chapter 5. force and motion - physics &...
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Chapter 5. Force and MotionChapter 5. Force and Motion
In this chapter we study causes of motion: Why does the windsurfer blast across the water in the way he does? The combined forces of the wind, water, and
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of the wind, water, and gravity accelerate him according to the principles of dynamics.
Chapter Goal: To establish a connection between force and motion.
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Topics:
• Force
• A Short Catalog of Forces
• Identifying Forces
Chapter 5. Force and MotionChapter 5. Force and Motion
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• What Do Forces Do?
• Newton’s Second Law
• Newton’s First Law
• Free-Body Diagrams
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Force: Properties
1. Push or Pull
2. Acts on an object
3. Force is a vector
4. Force is either a contact force or long range force
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Force: Properties
Force is a vector – The net force is the vector sum of the
individual forces
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How can we find the individual force?
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Major Forces:
1. Weight – gravitational force
pulls the objects down – determines its direction
magnitude: w mg====r rr rr rr r
m - Mass of the object
9.8m
g ==== - free-fall
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5
29.8
mg
s==== - free-fall
acceleration
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Major Forces:
1. Weight – gravitational force
2. Spring Force
w mg====r rr rr rr r
k - coefficient, which depends
only on geometric parameters
of the spring
spF kx====
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of the spring - change in the length of the spring | |x l= ∆= ∆= ∆= ∆
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Major Forces:
1. Weight – gravitational force
2. Spring Force
3. Tension Force
direction is always in the direction of the rope
magnitude - usually found from the condition of equilibrium
w mg====r rr rr rr r
Trrrr
spF kx====
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magnitude - usually found from the condition of equilibrium
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Major Forces:
1. Weight – gravitational force
2. Spring Force
3. Tension Force
4. Normal Force
direction is always perpendicular to the surface
magnitude - usually found from the condition of equilibrium
w mg====r rr rr rr r
Trrrr
spF kx====
nrrrr
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magnitude - usually found from the condition of equilibrium
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Major Forces:
1. Weight – gravitational force
2. Spring Force
3. Tension Force
4. Normal Force
5. Friction
w mg====r rr rr rr r
Trrrr
spF kx====
nrrrr
kfrrrr
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- Kinetic friction – opposes the motion
direction – opposite the velocity vector
- static friction – prevent the motion of the object
direction – opposite the direction in which the object would
move
sfrrrr
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Major Forces:
1. Weight – gravitational force
2. Spring Force
3. Tension Force
w mg====r rr rr rr r
Trrrr
spF kx====
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4. Normal Force
5. Friction
- kinetic friction
- static friction
nrrrr
kfrrrr
sfrrrr
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Force Identification
w mg====r rr rr rr r
sfrrrr
nrrrr
Trrrr
nrrrr
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w mg====
w mg====r rr rr rr r
kfrrrr
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Free-Body Diagram
1) Object – as a particle
2) Identify all the forces
3) Find the net force (vector sum of all individual forces)
4) Find the acceleration of the object (second Newton’s law)
5) With the known acceleration find kinematics of the object
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5) With the known acceleration find kinematics of the object
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It was Isaac Newton
(1642-1727) who realized
the importance of force
and its connection with
Three Laws of motion
• 1st Law: inertia
• 2nd Law: change in motion
• 3rd Law: action and
Newton’s Laws of Motion
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motion.
• 3rd Law: action and reaction pairs
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About NewtonIn 1665, shortly after getting a bachelor’s degree at Cambridge, Newton was
forced to return to his home because of the Great Plague. During the next 18
months he formulated most of his scientific discoveries: including, the
development of his three Laws of motion, the Law of gravitation, the
invention of the calculus, the dispersion of light, the building of a reflecting
telescope, and so on. That short period was probably the most creative
period in the history of man ... and it will never be repeated!
