2/9 Basic Physics

2/9 Basic Physics

I. Background concepts

A. Time (t)

- Definition= how long it takes for something of

interest to occur

- Time is measured in seconds (s) or divisions of

seconds such as milliseconds (ms)

B. Mass (m)

- Definition = amount of matter that is present

- Mass is measured in grams (g) or multiples of

grams such as kilograms (kg)

- Do not confuse with weight

- The gravitational force exerted on a mass by

the earth

- Do not confuse with density

- The amount of mass per unit volume

C. Length (l)

- Definition = extent of spatial separation

between any two points

- Does not take into account direction! (scalar)

- Length is measured in meters (m), multiples of

meters such as kilometers (km), or divisions of

meters such as centimeters (cm); you may see

also measured in the English system feet (ft) or

inches (in)

D. Elasticity (restoring force) (F_r)

- Definition = recovery from distortion to either

shape or volume

E. Newton's First Law of Motion : Inertia (F_i)

- Definition = All bodies remain at rest or in a

state of uniform motion unless another force

acts in opposition

- What it means = An object is going to keep

doing what it's been doing unless something

changes it

- Amount of inertia that an object has is directly

proportional to the mass of the object

- For example:

A massive object such as a steel ball with a

1 m circumference has a lot more inertia

than a ping-pong ball. If both of these

objects are rolling down a hill at you,

which would you rather try to stop? Why?

A larger opposition force (YOU) is

required to stop the steel ball than the ping-

pong ball. Also, the steel ball needs a larger

force to start its motion and change

direction of the motion

F. Newton's Third Law of Motion : Reaction

Forces (don't worry, we will get to the second

law in a few minutes)

- Definition = With every force there must be

associated an equal reaction force of opposite

direction

- What it means = For every action there is an

equal but opposite reaction

- Reaction force occurs because all materials

possess some degree of elasticity & because of

their elasticity, they can exert forces on other

objects

- For example:

When you push your hand against a desk, you

exert a force on the desk (it moves). However,

the desk also exerts a force on your hand (your

hand is "deformed" temporarily)

G. Displacement (x)

- Definition = the distance from a reference

(starting position) to a new or ending position

- Takes into account distance AND direction !

(vector)

- An object moves over a certain distance in any

# of directions à therefore, we must account

for BOTH direction moved AND distance

moved when specifying displacement

- Displacement is also measured in meters (m),

multiples of meters such as kilometers (km), or

divisions of meters such as centimeters (cm);

you may see also measured in the English

system feet (ft) or inches (in)

H. Velocity (v)

- Definition = amount of displacement per unit

time or the displacement accomplished during

some period of time

- Do not confuse with speed

- Speed only takes into account magnitude

and NOT direction (scalar) whereas

velocity has both magnitude AND direction

(vector)

- Calculation:

(x₂ - x₁)

v = ---------

(t₂ - t₁)

- From the above calculation, it can be seen that

velocity is measured in meters/second (m/s)

- Note: We have been talking about average

velocity. If we want to know velocity of an

object at a specific moment in time , then we

want to know its instantaneous velocity which

is the derivative of displacement :

v = ---

I. Acceleration (a)

- Definition = time-rate change in velocity or

change in velocity over time

- Calculation:

(v₂ - v₁)

a = ---------

(t₂ - t₁)

- From the above calculation, it can be seen that

acceleration is usually measured in

meters/second² (m/s²)

- If velocity increases, acceleration is positive &

if velocity decreases, acceleration is negative

J. Force (F)

- Definition = a push or a pull given by the

product of mass (m) and its acceleration (a)

- Calculation:

F = ma

- This equation is a version of Newton's Second

Law of Motion :

- The acceleration of an object is directly

proportional to the net force applied to the

object & inversely proportional to the

object's mass (a = F/m)

- Force is measured in the Newton (N) (1 N is the

force required to accelerate a mass of 1 kg from

a velocity of 0 m/s to 1 m/s in 1 s) or the dyne

(d) (1 dyne is the force required to accelerate a

mass of 1 g from a velocity of 0 cm/s to 1 cm/s

in 1 s) à 1 N = 100,000 d

K. Pressure (P)

- Definition = amount of force per unit area or

determining the sum of many forces on some

surface

- Calculation:

