Every Equation
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Transcript of Every Equation
Double Award PhysicsRevision
Motion
speed = distance ÷ timeor
velocity = displacement ÷ time
acceleration = change in velocity ÷ time
Unitsspeed and velocity - metres per second
distance and displacement – metres
time – seconds
acceleration – metres per second squared
force = mass x accelerationweight = mass x gravitational field strengthmoment = force x distance (pivot to force)
clockwise moment = anti-clockwise moment(for a balanced lever)
pressure = force / area
Unitsforce and weight – Newton (N)
mass – kilograms (kg)
moment – Newton-metre (Nm)
pressure – Newton per metre squared (N/m2) or Pascal (Pa)
area – metre squared (m2)
Forces
work done (energy transfer) = force x distance (in direction of the force)
power = work done ÷ timekinetic energy = ½ x mass x velocity2
gravitational potential energy = weight x height
efficiency (%) = useful output ÷ total input
Unitswork done and energy transfer – Joules (J)
power – Watt (W)
kinetic and gravitational potential energy – Joule (J)
height –metre (m)
efficiency – no unit!
Energy
current = charge ÷ timevoltage = energy ÷ charge
resistance = voltage ÷ currentpower = voltage x current
(in series) resistancetotal = resistance1 + resistance2
(in parallel) resistancetotal = resistance1 ÷ 2
Unitscurrent – Ampere (A)charge – Coulomb (C)voltage – Volt (V)resistance – Ohm (Ω)
Electricity
(paying for electricity)domestic energy kilo-watt hour = power x time
cost = domestic energy x unit price
(transformers)ratio of turns = ratio of voltage
Unitsdomestic energy unit – kilo-Watt hour (kWh)power – kilo-Watt (kW)time – hour (h)cost and unit price – pence (p)
More on Electricity
Get angry and be a Physicist who R.A.G.E.S. at the tough question
Really Read
Asked to Answer?
Gifts Given
Easy Equation
Simply Solve
Example
• Find the speed of a boat if its mass is 1200 kg and it has a kinetic energy of 9600 J. KE = 9600 JKE = 9600 J
m = 1200 kgm = 1200 kg
KE = ½ m x v2
9600 = ½ x 1200 x v2
9600 = 600 x v2
600 60016 = v2
4 m/s = v
v = ?v = ?
Equation ExamplePhysics
Work Done• Background-
• Mechanical work is done when anything is moved against a force or resistance. Work Done requires Energy. Two important factors- movement and the movement must be against a force
• e.g. when an object is lifted up (movement against the object’s weight)
Work Done• Definition-
• One joule of work is done when a force of 1 Newton moves through a distance of 1 metre in the direction of the force
Work Done• Word Equation-
• Work Done = Force x Distance
• The distance must always be measured in the direction in which the force is acting
Work Done• Units-
• Nm = N x m
• Nm = J
Work Done• Variations-
• Distance = Work Done / Force
Work Done• Sample Question-
• A lift of mass 250 kg carries a man of mass 76 kg. How much work is done by the wire rope which draws the lift through a height of 150 cm?
• Total Mass = 250 + 76 = 326 kg
• Total Force = 326 x 10 = 3260 N
• Distance travelled = 150 cm = 15 m
• Work Done = 3260 x 15
= 48 900 J or 48.9 kJ
WORK DONE• If the question requires you to do a calculation you MUST
show how you calculated the answer
1. Calculate the Work Done when-
a) 5 kg is lifted 50 cm
b) An object is pushed one metre against a frictional force of 40 N
2. How far vertically can a machine lift an object of 50kg if it is supplied with 1000 J?
3. What is wrong with the following statement-?• Work Done is measured in Joules or in N/m
Principle of Moments• Background
• When 2 forces are applied to an object, as in the case of a lever, they will be balanced when their turning effects in opposite directions are equal
Principle of Moments• Definition
• An object is in equilibrium (won’t move) if the clockwise moment is equal to the anticlockwise moment
Principle of Moments• Word Equation
• ForceA x DistanceA = ForceB x DistanceB
dB
FB FA
dA
Principle of Moments• Units
• N x m = N x m
Nm = Nm
Principle of Moments• Variation
• Finding the distance from a force to the pivot
- DistanceA = ForceB x DistanceB
ForceA
Principle of Moments• Practice Question• What force would be needed to balance
the beam shown below?