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Newton’s book of 1687:
the Principia Mathematica
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Newton’s Second Law
An object of mass subject to forces will
undergo an acceleration given by
netF
am
====
rrrrrrrr
1 2, , ...F F
r rr rr rr rm
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15w mg====r rr rr rr r
Trrrr
nrrrr
kfrrrr
kw n T f
am
+ + ++ + ++ + ++ + +====
rrrrrrrrr rr rr rr rrrrr
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Newton’s Second Law
Trrrr
nrrrr
netF
am
====
rrrrrrrr
kw n T f
am
+ + ++ + ++ + ++ + +====
rrrrrrrrr rr rr rr rrrrr
It is convenient to introduce
coordinate system and write the
Newton’s second law in terms of
vector components y
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w mg====r rr rr rr rk
frrrr
vector components
x No motion in y-direction:
0y
a ====
0y
w n+ =+ =+ =+ =
For motion in x-direction:
x x kma w T f= + −= + −= + −= + −
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Free-fall motion
w mg====r rr rr rr r
Then from the second
Newton’s law: w mg
a gm m
= = == = == = == = =
r rr rr rr rr rr rr rr r
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29.8
mg
s====
The acceleration is the same for all
objects (does not depend on the mass
of the object)
a gm m
= = == = == = == = =
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Newton’s First Law
An object that is at rest will remain at rest, or an object that
is moving will continue to move in a straight line with
constant velocity, if and only if the net force acting on the
object is zero.
0a ====rrrr
0F ====rrrr
then velocity is
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0a ====0net
F ==== then velocity is
constant Static equilibrium
Dynamic equilibrium
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Inertial reference frames
Inertial reference frame is the coordinate system in which
Newton’s laws are valid.
The earth is an inertial reference frame
Any other coordinate systems, which are traveling with constant
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Any other coordinate systems, which are traveling with constant
velocity with respect to the earth is an inertial reference frame
Car traveling with constant velocity is an inertial reference
frame
Car traveling with acceleration is NOT an inertial reference
frame (violation of Newton’s law)
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Chapter 5. Summary Chapter 5. Summary
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Chapter 5. Summary Chapter 5. Summary
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Chapter 5. QuestionsChapter 5. Questions
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Chapter 5. QuestionsChapter 5. Questions
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Two of three forces exerted on an object are shown. The net force points to the left. What is the missing third force?
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Two of three forces exerted on an object are shown. The net force points to the left. What is the missing third force?
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You’ve just kicked a rock, and it is now sliding across the ground about 2 meters in front of you. Which of these forces act on the ball?
A. Gravity, acting downward
B. The normal force, acting upward
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B. The normal force, acting upward
C. The force of the kick, acting in the direction of motion
D. Friction, acting opposite the direction of motion
E. A, B, and D but not C.
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You’ve just kicked a rock, and it is now sliding across the ground about 2 meters in front of you. Which of these forces act on the ball?
A. Gravity, acting downward
B. The normal force, acting upward
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B. The normal force, acting upward
C. The force of the kick, acting in the direction of motion
D. Friction, acting opposite the direction of motion
E. A, B, and D but not C.
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Two rubber bands stretched the standard distance cause an object to accelerate at2 m/s2. Suppose another object with twice the mass is pulled by four rubber bands stretched the standard length. The acceleration of this second object is
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A. 16 m/s2.
B. 8 m/s2.
C. 4 m/s2.
D. 2 m/s2.
E. 1 m/s2.
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Two rubber bands stretched the standard distance cause an object to accelerate at 2 m/s2. Suppose another object with twice the mass is pulled by four rubber bands stretched the standard length. The acceleration of this second object is
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A. 16 m/s2.
B. 8 m/s2.
C. 4 m/s2.
D. 2 m/s2.
E. 1 m/s2.
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Three forces act on an object. In which direction does the object accelerate?
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Three forces act on an object. In which direction does the object accelerate?
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An elevator suspended by a cable is moving upward and slowing to a stop. Which free-body diagram is correct?
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An elevator suspended by a cable is moving upward and slowing to a stop. Which free-body diagram is correct?
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