Download Forces part2

Four Types (review)
• weight: Non-contact (“action at a distance” means no contact required)
An Introduction to Forces
Part 2
PHYS& 114: Eyres
– Pulling
– Between 2 objects with mass
• Tension: contact required
– Pulling
– Must have a rope or string or spring attached
• normal: contact required
– Pushing
– Due to contact with a surface
• friction: contact required
– Opposite direction to motion or the direction of potential motion
– Rubbing (kinetic friction) or “Stickyness” associated with “trying to move
it” (static friciton)
Testing possible relationships between
force and motion
Testing the relationship between the sum of forces
and the motion of the system object
• Two possible relationships:
– 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.
Newton’s 2nd Law
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 equation we deduced for Newton's second
law is:
The force diagram and the motion diagram match.
• In non-inertial 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.
• Another way to write this equation is:
Σ
=
1
Mass and Weight
• Mass ( in kg) is a
fundamental quantity
• Weight is the
attractive force
between 2 objects
that have mass. ( in
N)
F=
Mass and Weight
Gm1m2
F=
r2
Gm1m2
r2
F=
Gmearth
(mobject )
r2
F = 9.8
Gravitational force
N
(mobject )
kg
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.
• These forces are exerted on different
objects and cannot be added to find the
sum of the forces exerted on one object.
© 2014 Pearson
Education, Inc.
© 2014 Pearson
Education, Inc.
Newton’s Laws
• Newton’s 3rd Law
If
Object 1 pushes on Object 2
then
Object 2 pushes on Object 1
Free-Body Diagrams
• Circle the object of interest
• Choose a coordinate system
On 2 By 1
N1on2
Is the object moving horizontal or vertical?
Pick a standard system
On 1 By 2
N2on1
Is the object moving up or down a slope?
Pick a slanted system
or
• This can help to identify forces
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Free-Body Diagrams
Free-Body Diagrams
• Identify your vectors
• Draw coordinate
system
• Add vectors (don’t
worry about length)
On and By and Direction
of Forces Table
By
On
B
Normal Ground B
normal Dad
On
Weight Earth
By
Weight Earth
B
NGB
B
Normal Ground B
normal
Dad
Use FBD to Solve
• Add component
information to the vector
table.
• Put in values if you know
them.
+
Use FBD to Solve
x
Weight 0
Normal 0
y
-wy
+ Ny
NGB
nDB
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.
y
-wy
+ Ny
Normal + nx 0
ΣFx = max
Skills for applying Newton's second law for
one-dimensional processes
© 2014 Pearson
Education, Inc.
• Write Newton’s 2nd Law
x
Equations in Component
Weight 0
Form
Normal 0
Normal + nx 0
+
WEB
nDB
WEB
B
+ nDB = max
ΣFy = may
− WEB + N GB = may
Skills for applying Newton's second law for
one-dimensional processes (Cont'd)
2. Simplify and diagram.
– Make appropriate simplifying assumptions
and represent the process with a motion
diagram and/or a force diagram.
© 2014 Pearson
Education, Inc.
3
Skills for applying Newton's second law for onedimensional processes (Cont'd)
Practice Problem
3. Represent mathematically.
– 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.
•
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Physics Principles
Circle the Object
Draw Coordinate
Identify Forces, On & By
Make Component Table
Write Newton’s Law in
Component Form
• List other information
• Solve
• Evaluate
A 7.0-kg bucket of
tools is raised from
the ground by a
rope. If the upward
acceleration of the
bucket is 4.0 m/s2,
find the force
exerted by the rope
on the bucket.
© 2014 Pearson
Education, Inc.
Practice Problem
•
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Physics Principles
Circle the Object
Draw Coordinate
Identify Forces, On & By
Make Component Table
Write Newton’s Law in
Component Form
• List other information
• Solve
• Evaluate
The parachute on a
race car of weight
8 500 N opens at the
end of a race when
the car is traveling at
40 m/s. What force
must be supplied by
the parachute to stop
the car in a distance
of 1 000 m?
Practice Problem
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Physics Principles
Circle the Object
Draw Coordinate
Identify Forces, On & By
Make Component Table
Write Newton’s Law in
Component Form
• List other information
• Solve
• Evaluate
A 50.0-kg wagon is towed
up a hill inclined at 20°
above the horizontal. The
tow rope is parallel to the
incline and has a tension
of 150 N. Assume that the
wagon starts from rest at
the bottom of the hill, and
neglect friction. How fast
is the wagon going after
moving 60.0 m up the
hill?
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
– You can also simply use Fsp for spring force.
Note: Why the minus sign?
Because ∆x is in the opposite direction to Fsp
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