object
📍 force of upthrust is significantly greater in liquids than in gases, this is because liquids are much denser than gases
📍UPTHRUST DIRECTLY PROPPORTIONAL TO PRESSURE
📍force on the bottom of the can will be greater than the force on top of the can. Resultant pressure causes a resultant upward force on the can known as upthrust
📍 why objects appear to weigh less when immersed in a liquid. If the upthrust is greater than the weight of the object, the object will rise up
📍For an object to float, it must have a density less than the density of the fluid it is immersed in
e.g 2m², experiences pressures of 3000 Pa and 7700 Pa at the top and bottom of the cube.
P = F/A. F = pressure x area = (7700 - 3000) x 2 = 4700 x 2 = 9400N.
DERIVAT Archimedes’ Principle
states that…
eqn… DERIVATION
📍”An object submerged in a fluid at rest has an
upward buoyancy force (upthrust)
equal
to the weight of the fluid displaced by the object”
📍📍 F = ρVg📍📍
UPTHRUST = density x 9.81 x V
BC F=ma where m = ρV, upthrust is equal to F = (m)g = (ρV)g
or ρ =m/V, F=ma equals m=F/a, so ρ = F/a ÷ V then ρV = F/a then a=g so ρVg = F
physics of Archimedes’ principle
📍object sinks until the weight of the fluid displaced is equal to its own weight
📍Therefore, the object floats when the magnitude of the upthrust equals the weight of the object
eqn how much of iceberg is not submerged?
density of ice / density of water = volume of water/volume of ice
pi / pw = vw / vi.
vw = pi x vi / pw = 917 Vi / 1020 = 0.9Vi
90% of iceberg submerged.
10% not submerged.
TIPS
Step 1: You need the volume of the submerged object, but only because you want to know how much fluid was displaced
Step 2: What you really want to know is the weight of the displaced fluid. F = density x g x V
Work & Energy
-work is done when an object is displaced by an external force applied in the direction of its displacement
W = Fs = force x displacement of obj
physics of work: When work is done, energy is transferred. Work done is equal to the amount of energy transferred. Usually, if a force acts in the direction that an object is moving, then the object will gain energy. If the force acts in the opposite direction to the movement, then the object will lose energy
TIP
-choose force parallel to the direction of movement of an object. You may have to resolve the force vector to find the component that is parallel. The force may not always be in the same direction as the movement, as shown in the worked example.
e.g vector triangle of weight where weight is hypotenuse. vertical component is parallel to force. therefore weight x sin(angle) = force.
DEFINE - principle of conservation of energy
Energy cannot be created or destroyed, it can only transferred from one energy store to another
physics of principle of conservation of energy
- total amount of energy in a closed system remains constant
energy stores + description
📍KINETIC: when object is moving = has energy in kinetic store
📍GRAVITATIONAL POTENTIAL: Objects gain energy in their gravitational potential store when they are raised through a gravitational field
📍ELASTIC: Objects have energy in their elastic potential store if they are stretched or compressed
📍ELECTROSTATIC: Objects with charge interacting with one another have energy in their electrostatic store
📍MAGNETIC: Magnets interacting with each other = have energy in magnetic store
📍CHEMICAL: Objects with energy in their chemical store can release energy in chemical reactions
📍NUCLEAR: Atomic nuclei release energy from their nuclear store during nuclear reactions
📍THERMAL: All objects have energy in their thermal store; the hotter an object is, the more energy it has in this store
energy transfers + description
📍MECHANICAL: When a force acts on an object - e.g. pulling, pushing, stretching, squashing
📍ELECTRICAL: A charge moving through a potential difference e.g. electrons flowing around a circuit
📍BY HEATING: Energy is transferred from a hotter object to a colder one
📍BY RADIATION: Energy is transferred by electromagnetic radiation
Energy dissipation
When energy is transferred from one store to another, not all the energy will end up in the desired store
Dissipation is used to describe ways in which energy is wasted
Any energy not transferred to useful energy stores is wasted because it is lost to the surroundings by heating, light or sound
so what counts as wasted energy?
examples?
📌depends on the system
📌For example, in a television: Energy is transferred electrically from the mains supply to the thermal store of the television. Energy is usefully transferred by radiation (light) and by heating (sound vibrations) to the surroundings. Energy is dissipated (wasted) by heating to the thermal energy store of the surrounding air
📌Another example, in a heater: Energy is transferred electrically from the mains supply to the thermal store of the heater. Energy is usefully transferred by heating to the surroundings. Energy is dissipated (wasted) by radiation (light) to the thermal energy store of the surrounding air
-a spring transfers energy from the elastic potential store to kinetic store.
DEFINE - efficiency of a system
EQNS.
- the ratio of the useful energy output from the system to the total energy input
efficiency =
(useful energy/power output ÷
total energy/power input) x 100
system HIGH efficiency…
-If a system has high efficiency, this means MOST OF ENERGY transferred is USEFUL
If a system has low efficiency, this means most of the energy transferred is wasted
e.g, efficiency = Pout/Pin = Pout/(Pout + Plost)
0.2ke = gpe (20% efficiency)
DEFINE power
eqns - energy/work
📌 rate of energy transfer 📌
work done per unit time (work done=energy transferred)
EQN: P = E/t = W/t
60W for e.g = amount of energy transferred electrically from the mains supply per second.
DERIVATION OF P = FV
power delivered to a moving object; only relevant where a constant force moves a body at constant velocity
Power is delivered to the object by a force in order to produce an acceleration
The FORCE must be applied in the SAME DIRECTION as the VELOCITY
TO DERIVE P=W/t, W=Fs, d=vt
W = Fvt
P = Fvt/t
cancel out t. P = Fv
DERIVATION Gravitational Potential Energy (in uniform grav field)
W = Fs, W=mg
F = mg. s = Δh.
W = mgs = mgΔh
ΔEp = mgΔh.
gpe physics
📌Gravitational potential energy is energy stored in a mass due to its position in a uniform gravitational field
When a heavy object is lifted, work is done since the object is provided with an upward force against the downward force of gravity
Therefore energy is transferred to the object.
📌If a mass is lifted up, it will gain gravitational potential energy. If a mass falls, it will lose gravitational potential energy
📌potential energy on the Earth’s surface at ground level is taken to be equal to 0
GPE v height graphs
Since the graphs are straight lines, GPE and height are said to have a linear relationship
These graphs would be identical for GPE against time instead of height
thrown up = positive slope. neg slope for falling ball’s gpe.
DERIVATION of kinetic energy = 1/2mv²
use W=Fs, F=ma, and v² = u² + 2as
-initial velocity is 0, u =0,
v² = 2as. a = v² / 2s.
so F = ma = m ⨯ v² / 2s.
W = mv²/2s ⨯ s = 1/2mv²
kinetic energy ..
-energy an object has due to its motion (or velocity)
-faster an object is moving, the greater its kinetic energy
When an object is falling, it is gaining kinetic energy since it is gaining speed
This energy transferred from the gravitational potential energy it is losing
An object will maintain this kinetic energy unless its speed changes
