Chapter 5 Lecture Notes Part 2

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29 Νοε 2013 (πριν από 4 χρόνια και 5 μήνες)

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Newtonian Forces

Tension is the pulling force away from an
object usually by a string, rope, or cable

Force is represented by mg

M stands for the mass of the object

G stands for the gravity constant on Earth (9.80
m/s
2
)

T

-
mg

If the mass is just hanging, then the
acceleration (ā) =
0

Σ
𝐹

̅

=
0

Σ
𝐹

=

Where m is the inertial mass

=
Σ
𝐹

= mg (down) + T (up)

T = mg (up)

M(
0
) = mg (down) + mg (up)

Where the mass of “mg (up)” is related to gravity

This is called the Gravitational Mass: this tells how
much weight the object has

In this class inertial mass ↔ gravitational mass

𝐹

=
(GM
1
M
2
)

𝑥

r
2

Where “r” is the distance between two objects with
different gravity

Tension must be the same if the rope is the same

𝐹

= (down) m
1
g

(down) m
2
g

|a|

|a|

Atwood

Machine

T

T

Σ
𝐹

1

= m
1
ā
1

= m
1
g (down) + T (up)

Σ
𝐹

2

= m
2
ā
2

= m
2
g (down) + T (up)

T (up) = [m
2
ā
2

= m
2
g (down) = m
1
ā
1

= m
1
g (down)]

ā
2
= a (down)

m
2
(a(down)

g (down)

ā
1
= a (up)

m
1
(a(up)

g(down) = m
1
(
-
a(down)

g(down))

m
2
a
-

m
2
g + m
1
a + m
1
g

= (m
2
+ m
1
)a

(m
2
+ m
1
)g =
0

A
=
(m
2

-

m
1
)g

(
m
2
+ m
1
)

The difference in the weights makes the
acceleration go up

The sum of the weights makes the
acceleration go down

(
m
2
+ m
1
)a = (m
2
+ m
1
)g

Inertial mass =
(
m
sys
)a

Gravitational mass =
(
m
sys
)g

Inertial
mass of the system ≠ gravitational
mass of the system

A new rope means you have two separate
tensions

T
1

T
1

T
2

Always acts against the motion

θ

-
mg

|

F
fr
|=

μ
s
N

or
|
F
fr
|=

μ
k
N

Where
μ
s
is the static friction constant and
μ
k

is the kinetic friction constant

μ
k

is like skating on ice

Pure slippage

μ
s
N

is like rubber on concrete

Very little motion

Σ
𝐹

=
mg
||

-

F
fr

= ma

mg
||
-

μ
k
N

= ma

mg
|

-

μ
k
N

= ma

g
||

-

μ
k
g
|

=
a

g
||
= g
cos
θ

g
|

= g sin
θ

g
sin
θ

-

μ
k
g
cos
θ

= a

g(sin
θ

-

μ
k

cos
θ
) = a

|
F
fr
|≤

μ
s
N

The static friction has a maximum balancing force

θ