P = --- where A= area

- Pressure is measured in the N/m² or d/cm² or

Pascal (Pa)

1 N/m² = 1 Pa = 10 d/cm²

II. Vibratory Motion

A. Characteristics of a spring

- One end of a spring is attached to a mass and

the other to a wall

- Spring at equilibrium = A à 0 displacement

- Compressed = Bà -1 displacement

- Stretched (extended) = C à +1 displacement

- When the spring is compressed or extended, the

restoring force of elasticity opposes the force

that acts to deform the spring. The more the

spring is compressed, the greater the force

needed to further compress the spring due to

this force.

- This is known as Hooke's Law

F_r = - k x

where F_r = elasticity (restoring force)

k = spring constant

x = displacement of the spring

There is a minus sign in front of the spring

constant because the direction of the restoring

force is opposite to the direction of spring

displacement

1. Stiffness

- Definition = how resistant a spring is to being

compressed or extended

- Although all springs are elastic, some require

a greater force than others to be compressed

or extended

- The spring constant in Hooke's Law

represents stiffness à the stiffer the spring,

the greater the value of k & the greater the

force that is required to compress or stretch

the spring some given distance

2. Compliance

-Definition = the ease with which a spring is

compressed or extended

- The inverse of stiffness à as compliance

increases, the force required to compress or

stretch the spring decreases

B. Vibration of a spring-mass system

- If the mass in the previous figure is moved left

& then released, the system will be set into

vibration

- The mass will pass through equilibrium toward

a maximum displacement to the left

- Then the restoring force of elasticity (F_r)

overcomes the inertial force (F_i), motion stops

momentarily

- Then the direction of motion is reversed

- The mass then passes back through equilibrium

toward a maximum displacement to the right

C. Tuning fork

- Tuning fork is a U-shaped metal bar

- The tines have mass & elasticity

- Before tines are set in motion, they are in a state

of equilibrium (resting position) - position X

- After being struck, the tines move to place of

maximum displacement in one direction -

position Y

- Then due to elasticity, the tines move back

toward position X

- Due to inertia, it goes through position X & to

place of maximum displacement in opposite

direction - position Z

- Elasticity and inertia cause the cycle to repeat

(not forever!)

III. Other things to consider

A. Momentum (F_m)

- Definition = the product of mass and velocity

- When considering vibratory motion, it is

convenient to substitute the effect of

momentum for inertia

-Calculation :

F_m = mv

- So momentum is directly proportional to both

mass and velocity

B. Law of conservation of energy

- Definition = energy cannot be created or

destroyed

- What does it mean? Any system that can do

work (i.e. any body that can be set into

vibratory motion) must receive a supply of

energy from somewhere

1. Energy

- Definition = a measure of the capacity to do

work or something that can produce a change

in matter such as a displacement of mass

- Something that a body possesses

2. Work (w)

- Definition = when a force succeeds in moving

the body that the force acts upon

- The product of the magnitude of force applied

& the displacement

- Calculation:

w = Fx

- Something that a body does

- Work is measured in the joule (J) or erg

1 joule = 10,000,000 ergs

3. Power (P)

- Definition = the rate at which work is done

- Calculation:

P = ---

- Power is measured in the watt (W)

1 W = 1 J/s = 10,000,000 ergs/s

4. Intensity (I)

- Definition = the amount of power per unit of

area

- Calculated :

I = ---

- Intensity is measured in W/m²

C. Transformation of energy

- Remember that energy cannot be depleted à it

is transformed from one form to another

- Think back to the tuning fork:

- When the tine is struck and moved to

maximum displacement (position C), it gains

potential energy (PE) which is stored energy

or the potential to do work

- As the tine moves, potential energy is

converted to kinetic energy (KE) which is

the energy of motion

- Must also consider the force of friction (F_f)

- Vibratory motion does not continue

indefinitely - why?

- Definition = opposition to motion

- Calculation :

F_f = Rv where R = coefficient of friction

- In the tuning fork, air resistance causes

kinetic energy to be transformed to

thermal energy