• ForceA x DistanceA = ForceB x DistanceB
F x 2 = 600 x 3F = 1800 / 2F = 900 N
3 m
600 N FA
2 m
Principle of Moments1. Complete the sentence-
• If a pivoted lever is balanced, then the clockwise moment is equal to the anticlockwise moment (2 marks)
2. A see-saw, with the pivot in the middle, is balanced when one person sits on each side. Dave sits 2 m from the pivot and has a mass of 50 kg. Where must Dave’s wee brother Jim sit if Jim’s weight is 250 N? (g = 10 kg/N) (4 marks)
Conservation of Energy• Background
• Energy cannot be created or destroyed, it can only be converted into another form. The total energy of the universe is constant.
Conservation of Energy• Definition
• For a moving object the potential energy lost is equal to its gain in kinetic energy (provided that heat loss is ignored)
Conservation of Energy• Word Equation• Potential Energylost = Kinetic Energygain
(initial) m x g x h = (final) ½ m x v2
Conservation of Energy• Units
• kg x m/s2 x m = kg x m/s
• Joules = Joules
Conservation of Energy• Variation
• Question gives the potential energy of an object and asks you to calculate the maximum speed it can reach
• GPEstart = KEend
• GPE = ½ m v2
• GPE x 2 / m = v2
Conservation of Energy• Example
Cow of mass 200 kg falls out of an oriental building which is 50 m high. What speed does the cow reach the instant before it hits the ground?
GPEstart = m x g x h= 200 x 10 x 50 = 100 000 J
KEend = 100 000 J
KEend = ½ m x v2
100 000 = ½ x 200 x v2
1000 = v2
31.6 m/s = v
Conservation of Energy• What does the conservation of energy
mean? (2 marks)• Complete the sentences for the pendulum
bob shownWhen the bob is at position 1 it has potential
energy. When it is released and reaches position 2 it has kinetic energy. The energy it had at 1 is equal to the energy it has at 2 (3 marks)
• A kid playing on a swing has 250J of energy when he is furthest from the ground. If the maximum speed he reaches is 5m/s then what is the mass of the kid?
(4 marks)
21
Weight• Background
• Hang something from the end of a spring balance and the downward pull from the Earth can be measured
• When an object is released and allowed to fall to the ground freely, it will accelerate as it falls
Weight• Definition
• The pull due to the Earth is called the gravitational force and will cause an object which is free falling to accelerate towards the Earth at 10 m/s2
• 1 kg has a downward pull of 10 N
Weight• Word Equation• Resultant Force = Mass x
Acceleration• Weight = Mass x Gravity Constant
On Earth, Gravity Constant = 10Weight = Mass x 10
Weight• Units
• N = kg x m/s2
Or
• N = kg x N / kg
Weight• Variation
• Mass = Weight / Gravity Constant
On Earth,
Mass = Weight / 10
Weight• Example
• Which has the most weight?
Objects on Earth – Objects on Earth –
g = 10 N/kgg = 10 N/kg
Object on the Moon – Object on the Moon –
g = 1.6 N/kgg = 1.6 N/kg
5 kg 50 kg
100 kg15 kg500 kg
5000 N5000 N
160 N160 N
50 N50 N
150 N150 N
500 N500 N
Weight1 Weight is another name for the gravitational force
on something
Weight is measured in Newtons
2 ‘A bag of sugar weighs 20 kg’ What is wrong with this sentence? What should it say?
3 Three aliens land on several planets.
a) Which alien landed on Earth?
b) Which two aliens landed on the same planet?
c) If they were all on Earth which would weigh the most?
Alien
Mass
Weight
1 2 3
40 20 20
80 200 40
Acceleration• Background
• If the speed or the velocity of an object is not constant (changing- either speeding up or slowing down), then the motion of the object is said to be accelerating
Acceleration• Definition
• Acceleration is the rate of change of velocity
• 1. Change (difference)
• 2. Rate (time)
Acceleration• Word Equation
• Acceleration = Change in velocity
• If initial velocity is larger than final velocity then the object is decelerating
Time
Acceleration• Units
• m/s2 = m/s /s
Acceleration• Variation
• Final Vel = (acc x time) + Initial Vel
Acceleration• A motor cycle accelerates at 2.5 m/s2
from a starting velocity of 10 m/s. What is the final velocity of the motorcycle after 8 seconds?
• Final Velocity = (2.5 x 8) + 10
= 20 + 10 = 30 m/s