PHY2053, Lecture 8:
Applying Newton’s Laws
PHY2053, Lecture 8: Applying Newton’s Laws
Applying Newton’s Laws
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Book-Proposed Strategy:
Decide which object will have Newton’s 2nd law applied
Identify all the external forces acting on that object
Draw a FBD to show all the forces acting on the object
Choose a coordinate system.
If the direction of the net force is known, choose axes so
that the net force is along one of the axes
● Find the net force by adding the forces as vectors
● Use Newton’s second law to relate the net force to the
acceleration
● Relate the acceleration to the change in the velocity
vector during a time interval of interest
PHY2053, Lecture 8: Applying Newton’s Laws
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Friction
● Force due to imperfections of surfaces in contact
● For a pair of surfaces, the frictional force depends (only)
on the normal force between the surfaces:
Frictional
force
Normal force
Coefficient of friction
● To a good approximation, doesn’t depend on size or
shape of surface, only the materials in contact
● Always opposite to the direction of motion
● Static friction – objects not moving w.r.t. each other
● Kinetic friction – one object is being dragged across
the (surface of the) other
PHY2053, Lecture 8: Applying Newton’s Laws
Problem: Pushing a crate at an angle
● A crate with a mass of 100 kg is
being pushed forward across a
horizontal surface.
● The coefficient of friction
between the crate and the
surface is 0.2.
● The force is being applied to the
crate at a 30º angle with respect
to the vertical axis.
● What is the minimum force at
which the crate will move from
its prone position?
[use g = 10 m/s2]
PHY2053, Lecture 8: Applying Newton’s Laws
∘
30
F
100 kg
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Solution:
PHY2053, Lecture 8: Applying Newton’s Laws
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Solution, continued:
PHY2053, Lecture 8: Applying Newton’s Laws
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Tension Force
● “Ideal String” concept:
● massless, infinitely thin, fixed length
● withstands any force applied to it without breaking
● Tension (T) is the magnitude of the force propagating
through the string
“String with tension T”
m1
PHY2053, Lecture 8: Applying Newton’s Laws
m2
Problem: Edge Pulley
Consider the system on the
picture. The 100 kg block is
initially held in place. The
coefficient of friction between
the 100 kg block and the surface
is 0.2. Ignore the mass of the
pulley and string. [g = 10 m/s2].
100 kg
(a) If the 100 kg block is released, does
the system move?
(b) If so, what is the acceleration of the system?
PHY2053, Lecture 8: Applying Newton’s Laws
50 kg
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Solution 4,
if m2g < fk ,
the system does
not move
PHY2053, Lecture 8: Applying Newton’s Laws
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H-ITT 1: Pulley
Consider the depicted system which is
released from a fixed position. The two
weights have masses 120 kg and 80 kg,
respectively. Assume g = 10 m/s2. The
120 kg weight will start moving:
a)
b)
c)
d)
e)
2
m/s
downward at 4
downward at 2 m/s2
the weight is not moving
upward at 4 m/s2
2
upward at 2 m/s
PHY2053, Lecture 8: Applying Newton’s Laws
120 kg
80 kg
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Solution to HITT #1
PHY2053, Lecture 8: Applying Newton’s Laws
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Concept: Inertial Reference Frames
Newton’s first law defines a set of reference frames for
which the observed physics will be the same.
All systems which move with constant velocities with respect
to each other will record the same velocity changes when
performing measurements:
An inertial system is an idealized construction.
In our calculations, we will assume that a fixed observer on
the Earth’s surface is in an inertial reference frame.
PHY2053, Lecture 8: Applying Newton’s Laws
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Concept: Apparent Weight
Classic application of non-inertial reference frames is an
elevator accelerating or slowing down.
Objects inside the elevator appear to be gaining or losing
weight depending on the direction of the acceleration.
Newton’s 2nd law for the object:
a
N
y
Apparent Weight:
x
PHY2053, Lecture 8: Applying Newton’s Laws
mg
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Problem: Apparent Weight
In an elevator that has a constant acceleration upward,
Luke is standing on a scale. The scale reads 960 N.
When Luke picks up a 20 kg box, the scale reads 1200
N. The acceleration of the elevator stays the same.
a) Find the acceleration of the elevator
b) Find Luke’s weight
PHY2053, Lecture 8: Applying Newton’s Laws
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Solution:
PHY2053, Lecture 8: Applying Newton’s Laws
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H-ITT 2:
Apparent Weight
PHY2053, Lecture 8: Applying Newton’s Laws
H-ITT 2: Apparent Weight
Luke’s mass is 100 kg. He is standing on a scale in
an elevator that is slowing down at 5 m/s2 as it
reaches the top floor of a building.
Assume g = 10 m/s2. The scale will show an
apparent weight of:
1)0 N
2)500 N
3)750 N
4)1000 N
5)1500 N
PHY2053, Lecture 8: Applying Newton’s Laws
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Solution to HITT #2
PHY2053, Lecture 8: Applying Newton’s Laws
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H-ITT 2: Apparent Weight
Luke has a mass of 100 kg. He is standing on a
scale in an elevator which is accelerating as it
heads for the top floor of a building at 5 m/s2.
Assume g = 10 m/s2.
The scale will show an apparent weight of:
1)0 N
2)500 N
3)750 N
4)1000 N
5)1500 N
PHY2053, Lecture 8: Applying Newton’s Laws
✔
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Solution to HITT #2
PHY2053, Lecture 8: Applying Newton’s Laws
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Concept: Air Resistance
● air resistance: the force with which air opposes
movement of objects through air
● air resistance is velocity dependent - the higher the
velocity of the object, the higher the air resistance
● a simple model is that in which Fair resist = αvobject
● consequence: terminal velocity during freefall
Fair
Fair
Fair
mg
mg
mg
v = vterm
v > vterm
v < vterm
PHY2053, Lecture 8: Applying Newton’s Laws
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