Physics Unit 3 Cheat Sheet (Motion and Gravity)

q

p pico 10−12 n nano 10−9 μ micro 10−6 m milli 10−3 c centi 10−2 k kilo 103 M mega 106 G giga 109 t tonne 103kg

𝐸𝑘 =1

2𝑚𝑣2

𝑊 = 𝐹𝑥 cos 𝜃

𝑈𝑠 =1

2𝑘𝑥2

𝐹 = 𝑘𝑥 𝐹 = 𝑚𝑎 sin 𝜃

Energy (J) and

Force (N)

𝑈𝑔 = 𝑚𝑔ℎ

(only if gravity is constant!)

𝑃 = 𝑉𝐼

𝑃 =𝐸

𝑡

𝑃 = 𝐹𝑣

Power (W)

𝑝 = 𝑚𝑣 𝑚1 𝑣1 − 𝑢1 = 𝑚2(𝑣2 − 𝑢2) Impulse = ∆𝑝 = Σ𝐹∆𝑡 = 𝑚∆𝑣

Momentum (𝐤𝐠 𝐦 𝐬−𝟏)

and Impulse (𝑵 𝒔)

note that impulse does

not depend on

acceleration, ie. a collision

will have the same

impulse regardless of the

presence of padding

Motion

(𝐦, 𝐦 𝐬−𝟏, 𝐦 𝐬−𝟐) 𝑣 = 𝑢 + 𝑎𝑡

𝑥 =𝑡 𝑢 + 𝑣

2

𝑥 = 𝑢𝑡 +1

2𝑎𝑡2

𝑥 = 𝑣𝑡 −1

2𝑎𝑡2

𝑣2 = 𝑢2 + 2𝑎𝑥 𝑉𝐵𝑟𝐴 = 𝑉𝐵 − 𝑉𝑎

Σ𝐹 = 𝐹𝑔 sin 𝜃

𝑎 = 𝑔 sin 𝜃

Inclined Planes

(normal force acts at right angles to the surface)

Driving force = weight force - normal force

Σ𝐹 = 𝑚𝑎 =𝑚𝑣2

𝑟=

4𝜋2𝑟𝑚

𝑇2

𝑎𝑐𝑒𝑛𝑡𝑟𝑖𝑝𝑒𝑡𝑎𝑙 =𝑣2

𝑟=

4𝜋2𝑟

𝑇2

𝑆𝑝𝑒𝑒𝑑 =𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒

𝑇𝑖𝑚𝑒=

2𝜋𝑟

𝑇

Centripetal Motion

Collisions Elastic:

Energy conserved

Momentum conserved

Inelastic:

Energy lost as heat / sound / deformation

Momentum conserved

SI Units Speed: ms

-1

Acceleration: ms-2

Distance: m Time: s Mass: kg Force: N Energy: J Power: W Current: A Resistance: Ω Voltage: V

𝑎 = 𝑔 =𝐺𝑀

𝑟2=

4𝜋2𝑟

𝑇2=

𝑣2

𝑟

𝐹 =𝐺𝑀𝑚

𝑟2=

4𝜋2𝑚𝑟

𝑇2=

𝑚𝑣2

𝑟

𝑣 =2𝜋𝑟

𝑇=

𝐺𝑀

𝑟

𝑟3

𝑇2=

𝐺𝑀

4𝜋2

𝑣1 𝑅1 = 𝑣2 𝑅2

Gravity g gravitational field

strength (N Kg−1) a acceleration (𝑀 𝑠−2) F Force (N) v velocity (M s−1) M Central mass (kg) m Orbiting mass (kg) r radius or orbit (m) T period of orbit (s)

𝐺 = 6.67 × 10−11 N m2kg−2 Acceleration is

independent of mass

Force acts equally on

both bodies

Velocity is directed at

a tangent to the path

Normal Force

Newton's Laws 1. Every object continues in a state of rest or constant velocity unless acted

on by an unbalanced force. 2. The rate of change of momentum is directly proportional to the magnitude

of the net force and is in the direction of the net force. 3. For every action there is an equal and opposite reaction. Action-reaction

forces act on different objects, e.g.. Joe and wall Newton's laws assume that space and time are absolute, in contrast with Einstein, who proposed that space and time are relative. The inertial frame of reference refers to objects moving at a constant speed, where Newton’s laws work (ie. the third law wouldn’t work if Joe broke the wall down).

Graph interpretation X-axis Y-axis Area under Gradient

Extension Force 𝑈𝑠 Spr. const Time Velocity Displ. Accel. Time Accel. Velocity - Time ΣF Impulse - Displ. Force Work - Dist 𝐹𝑔 Work -

Strain Stress 𝐸𝑠𝑡𝑟 /𝑚3 YM (𝐸)

Action/reaction forces:

Always exist in pairs

Are equal in magnitude

Act in opposite directions

Act on separate objects

Act

ion

/ R

ea

ctio

n

Sources of centripetal force:

Tension, eg:

o Gravity

o Along a string

Sideways frictional forces

This value is a constant for

bodies orbiting the same

central mass

AVOID

Physics Unit 3 Cheat Sheet (E/P and M/S)

