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Four Types
• weight:
An Introduction to Forces
Part 2
PHYS& 114: Eyres
– Pulling
– Between 2 objects with mass
• Tension:
– Pulling
– Must have a rope or string or spring attached
• normal:
– Pushing
– Due to contact with a surface
• friction:
– Opposite direction to motion or the direction of potential motion
– Rubbing (kinetic friction) or “Stickyness” associated with “trying to move
it” (static friciton)
Testing a hypothesis
Patterns observed in the experiments
1. Accept the hypothesis as true.
2. Design an experiment whose outcome can be predicted
using this hypothesis.
3. Compare the outcome of the experiment and the
prediction.
4. Make a preliminary judgment about the hypothesis.
– If the outcome matches the prediction, the hypothesis
has not been disproved.
– If the outcome and the prediction do not match,
reconsider the hypothesis and possibly reject it.
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Education, Inc.
Observational experiments for a bowling
ball rolling on a very hard, smooth surface
• In all experiments, the vertical forces add to zero
and cancel.
– We consider only forces exerted in the horizontal
direction.
• In the first experiment, the sum of the forces
exerted on the ball is zero.
– The ball's velocity remains constant.
• When the ruler pushes the ball, the velocity
change arrow points in the same direction as the
sum of the forces.
© 2014 Pearson
Education, Inc.
© 2014 Pearson
Education, Inc.
Testing possible relationships between
force and motion
• Two patterns are commonly proposed:
– The sum of the forces exerted is in the same direction
as the velocity of the system object.
– The sum of the forces exerted is in the same direction
as the change in velocity of the system object.
• We must do testing experiments to
determine which pattern is consistent with
the relationship between force and motion.
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Education, Inc.
1
Testing possible relationships between
force and motion
• Two possible relationships:
Testing the relationship between
the sum of forces and the motion of
the system object
– The sum of forces is in the same direction as the
velocity.
– The sum of forces is in the same direction as the
change in velocity.
1. Use each relationship to predict the outcome of
testing experiments.
2. Perform the experiments and compare the
outcomes with the predictions.
3. From this comparison, decide whether we can
reject one or both of the relationships.
© 2014 Pearson
Education, Inc.
© 2014 Pearson
Education, Inc.
Testing the relationship
between the sum of forces and
the motion of the system object
Inertial reference frame
• An inertial reference frame is one in which an
observer: Sees no change in the velocity if the
sum of all forces exerted on the system object is
zero
The force diagram and the motion diagram match.
• In noninertial reference frames, the velocity of
the system object can change even though the
sum of forces exerted on it is zero.
The force diagram and the motion diagram do not
match.
© 2014 Pearson
Education, Inc.
Workbook Exercises
• Complete, with your team the workbook
exercises related to inertial frame of
reference
Cause-effect relationships
• The equation we deduced for Newton's second
law is:
• The right side of the equation (the sum of the
forces being exerted on the system) is the cause
of the effect (the system's acceleration) on the
left side.
© 2014 Pearson
Education, Inc.
2
Workbook Exercises
• Complete, with your team the workbook
related to patterns.
Mass and Weight
• Mass ( in kg) is a
fundamental quantity
• Weight is the
attractive force
between 2 objects
that have mass. ( in
N)
Mass and Weight
Gm1m2
F=
r2
F=
F=
Gm1m2
r2
Gravitational force
Gmearth
(mobject )
r2
F = 9.8
N
(mobject )
kg
© 2014 Pearson
Education, Inc.
Newton's third law of motion
• When two objects interact, object 1 exerts
a force on object 2. Object 2 in turn exerts
an equal-magnitude, oppositely directed
force on object 1.
Newton’s Laws
• Newton’s 3rd Law
If
Object 1 pushes on Object 2
then
Object 2 pushes on Object 1
On 2 By 1
N21
On 1 By 2
N12
• These forces are exerted on different
objects and cannot be added to find the
sum of the forces exerted on one object.
• This can help to identify forces
© 2014 Pearson
Education, Inc.
3
Free-Body Diagrams
Free-Body Diagrams
• Identify your vectors
• Circle the object of interest
• Choose a coordinate system
On and By and Direction
of Forces Table
Is the object moving horizontal or vertical?
Pick a standard system
By
Is the object moving up or down a slope?
Pick a slanted system
or
Free-Body Diagrams
By
Weight Earth
On
B
• Add component
information to the vector
table.
• Put in values if you know
them.
B
B
NGB
+
x
Weight 0
Normal 0
y
-wy
+ ny
Normal + nx 0
NGB
+
nDB
WEB
Dad
Use FBD to Solve
Normal Ground B
normal Dad
B
Normal Ground B
normal
• Draw coordinate
system
• Add vectors (don’t
worry about length)
On
Weight Earth
WEB
Skills for applying Newton's second law for
one-dimensional processes
Use FBD to Solve
• Write Newton’s 2nd Law
x
Equations in Component
Weight 0
Form
Normal 0
nDB
y
-wy
+ ny
1. Sketch and translate.
– Sketch the process, choose the system object
and coordinate system, and label the sketch
with everything you know about the situation.
Normal + nx 0
ΣFx = max
+ nDB = max
ΣFy = may
− wEB + N GB = may
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Education, Inc.
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Skills for applying Newton's second law for
one-dimensional processes (Cont'd)
Skills for applying Newton's second law for
one-dimensional processes (Cont'd)
3. Represent mathematically.
2. Simplify and diagram.
– Make appropriate simplifying assumptions
and represent the process with a motion
diagram and/or a force diagram.
– Convert the representations into quantitative
mathematical descriptions using kinematics and
Newton's second law.
4. Solve and evaluate.
– Substitute the known values and solve, and then
evaluate your work to see if it is reasonable. Check
whether all representations are consistent.
© 2014 Pearson
Education, Inc.
© 2014 Pearson
Education, Inc.
Other Force Information
•
•
•
•
Weight: w=mg
Friction: f=µn
T is the same all along a taught rope/string
Springs: nbyspring=-ksp∆x or Tbyspring=-ksp∆x
– Springs push (n) when they are constricted
– Springs pull (T) when they are extended
Note: Why the minus sign?
Because ∆x is in the opposite direction to Fsp
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