Chapter 3 Force and Newton

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Chapter 3 Force and Newtons laws
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Section 3-1 Classical mechanics

• The approach to the dynamics we consider here is
  generally called classical mechanics.

Issac Newton (1642-1727)
Galileo Galilei (1564-1642)
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• In this chapter, we will study in detail the
  bases of classical mechanics Newtons three laws.

• Classical mechanics was found not to describe
  well the motions in certain realms.

• For ordinary objects, classical mechanics is
  important and very useful.

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Section 3-2 Newtons first law

• What can cause the motion of a body?

Force
Take the apples freely falling motion as an
example

• What will be the states of the body if there is
  no any interactions between it and its
  environment?
• (an isolated system)

At rest
or 1D uniform motion

• Newtons first law
• Every body continues in its state of rest or
  uniform motion in a straight line, unless it is
  compelled to change that state by forces
  impressed on it.

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• 1. Newtons first law tells us
• Consider a body on which no net force acts.
• 1) If the body is at rest, it will remain at
  rest
• 2) If the body is moving with constant
  velocity, it will continue to do so, no force is
  needed to keep it moving.

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2. The correctness of Newtons laws is dependent
on the reference frames!
See an example in ???/???/2-01??????????.exe 1
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• 3. Inertial frames(?????)

• The reference frames to which Newtons law
  applies (??) are called inertial frames.

• The tendency of a body to remain at rest or in
  uniform linear motion is called inertia.

• Can we find inertial frames in the nature?

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???, ??????? a3.4x10-2m/s2
???, ????????? a6x10-3m/s2
???, ??????? a3x10-10m/s2

• A frame that keeps rest or uniform linear
  motion,
• relative to any inertial frames, is an inertial
  frame.

• Newtons first law is often called the law of
  inertia.

• See ???/???/2-01?????.exe

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Section 3-3 Force

• Newtons first law tell us that force causes the
  change in the motion states ( ).

• For a fixed body, a larger force applied to the
  body will generate a larger acceleration for the
  body.

• The force is determined through the measure of
  acceleration the body gets under the force.

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Section 3-4 Mass

• It is much easy to accelerate a bicycle than a
  car by pushing it.

Clearly same force produces different
acceleration when applied to different bodies.
What makes the difference???
Mass
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• In experiments, it is easy to prove that the
  magnitude of the acceleration is proportional to
  that of the force applied to a given body.
• This ratio is called the mass of the body.
  Thus mF/a
• or Fma

Mass The property of a body that determines its
resistance to a change in its motion.
The mass defined in Newtons law is an inertial
mass.
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One method to quantitatively determine the mass
of a body, (relative to others)
Suppose we apply a certain force to a
body having mass and observe an acceleration
of . We then apply the same force to
another body of mass ,observing an
acceleration . Thus
or
(3-3)






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Section 3-5 Newtons second law

• The mathematical statement of Newtons second
  law of motion is
• 1. Here is the vector sum of all the
  forces acting on the body.

(3-4)
2. Is the first law not totally contained in
second law?
No.
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• 3. Equation (3-4) is a vector equation. We can
  write it as three one-dimensional equation
• Here (or , ) is the algebraic
  sum of the x (or, y, z) components of all the
  forces acting on m.
• 4. If we measure the mass in kg and the
  acceleration in ,Newtons second law
  gives the force in N.

(3-5)
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Sample problems
1. A worker pushes a loaded sled, whose mass m is
240 kg for a distance d of 2.3 m over the surface
of a frozen lake. The sled moves with negligible
friction on the ice. The worker exerts a constant
horizontal force of 130 N as she does so. If the
sled starts from rest, what is its final
velocity?
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2. The worker in Sample Problem 1 wants to
reverse the direction of the velocity of the sled
in 4.5s. With what constant force must she push
on the sled to do so?
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(D)
(B)

• 3. An object is moving north. From only this
  information one can conclude
• that there is a single force on the object
  directed north.
• that there is a net force on the object directed
  north.
• that there may be several forces on the object,
  but the largest must be directed north.
• nothing about the forces on the object.

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Section 3-6 Newtons third law

• 1)Newtons third law is
• To every action there is an equal and opposite
  reaction. If the body B exerts a force on
  body A experiment shows that body A exerts a
  force on body B. These forces are related
  by
• 
  
• 
  (3-6)
• Note the action and reaction forces always
  act on different bodies.

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• 2)Dynamical analysis using Newtons laws
• In analyzing problems using Newtons law,
  there are several steps that we should follow
• 1. choose a suitable inertial reference frame.
  
  
• 2. For each object in the problem, draw a
  free body diagram, showing all of the forces
  acting on that body.
• 3. For each body, find the vector sum of all
  the forces. In practice, this usually means
  separately adding the x, y, z components of the
  forces. Then use Eqs (3-5) to find acceleration
  components

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Sample problems
1. A worker W is pushing a packing crate of mass
m14.2 Kg. In front of the crate is a second
crate of mass m21.4 Kg. Both crates slides
across the floor without friction. The worker
pushes on crate 1 with a force F1w3.2 N. Find
the accelerations of the crates and the force
exerted by crate 1 on crate 2.
2. See ???/???/2-02?????? ?1