Transistor Amplifier

𝐼𝑒 = 𝐼𝑐 + 𝐼𝑏

𝑉𝑏 = 𝑉𝑏𝑒 + 𝑉𝑒

𝑉𝑐 = 𝑉𝑐𝑒 + 𝑉𝑒

𝑉𝑐𝑐 − 𝑉𝑐 = 𝑅𝑐𝐼𝑐

𝑉𝑏 =𝑅2

𝑅1 + 𝑅2𝑉𝑐𝑐

∆𝑉𝑐 = ∆𝐼𝑐𝑅𝑐

𝐼𝑏 is very small ∴ 𝐼𝑒 ≈ 𝐼𝑐

𝑉𝑏𝑒 ≈ 0.7v

𝑉1

𝑅1=

𝑉𝑏

𝑅2

𝑉out ≈1

2𝑉𝑠

𝐴𝐼 =𝐼𝑒𝐼𝑏

=𝐼𝑐𝐼𝑏

𝐴𝑉 =𝑉𝑜𝑢𝑡

𝑉𝑖𝑛=

𝑅𝑐

𝑅𝑒

Voltage Divider

𝑅1 = 𝑅2

𝑉𝑐𝑐 − 𝑉𝑅

𝑉𝑅

𝑅2 = R1

VR

𝑉cc − VR

𝑉cc = 𝑉R 𝑅1 + 𝑅2

𝑅1

𝑉R = 𝑉cc 𝑅1

𝑅1 + 𝑅2

Phototransducers LDRs Phototransistors Photodiodes

Vary resistance with illumination

Ohmic

As illumination increases, resistance decreases

Operate as transistors with base as light source

Vary conductance (resistance) with illumination

Non-ohmic

Work in reverse bias

Advantages Disadvantages Advantages Disadvantages Advantages Disadvantages

Simple, sensitive

Wide range

Can be used in voltage dividers

Very slow response time

Sensitive

Gain of 10 to 100

Not as fast as photodiodes

Very fast response time

Not sensitive

∴ 𝜏 = 𝑟𝐹 sin 𝜃

Torque (𝐍 𝐦)

Torque is equal to the product of radius and the perpendicular force component 𝐹⊥. 𝐹⊥ = 𝐹 sin 𝜃 and 𝜏 = 𝑟𝐹⊥

Torque ≠ Work

Jargon

tough materials which can absorb large amounts of strain energy per unit volume before failing

brittle materials with little or no plastic region

stiff materials with a high value for Young’s Modulus

malleable *not needed*

ductile materials with a large plastic region

strength how much stress a sample can be subjected to before failing

clipping flat points in an output signal caused by the input signal being out of range

saturation when the input voltage is greater than the linear region

cut-off when the input voltage is less than the linear region

linear gain the gain of an amplifier where the signal is not clipped

de-coupling the ‘DC blocking’ effect of a capacitor

Stress = σ =𝐹

𝐴

Strain = ε =∆𝐿

𝐿 or

𝑥

𝐿

Young′s Modulus = E =σ

ε=

𝐹𝐿

𝐴∆𝐿=

𝐹𝐿

𝐴𝑥

Area =Est

Vol=

1

2σε =

1

2Eε2 =

σ2

2E

∴ 𝐸𝑠𝑡 = Area × Vol

Stress (𝐍 𝐦−𝟐) and strain

Area under 𝛔 vs. 𝛆

Young’s Modulus is independent of

thickness and therefore the same for

every sample of a given material

Total current, voltage and resistance Series Parallel

Current 𝐼𝑇 = 𝐼1 = 𝐼2 … 𝐼𝑇 = 𝐼1 + 𝐼2 …

Resistance 𝑅𝑇 = 𝑅1 + 𝑅2 … 𝑅𝑇 =1

1𝑅1

+1𝑅2

…

Voltage 𝑉𝑇 = 𝑉1 + 𝑉2 … 𝑉𝑇 = 𝑉1 = 𝑉2 …

Equilibrium

Translational Rotational Static Σ𝐹 = 0 Σ𝜏 = 0 Σ𝐹 = 0 and Σ𝜏 = 0

N m−2 = Pa

Remember that this energy is per unit volume

The torque = 0 in

equilibrium

regardless of the

reference point.

Note that maximum

stress is not equal to

breaking stress

LEDs LDs

< 1μs Forward bias

Wide beam

Wide wavelength

Slow switch speed

> 1ns Forward bias

Narrow beam

Narrow wavelength

Fast switch speed

𝑉𝑐𝑐 ≡ 𝑉𝑠

Copper Glass fibre

one signal per wire

skin effect

thick fibres

expensive

affected by EM interference

convenient to branch and join

1000+ signals per wire

no skin effect

thin fibres

cheap

not affected by EM interference

inconvenient to branch and join

Skin effect Low frequencies can travel along the entire wire, whereas

high frequencies can only travel along the skin. Therefore,

high frequencies encounter more attenuation than low

frequencies, limiting data transfer rates. This doesn’t

happen to optic fibres.

Strength (MPa)

Tensile Compressive

Concrete 2 20

Steel 820 500

Cast iron 170 550

note that if one of

the components is

a diode then the

maximum voltage

consumed by it is

the bias (0.7v)