phy201_5

1
Physics 201
5 Some Application of Newtons Laws

• Newtons Second law and Uniform Circular Motion
• Newtons Second law and Nonuniform Circular Motion
  
• Motion in Accelerated Frames of Reference
• Motion in the Presence of resistive Forces.

2
In uniform circular motion the acceleration of
the object is
v
2
ˆ
a

-
r
r
c
ˆ
r
is the unit vector pointing from the
center of motion to the object
What causes this acceleration?
It must be a force
m
v
2
ˆ
F

-
r
r
c
where
m
is the mass of the object.

This force is called the CENTRIPETAL
force

3

• Where do centripetal forces come from?
• gravity
• tension
• friction

4
W

ma

mg
(
r
)
c


mM
v
2
(
)
G

m

G
is Newtons Gravitational constant
e
r
r
2


GM
v

in order that gravitational force
e
r
sustains uniform circular motion

5
The force of gravity continually changes the
direction of motion of the object, thus keeping
it a constant orbit at constant speed as long
as the speed is given by

• If the speed increases the radius of the orbit
  increases
• If the speed decreases the radius of the orbit
  decreases

6
If speed increases and length of string is fixed
then the tension increases
7
Car turning on flat road
Ff
v

• If the speed increases and the force of friction
  does not the radius of turning increases
  (skidding outward)

8
Car turning on banked road

• 3 situations
• 1 Force of friction plays no role and banking
  provides necessary centripetal force
• 2 Banking too great and need outward force of
  friction
• 3 Banking not enough and thus need force of
  friction to stop outward motion

N
Ff,out
Fc
Ff,in
?
W
9
For turning speed v
,
total centripetal force required
toward center of motion
m
v
2
ˆ
F

-
r
c
r
this force continually deflects velocity to turn
car in circle of radius
r

N
Ff
direction of Ff is determined by the speed v
radius r and banking ?
Fc
?
W
Forces on car
10
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11
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12
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13
Motion in Accelerated Frames of Reference
N
noninertial observer
T
Ffict
W
inertial observer
only seen by noninertial observer
14
Motion in the Presence of resistive Forces.
R

-
b
v
consider object dropping in air or a liquid
Total vertical force


b
v
-
mg
d
v
Newtons
2
nd law
Þ
m

b
v
-
mg
dt
d
v
b
v
Þ

-
g

º
Differential Equation
dt
m
which has the solution
(
)
mg
(
)
-
bt
v
t

1
-
e
m
b