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More of Newton’s Laws
Announcements:
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Tutorial Assignments due tomorrow.
Pages 19-21, 23, 24 (not 22,25)
Note Long Answer HW due this week.
CAPA due on Friday.
Have added together the clicker scores so far and will
try to have results placed on D2L (Desire to Learn –
replacement for CULEARN). There are still several
clickers not registered.
•  Exam – Feb. 16 – can use calculator and 1 sheet
(8.5”x11”) either side – not xeroxed.
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Web page: http://www.colorado.edu/physics/phys1110/phys1110_sp12/
Force review
Force is a vector so superposition of forces is true (can
combine all forces into one net force using vector addition).
We draw a free body diagram to figure out the effect of
the various forces and to calculate the net force.
Newton’s 1st law: A body will stay at a constant velocity
unless acted upon by a net force.
Newton’s 2nd law:
. Can split:
&
A net force causes an acceleration which is
inversely proportional to the mass of the object
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Clicker question 1
Set frequency to BA
Q. An astronaut in intergalactic space is twirling a rock on a
string. Suddenly the string breaks when the rock is at the
point shown. Which path
does the rock follow after
the string breaks?
Before the string breaks,
the astronaut must be
exerting a force on the rock causing the
centripetal acceleration
Snap!
A
B
D
C
After the string breaks, no net force is acting so the rock
travels at constant velocity which was horizontal to the
right (tangent to circle) at the moment the string broke.
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Force of gravity
We all feel the force of gravity. It keeps the
Earth together and keeps us from floating off.
We have also learned that if there is no opposing force
(free fall) the acceleration due to gravity is
Thus, from Newton’s 2nd law we can deduce that
the force of gravity is
We call the force due to gravity the weight:
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Clicker question 2
Set frequency to BA
Q. An object is being lowered on a cord at a constant speed.
How does the tension T in the cord compare to the weight
mg of the object?
A.  T > mg
B.  T = mg
constant velocity
C.  T < mg
D.  Impossible to tell
Constant speed in a straight line means
acceleration is 0 so
and therefore
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Clicker question 3
Set frequency to BA
Q. An object is being lowered on a cord at a speed which is
decreasing. The acceleration of the object is
A.  Up
B.  Down
C.  0
velocity down,
D.  Impossible to tell
speed decreasing
If the speed is decreasing the acceleration direction must
be opposite to the velocity direction.
If v1 and v2 are positive and v2 is less than v1 (slowing down)
then Δv is negative (opposite direction from v1 and v2)
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Clicker question 4
Set frequency to BA
Q. An object is being lowered on a cord at a speed which is
decreasing. How does the tension T in the cord compare to
the weight mg of the object?
A.  T > mg
B.  T = mg
velocity down,
C.  T < mg
speed decreasing
D.  Impossible to tell
Let up be positive. From the previous question
and ay is positive
and therefore T > mg
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More on weight
We will use the term weight to refer to the
force on an object due to gravity alone.
We may also use the term apparent weight
to describe the value returned by measuring
the weight in an accelerated environment.
A spring scale effectively measures the tension
in a string holding up the object to be measured.
As we just found out, the tension may not equal
the weight (mg) if there is acceleration and so
an apparent weight will be measured. This
applies to most scales like a bathroom scale.
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Units of force
From Newton’s 2nd law we can deduce the units of force.
has units of kg·m/s2 also known as a newton (N)
That is,
Mass is an intrinsic property of an object independent of
where it is measured. Weight is the force due to gravity
and depends on the gravitational field the object is in.
In SI units, kilogram is a unit of mass and
newton is a unit of force (including weight)
In the English system, pound measures force (including
weight) and slug is the unit of mass:
A mass of 1 kilogram weighs about 2.2 lbs on Earth
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Newton’s third law
Two formulations of Newton’s 3rd law.
For every action there is an equal and opposite reaction.
If a force is exerted on body A due to B then, there is a
force which is equal in magnitude
 but opposite in
direction on body B due to A. Fon A due to B = − Fon B due to A
This is how a rocket works. Hot gas is ejected out the
back which creates an equal force on the rocket in the
opposite direction.
€
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Newton’s third law
Imagine being on a stationary skateboard and someone
throws a basketball at you from the left which you catch.
What would happen to you and the skateboard? Would
you move left, right, or not move at all?
The basketball exerts a force on you
moving you left and you exert a force on
the basketball, slowing it down
Imagine being on a stationary skateboard and throwing a
basketball to the left. What would happen to you and the
skateboard? Would you go left, right, or not move at all?
You exert a force on the basketball moving it left and the
basketball exerts a force on you moving you right.
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Newton’s third law
The equal and opposite forces in Newton’s third law
for a particular situation are sometimes referred to
as an action-reaction pair.
Let’s identify action-reaction forces in
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the diagram. For each pair, exactly one
ton
force acts on one object and the
“reaction” force acts on the other object.
Normal force pushing object up and object pushing ground down
Friction pushing object right and object pushing ground left
Tension pulling object left and object pulling rope right
Gravity pulls object toward Earth; object pulls Earth toward object
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Newton’s laws relationship
Newton’s 1st law is basically a special case of
Newton’s 2nd law when force and acceleration are 0.
Newton’s 2nd law deals with individual objects. We
draw free body diagrams to show the forces acting
on an object.
Newton’s 3rd law deals with the forces between
two objects (equal and opposite). Sometimes
we need this to determine the force acting on
the object of interest.
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Clicker question 5
Set frequency to BA
Situation I: A car on Earth rides at a constant speed of 35 mph
over the top of a round hill with a radius of curvature of 100 m.
Situation II: A monorail car in space moves at constant speed of
35 mph along a round monorail, with a 100 m radius of curvature.
Which car experiences the larger acceleration?
A.  Earth car
I
B.  Space car
C.  Both cars have the
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same acceleration
D.  Impossible to tell
The speed is constant so there is no linear acceleration.
But the velocity vector direction is changing so there is
centripetal acceleration which is the same for both.
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Clicker question 6
Set frequency to BA
Q. A car of mass m, traveling at constant speed, rides over
the top of a hill. At the top of the hill, the magnitude of the
normal force N of the road on the car is…
A.  N = mg
B.  N > mg
C.  N < mg
D.  Impossible to tell
Picking the up direction as the positive y-axis we get
We know the acceleration is down so
and therefore
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Clicker question 7
Set frequency to BA
Q. Assuming the girls have a mass of 40 kg and the
men have a mass of 80 kg, what is the magnitude
of the downward force on one shoulder of a skier in
the bottom row? (Assume g = 10 m/s2.)
No acceleration in the y direction
A. 200 N
so the forces have to add to 0.
B. 300 N
C. 400 N Weight of top girl is 400 N (W=mg),
D. 800 N split equally between two middle girls.
E. 0 N
Total downward force of a middle row girl is 400 N of
her own weight plus 200 N of the girl above weight.
The middle row girl’s total downward force is 600 N which is split
onto two shoulders. Each bottom row shoulder has 300 N on it.
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A real pyramid
Be thankful I
didn’t ask you
to calculate
the forces for
this pyramid!
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