[Notes] Elementary Physics

8/6/2019 [Notes] Elementary Physics

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2 Equation 4d=t vi +vf 2

y=t

vi +vf2

3 Equation 5

d=tvi + a t2

2 y=tvi + gt

2

2

4 Equation 6

d=vf

2 -vi22a

y=v

f

2

-v

i

2

2a vf

2 =2g(y)+vi2

Summary of Kinematic Equations

Type ofmotion

Displacement Velocity Acceleration

stationary

objectconstant 0 0

constant

velocity constant 0

constantacceleration

constant

Graphical analysis of motion (recap: slope= [rise] [run] )y velocity is the slope of the graph of displacement against

time

y acceleration is the slope of the graph of velocity against

time

Given

Formula

x=t

y=d

x=t

y=v

x=t

y=a

v= d t

a= v t

Hint in memorizing:

A projectile motion is a combination of vertical

component with constant acceleration and horizontalcomponent with constant velocity that are independent toeach other

y vertical component = constant a = g = 9.8 ms2

y horizontal component = constant v = 0 ms2

y Components:

1] the projectile is the object thrown with an initialvelocity and acted upon by gravity

2] the trajectory is the parabolic path travelled by theprojectile

3] the maximum height (ymax) is the highest point of

the trajectory with a velocity of 0 m s 4] the range (R) is the total horizontal distance

travelled

Formulas:

Equation 3 a=vf-vi

t vf=at+v1 vfx=vixvfy=viy+gtEquation 5 d=vit+ at

2

2 R=vixt

ymax=viyt+gt

2

2 Equation 6

d=vf

2+vi2

2a vf2=vi2+2ad vfx2 =vix2

vfy2 =viy

2 +2gy

vix=vi cos viy=vi sin

Getting the value oft1 (maximum height is reached)

1] vfy=viy+gt1 2] 0=viy+gt1 3] gt1=-viy

4] t1=-viy

g 5] t1= viy 9.8 m

s2 6] t1= viy g = visin g Getting the value oft2 (projectile has landed)

t2=2t1=2visin g

Getting the maximum height (given: initial velocity andangle)

1] ymax

=viyt+gt

2

2 2] y

max=

gt2

2

3] ymax

=

g

viysin g

2

2

4]

ymax

=

gviy

2

sin2

g2 2

5] ymax

=viy

2 sin2

2g

Getting the Range:1] R=vixt 2] R=vix cos 2visin g 3] R=

2vix2 cos sin

g 4] R= vix2 sin2 g Trivia:

To achieve the maximum range, must be 45 if there isno air resistance. Less than 45 if there is air resistance.

According to Aristotle during the 4th

century BC, there aretwo types of motion:

1] Natural

y movement is either straight up or down

y objects seek their natural resting places2] Violent

y imposed motion/external force

y result to forces that are pulled/push


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Therefore, force is necessary to keep an object moving.

However, Galileo disproved Aristotles observations and

created another observation.

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Inertia is the tendency of an object to resist changes inits motion

Isaac Newton created the three laws of motion:1] Law of Inertia

y an object at rest remains at rest while an object

at motion remains at motion unless acted uponby an external force

y net force is the sum of all the forces acted on anobject

2] Law ofAccelerationy F =ma

3] Law of Interaction / Action-Reaction

y for every action there is an equal (magnitude) butopposite (direction) reaction

y only occurs in pairs

3Check it here:

http://zonalandeducation.com/mstm/physics/mechanics/forc

es/galileo/galileoInertia.html


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Force

y push or pull

o causes an object at rest to start movingo

causes a moving object to change its directiono causes a moving object to stop may be balanced (Fnet=0)

may be unbalanced (Fnet0)

may be non-contact/field

y action at a distance force

y doesnt need a direct contact

y examples:

y gravitational, magnetic, electrical

may be contact

y needs a direct contact

y examples:

y spring/elastic force, tensional force, friction/air

resistance

Friction

y is the force that resists motion whenever two materials ormedia are in contact with each other and are sliding or

rolling over each other

y force that resists motion whenever two materials are in

contact

y main causes:

y (mechanical/physical level) mechanical interlocking of

irregularities on the two surfaces in contacty (atomic level) attractive forces between the surfaces

representative atoms

y types of friction:

y static friction includes all cases in which the frictionalforce is enough to prevent relative motion between

surfaces in contact

y sliding or kinetic friction occurs when there is

relative motion at the interface of the surfaces incontact

y rolling friction takes place when one surface rotates

as it moves over another surface but doesnt slip norslide the area of contact

Principles of friction:

y friction acts parallel to the surfaces that are in contact

and is in the direction opposite to the motion of the object

y friction depends on the nature of materials in contact and

the smoothness of the surfaces

y sliding friction is usually less than starting friction

y sliding friction is practically independent of speed

y friction is practically independent on the area of contact

y friction is directly proportional to the force pressing the

two surfaces together

Ff SFN Ff is frictional forceFf =KFN FN is normal force=

Ff FN Fapp is applied forceS is the coefficient of

static friction

Ff =Fapp (if direction of force ishorizontal)

K

is the coefficient of

kinetic friction

other symbol for Fnet is

(eta)

is the coefficient of

friction

Normal force is the pressing force between two objects

FBD orfree body diagram

y a diagram that shows all the forces acting on an object

y treats objects as points and the forces as arrows

[Notes] Elementary Physics

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