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Newton’s Third Law

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Newton’s Third Law

ISP 209 - 2B

Newton’s Third Law

ISP 209 - 2B

Which vehicle exerts a greater force ― the tow truck or the car?

ISP 209 - 2B

Action means force.

Newton’s laws of motion

- The law of inertia. An object in motion remains in motion with constant velocity if the net force on the object is 0.
- 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.
- Action and reaction. For every action there is an equal but opposite reaction.

ISP 209 - 2B

force on B due to A

force on A due to B

For every action there is an equal but opposite reaction.

Newton’s third law

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.

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

ISP 209 - 2B

Which vehicle exerts a greater force ― the tow truck or the car?

ISP 209 - 2B

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

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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)

Henry Cavendish, 1798 : first measurement of G

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9.81 m/s2

What makes g?

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

By Newton’s theory of universal gravitation,

the mass of the Earth, relying on the Cavendish measurement

Weighing the Earth

Calculate the mass of the Earth.

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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 spring force ---another example of 3rd law

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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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.

ISP 209 - 2B

String tension

String tension

Contact force

Contact force

A puzzle : Tug of War

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 = mv.

Newton’s third law implies conservation of momentum.

Total momentum is constant.

ISP 209 - 2B

Momentum, p = mv

Total momentum is conserved:

Proof

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A puzzle …

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

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?

equal

equal

ISP 209 - 2B

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.

ISP 209 - 2B

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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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).

A puzzle

Horse and Cart

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.

ISP 209 - 2B