Newton’s Laws (Part II, Concepts)!
Free Body Diagrams!
Questions involving forces almost always require a
diagram to solve them!
!! The diagram should contain all the forces acting on
the relevant object (or objects) and approximately
where they act!
!!
!!
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Be very careful when drawing the diagram: if you miss
any of the forces acting on an object you may well
waste a lot of time trying to solve an impossible
problem!!
!! Remember that objects in equilibrium must have forces
that balance%
!!
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Force Diagrams!
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A
B
C
D
E
When the word “rough” is used, you know what is coming: Friction (literally
and figuratively)
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Resistive force of motion !
Friction is a force that resists the motion of an object
that is in contact with another object or material. If
the objects are not moving relative to each other, the
friction force is called static. If they are moving, the
friction is kinetic.!
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Friction depends on normal sources to surface,
also strongly dependent on the surface
smoothness (or, roughness).!
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Maximum friction force is proportional to normal force!
*
The
surfaces
‘stickier’
surfaces
coefficient of friction depends on the two
pressed together. High coefficient means
surface. On the other hand, Air tracks or ice
represent low frictional coefficients.!
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About Rolling friction!
A ball is rolling downhill (relatively low height)
will experience friction. Is that static friction
or kinetic friction that the ball mostly
experiences?!
A. Kinetic Friction associated with rolling!
B.!Sliding kinetic Friction!
C.!Static Sliding friction!
D.!Static friction associated with rolling motion!
E.!None of the above Hint (think of this !
problem as a ball with legs)!
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a = (µs " µk )g
Db.MHP9LV&8bP9PV&8HP9LP&8%%H&,%
= 0.30 # 9.81 = 2.94 me% /s2
!
Tension Force!
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Tension!
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Simple machinery: Pulleys
Case 1:
Single Fixed Pulley
!
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!!
This is the only “wasteful” pulley as far as the
amount of tension force I have to apply to lift
the weight: wasteful if there is friction on the
pulley (even if assume mass of pulley=0) !
Case 2:
f!
f!
Single moveable Pulley
!
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Case 3:
Double Pulley systems (A, B)
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Caution: In case A, it is NOT friction
that helps to supply 1 T of force!
T
T
f!
f!
44%
2T
m
A
mg
B
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Other Garden Varieties!
The applied tension force at each part of the rope is as suggested.
Again the cost is the rope length need to triple or quadruple. 4L%
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Case Considerations
Case 1: A parachute jumper falling through the air at a constant velocity,
called the terminal velocity. Stable or unstable equilibrium?
Stable. If you hang a bag around him for a sec, then drop it. He will return to the
same terminal velocity as before.
Case 2: A ball inside a glass bowl, originally motionless. Stable or
unstable?
Stable. If you move it a bit, it will return to the original state.
Case 3:
That pencil standing on top of your finger tip?
Unstable, enough said…
50N
Case 4: Balance, stable or unstable?
50N
Stable
Case 5: a block acted on
by these forces, stable or
unstable?
50N
50N
Actually, it is not even at equilibrium
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Consider two masses, m1 and m2 connected by a string
which is placed over a pulley. Calculate the acceleration
of each mass and the tension in the string.!
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T " m1g = m1a1
!!
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T " m2 g = m2 a2
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!
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Write
! the final acceleration as
T
."I.XI^.V
Replace a2 by a1 by a with the suitable sign,
T " m1g = m1a
T
a1
a2
m1 g
T " m2 g = "m2 a
m2 g
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j'-?-2)1@%%We
get two equations and two unknowns T
and a!
T " m1g = m1a
T " m2 g = "m2 a
W,0"169/(.*/"/&'"'R6.+,-1
"m1g + m2 g = m1a + m2 a
!
m2 " m1
a=g
!
m1 + m2
!W,0"1691+/6/'".")-/,"/&'"\(1/"'R6.+,T = m1g
!
!
!
m2 " m1
+ m1g
m1 + m2
T
T
a1
a2
m1 g
m2 g
# m " m1 &
# 2m2 & 2m1m2 g
= m1g% 2
+ 1( = m1g%
(=
m
+
m
m
+
m
m1 + m2
$ 1
'
$ 1
2
2'
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