Transcript 9/7/2006 ISP 209 - 2B - MSU Physics and Astronomy Department

Newton’s Third Law
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Newton’s Third Law
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Which vehicle exerts a greater force ―
the tow truck or the car?
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Newton’s laws of motion
1. The law of inertia. An object in motion
remains in motion with constant velocity if the net
force on the object is 0.
2. Force and acceleration. If the net force acting
on an object of mass m is F, then the acceleration
of the object is a = F/m. Or, F = ma.
3. Action and reaction. For every action there is
an equal but opposite reaction.
Action means force.
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Newton’s third law
For every action there is an
equal but opposite reaction.
Whenever one object exerts a force on
another object, the second object exerts an
equal but opposite force on the first object.
force on B due to A
force on A due to B
Forces always occur like this, in pairs.
We will see that this is very hard to accept! It is just not
common sense. That is why it took a great genius like
Newton to figure it out.
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Example – A collision
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Playing catch with
a medicine ball
A
B
A throws the ball and B catches it.
 four forces
When A throws the ball he exerts a force on the ball
(toward the right) and the ball exerts a force on him
so he recoils (toward the left).
► Newton’s third law for the throw
When B catches the ball he exerts a force on the ball
(toward the left to stop it) and the ball exerts a force on
him so he is knocked back (toward the right).
► Newton’s third law for the catch
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Which vehicle exerts a greater force ―
the tow truck or the car?
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Forces obey Newton’s third law.
We’ll consider two examples:
• The force of universal gravitation
• The spring force
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Universal Gravitation
--- an example of Newton’s third law
Gm1m2
F1 
nˆ 1
2
r
Gm1m2
F2 
nˆ 2
2
r
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The Earth pulls the apple down (“action”).
The apple pulls the Earth up (“reaction”).
The two forces are equal (but opposite).
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When does a scientific theory become
accepted as true?
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For a laboratory measurement, the
gravitational force is really very weak.
The force on the 1 kg mass is +3.3 x 10-10 N.
The force on the 5 kg mass is –3.3 x 10-10 N.
( + means to the right, i.e., increasing x)
G  6.67  10
11
3
-2
m s kg
-1
Henry Cavendish, 1798 : first measurement of G
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What makes g?
GMm
weight  mg  force of gravity  2
R
GM
g 2
9.81
R
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Weighing the Earth
Calculate the mass of the Earth.
The force of gravity on m
is, by definition, its
weight,
F  mg
By Newton’s theory of
universal gravitation,
gR 2 9.81  (6.4 E 6)2
M

kg
G
6.67 E 11
 6.02 10
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kg
GMm
F 
R2
the mass of the Earth,
relying on the Cavendish
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The spring force
---another example of 3rd law
Suppose the spring is stretched beyond its
equilibrium length by a length x.
The force on the mass m1 is F1 = +kx.
(k = Hooke’s constant)

The force on the mass m2 is F2 = kx.

The forces are equal but opposite.
( + means to the right; - means to the left.)
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Example
One end of a spring is attached to a wall.
When the other end is pulled with a force
of 50 N, the spring is stretched by 3 cm.
What force would be required to stretch
the spring by 5.5 cm?
Answer: 91.7 N
Hooke’s law: The strength of a spring force is
proportional to the displacement (extension or
compression). F = k x where k is called Hooke’s
constant for the spring.
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A puzzle:
The truck pulls to the right. According to Newton’s
third law, the car pulls to the left with an equal
force. So how can they start moving, or accelerate?
Resolution: Consider each part separately, and
don’t forget that other forces are also acting.
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A puzzle : Tug of War
String tension
String tension
Contact force
Contact force
Which team will end up in the puddle?
But aren’t the forces equal but opposite !?
Resolution: Don’t forget that there are other forces acting.
Each team exerts a force on the Earth, so the Earth exerts a
force on the team (3rd law!). The net force on either team is
toward the left.
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Momentum,
p = mv
momentum = mass x velocity
As vectors, p = m v.
Newton’s third law implies conservation of
momentum.
Total momentum is constant.
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Momentum,
p = mv
Total momentum is conserved:
Proof
F1  F2 (third law)
v 1
v 2
m1
 m2
t
t
m1 v 1  m2 v 2  0
p1  p2  0
p1  p2 is constant.
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A puzzle …
A small car (Cooper Mini) collides
with a big truck (Mack).
Which is greater – the force
exerted by the truck or the
force exerted by the car?
The two forces are equal.
They must be, by Newton’s
third law!
equal
forces
F1  F2
 momentum
m1v 1  m2 v 2
equal
 velocity
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Δv 1 is small
Δv 2 is large
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When does a theory become
accepted as true?
The law of conservation of momentum
states that the combined momentum is
constant when particles interact.
It is verified by many experiments.
Since momentum conservation is
equivalent to Newton’s third law, the third
law became an accepted fact: a law of
nature not just a hypothesis.
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Harold Edgerton’s high
speed photograph of Wes
Kessler kicking a football.
The force exerted by the
ball on the toe (reaction) is
equal to the force exerted
by the toe on the ball.
Really hard to accept!
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Quiz Question
The planet is pulled toward the moon (and vice versa).
Calculate the gravitational force on the planet.
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When you walk or run, what forces occur?
• At constant velocity the horizontal force is 0 and you
continue to move because of inertia.
• To accelerate, you push backward against the floor; the
reaction force, which is a friction force exerted by the
floor on your foot, pushes you forward.
This reaction force may be hard to
visualize, but imagine what would
happen if you were on a frictionless
surface – can’t accelerate!
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A puzzle
Horse and Cart
The horse pulls the cart with a force A (to the right).
According to Newton, the cart pulls the horse with a
force –A (to the left).
So how can they start moving, or accelerate?
Resolution: Consider each part separately, and don’t
forget that there are other forces acting.
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The four fundamental forces
• Gravity
• Electromagnetic forces
• Strong nuclear force
• Weak nuclear force
All the fundamental interactions obey conservation
of momentum (verified by experiments), which is
equivalent to Newton’s third law.
Nature appears to be complex; but beneath the surface, nature
is simple.
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