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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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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.

Newton’s laws of motion

Action means force.

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force on B due to A

force on A due to B

Newton’s third law

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.

Whenever one object exerts a force on another object, the second object exerts an equal but opposite force on the first object.

Forces always occur like this, in pairs.

For every action there is an equal but opposite reaction.

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Example – A collision

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Playing catch with a medicine ball

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).

A B

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 throw

► 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

ˆ

ˆ

2221

2

1221

1

nF

nF

rmGm

rmGm

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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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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)

1-2- kg s m 31110676 .G

For a laboratory measurement, the gravitational force is really very weak.

Henry Cavendish, 1798 : first measurement of G

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What makes g?

2

2

RGM

g

RGMm

mg

gravity of force weight

9.81 m/s2

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Weighing the EarthCalculate the mass of the Earth.

The force of gravity on m is, by definition, its weight,

By Newton’s theory of universal gravitation,

mgF

2RGMm

F

kg .

.

).(.

24

22

10026

kg11E676

6E46819G

gRM

the mass of the Earth, relying on the Cavendish measurement

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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.

( + means to the right; - means to the left.)

The forces are equal but opposite.

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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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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?

A puzzle:

Resolution: Consider each part separately, and don’t forget that other forces are also acting.

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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.

A puzzle : Tug of War

String tension

String tension

Contact force Contact force

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MomentumMomentum, , p = mvp = mv

Newton’s third law implies Newton’s third law implies conservation of conservation of momentummomentum..

As vectors, p = m v.

momentum = mass x velocity

Total momentum is constant.Total momentum is constant.Total momentum is constant.Total momentum is constant.

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MomentumMomentum, , p = mvp = mv

Total momentum is conserved:Total momentum is conserved:

constant. is

law) (third

21

21

2211

22

11

21

0

0

pp

pp

vmvm

tv

mtv

m

FF

Proof

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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?

A puzzle …

The two forces are equal. They must be, by Newton’s third law!

large is

small is velocity

m momentum

forces

1

Δv Δv

vmvFF

2

1

221

21

equal

equal

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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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Resolution: Consider each part separately, and don’t forget that there are other forces acting.

So how can they start moving, or accelerate?

A puzzleHorse 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).

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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.