Transcript Chapter Four

Chapter Four
Newton's Laws
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Newton's Laws
In this chapter we will consider Newton's
three laws of motion.
 There is one consistent word in these
three laws and that is "body" (newtonian
body).
 We will define force through the motion it
cause on mass.

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Newton's Laws (1)
First Law: Every body of matter continue
in a state of rest or moves with constant
velocity in a straight line unless compelled
by a force to change state.
 Second Law: When net unbalanced forces
act on a body, they will produce a change
in the momentum (mv) of that body
proportional to the vector sum of the force.
The direction of the change in momentum
is that of the line of action of the resultant
force.

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
Third Law: Forces, arising from the
interaction of particles, act in such a way
that the force exerted by one particle on
the second is equal and opposite to the
force exerted by the second on the first
and both are directed along the line
joining the two particles. (Or, action and
reaction are equal and opposite).
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Newton's Laws (2)

The average force is defined as

Let a = dv/dt, the force is define as

The forms of Newton's law that we will use
are
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Mass

Let m0 be the standard kilogram. If we
exert a force on the mass with no other
forces to interfere, we can measure an
acceleration a0. If we apply this same
force to a different mass m1, we measure
a different acceleration a1. Then
and
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Force has units of mass
length/time2 or
kilogram-meter per second2 (newton, N).
 A force of 1 N is that force which causes a
mass of 1 kg to be accelerated at a rate of
1 m/sec2.

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Weight
The rate of free fall of all objects in a
vacuum at a given point on earth is the
same.
 The downward acceleration at sea level is
approximately the same at all locations, or
g= 9.8 m/sec2.
 Weight = mg.
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Applications of Newton's Laws-Example 4-2
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A child pulls a toy boat through the water at
constant velocity by a string parallel to the
surface of the water on which he exerts a
force of 1 N. What is the force of resistance of
the water to the motion of the boat? See Fig.
4-2.
Sol : Because constant velocity means zero
acceleration,
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Applications of Newton's Laws-Example 4-3

Two ropes attached to a ceiling at the
angles shown in Fig. 4-3 support a block
of weight 50 N. What are the tensions T1
and T2 in the ropes?
Sol :
If we examine the newtonian body, we see
that it is not accelerating in either the x or y
directions. We have
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Thus,
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Substituting into second equation
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Applications of Newton's Laws-Example 4-5

A block of mass 8 kg is released from rest
on a frictionless incline that is at an angle
of 37o with the horizontal (Fig. 4-6a).
What is its acceleration down the incline?
Sol: See Figure 4-6b.
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
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From Newton's second law, we have
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Two important points:
 Because the acceleration is independent of
the mass, all masses starting from rest at
the same height on the same plane will
have the same acceleration and, therefore,
reach the bottom at the same time.
 The acceleration is less than the
acceleration of gravity because only a
component of the force of gravity on the
body is directed down the plane.
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Applications of Newton's Laws-Example 4-6

Masses of 2 kg and 4 kg connected by a
cord are suspended over a frictionless
pulley (Fig. 4-7a). What is their
acceleration when released?
Sol: Three important facts:
1. Because the pulley is frictionless, the
tension in the rope is the same on both
sides.
2. The tensions are not the same as in a
static situation.
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3. There are two newtonian bodies and
while m1 moves upward with a positive
acceleration, m2 moves with an
acceleration having the same magnitude
but directed downward.
 See Figure 4-7b.
For body m1 we have
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For body m2 we have
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Friction
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There is a force equal and opposite to the force
that we exert that resists the motion of the
object. This resistive force is called the force of
friction.
There are two types of friction, static and kinetic.
The starting friction is called static. The friction of
motion is called kinetic.
Static friction is larger than kinetic friction. We
will only consider kinetic friction.
The force of friction is proportional to the normal
force (mg = N). See Figure 4-8.
The force of friction is f = μN, where μ is called
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the coefficient of friction.
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Example 4-7

A force of 10 N is required to keep a box
of mass 20 kg moving at a constant
velocity across a level floor (Fig. 4-9).
What is the coefficient of friction?
Sol: Since ax = 0 and ay = 0, we have
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
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and
But
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Example 4-8

A block is places on a plane inclines to the
horizontal at 37o. The coefficient of friction
between the plane and the block is μ =
0.4. When the block is released what is its
acceleration down the plane? (See Fig. 410)
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
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Sol

The forces along the plane are the force of
friction f upward and the component of
the force of gravity FD downward. Choose
the downward direction as positive and we
have
since
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we have
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Homework

2. 4. 7. 9. 11. 14. 16. 19. 21. 24.
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