Mechanics - General Physics I - Lecture Slides, Slides of Physics

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Mechanics

Potential

Energy

and

Energy

Conservation

-^

Work

-^

Kinetic

Energy

-^

Work

‐Kinetic

Energy

Theorem

-^

Gravitational

Potential

Energy

-^

Elastic

Potential

Energy

-^

Work

‐Energy

Theorem

-^

Conservative

and

Non

‐conservative

Forces

-^

Conservation

of^

Energy

Work

Done

by

Multiple

Forces

-^ If

more

than

one

force

acts

on

an

object,

then

the

total

work

is^ equal

to^

the

algebraic

sum

of^

the

work

done

by

the

individual

forces

-^ Remember

work

is^ a

scalar,

so

this

is^ the

algebraic

sum

r

F

W

W

W

W^

F N g net^

^

cos(



^ 

net^

by individual forces

W

W

Kinetic

Energy

and

Work

-^ Kinetic

energy

associated

with

the

motion

of^

an

object • Scalar

quantity

with

the

same

unit

as^

work

-^ Work

is^ related

to^

kinetic

1 2 mv 2 energy

KE

x

F mv mv^

net^



 ^

) cos ( 1 2 1 2

(^20) 2



net^

f^

i

W^

KE

KE

KE

^

^

 

Potential

Energy

-^ Potential

energy

is^ associated

with

the

position

of^ the

object

-^ Gravitational

Potential

Energy

is^ the

energy

associated

with

the

relative

position

of^ an

object

in^ space

near

the

Earth’s

surface

-^ The

gravitational

potential

energy

-^ m

is^ the

mass

of^ an

object

-^ g is^ the

acceleration

of^ gravity

-^ y^

is^ the

vertical

position

of^ the

mass

relative

the^ surface

of^ the

Earth

-^ SI

unit:

joule

(J)

mgy

PE

Reference

Levels

-^ A

location

where

the

gravitational

potential

energy

is^ zero

must

be

chosen

for

each

problem

-^ The

choice

is^ arbitrary

since

the

change

in^ the

potential

energy

is^ the

important

quantity

-^ Choose

a^ convenient

location

for

the

zero

reference

height^ •^ often

the^

Earth’s

surface

-^ may

be^ some

other

point

suggested

by^ the

problem

-^ Once

the

position

is^ chosen,

it^ must

remain

fixed

for

the^

entire

problem

Extended

Work

‐Energy

Theorem

-^ The

work

‐energy

theorem

can

be^

extended

to^ include

potential

energy:

-^ If

we

only

have

gravitational

force,

then

-^ The

sum

of^ the

kinetic

energy

and

the

gravitational

potential

energy

remains

constant

at^ all

time

and

hence

is^ a

conserved

quantity

net^

f^

i

W^

KE

KE

KE

^

^

  f

i

grav ity

PE

PE

W^

gravity net^

W

W^

f i i f^

PE PE KE KE^

  

i i f f^

KE PE PE KE^

  

Extended

Work

‐Energy

Theorem

-^ We

denote

the

total

mechanical

energy

by

-^ Since •^ The

total

mechanical

energy

is^ conserved

and

remains

the

same

at^ all

times

PE KE E^

 

f f i i^

mgy

mv

mgy

mv^

^

2

2

i i f f^

KE

PE

PE

KE^

Platform

Diver

-^ A

diver

of^

mass

m^

drops

from

a

board

m^

above

the

water’s

surface.

Neglect

air

resistance. • (a)^

Find

is^ speed

m^

above

the

water

surface

-^ (b)

Find

his

speed

as^

he^

hits

the

water

Platform

Diver

-^ (a)

Find

is^ speed

5.^

m^ above

the^

water

surface • (b)^ Find

his^ speed

as^ he

hits

the^

water

f f i i^

mgy mv mgy mv^

  ^

2

2

1 2

1 2

f f i^

mgy v gy^

  ^

12 2 0

sm gy v^

i f^

/ 14 2

 

0 1 2 0

2   ^

f i^

mv mgy

sm m m yy sm g v^

f i f

/ (^9). (^9) ) 5 (^10) )( / (^8). (^9) ( 2

) ( 2 2

 



 

Potential

Energy

in

a^

Spring

-^ Elastic

Potential

Energy:

-^ SI

unit:

Joule

(J)

-^ related

to^ the

work

required

to

compress

a^ spring

from

its^

equilibrium

position

to^ some

final,

arbitrary,

position

x

-^ Work

done

by

the

spring

2 2

(^

f i

x x s^

kx

kx

dxkx

W^

f i

^ 

sf si s^

PE

PE

W^

2 1 kx 2 PE^

 s

Extended

Work

‐Energy

Theorem

-^ The

work

‐energy

theorem

can

be^

extended

to^ include

potential

energy:

-^ If

we

include

gravitational

force

and

spring

force,

then

net^

f^

i

W^

KE

KE^

KE

^

^

f i

grav ity

PE

PE

W^

s gravity net^

W

W

W^

(^0) )

()

()

(^

     ^

si sf i f i f^

PE PE PE PE KE KE

si i i sf f f^

KE KE PE PE PE KE^

    

sf si s^

PE

PE

W^

A^

block

projected

up

a^

incline

-^ A

‐kg^

block

rests

on^

a^ horizontal,

frictionless

surface.

The

block

is^ pressed

back

against

a^ spring

having

a^ constant

of^ k

=^625

N/m,

compressing

the

spring

by^

cm

to^ point

A.

Then

the

block

is^ released.

-^ (a)

Find

the

maximum

distance

d^ the

block

travels

up^

the

frictionless

incline

if^ θ

=^30

°.

-^ (b)

How

fast

is^ the

block

going

when

halfway

to^ its

maximum

height?

A^

block

projected

up

a^

incline

-^ Point

A^ (initial

state):

-^ Point

B^ (final

state):

m cm x y v^

i i i^

(^1). 0

10 , 0 , 0

   

2

2 2

2

1 2

1 2 1 2

1 2

f f f i i i^

kx mgy mv kx mgy mv^

     m

s

m

kg

m

m

N

kx mg

d^

i

sin)

sin

2

2

2 1 2





0 , sin

, 0



  ^

f

f f^

x d h y v

^ sin

1 2

2

mgd mgy kx^

f i^

 