Newtons Third Law

ISP 209 - 2B

Newtons Third Law

ISP 209 - 2B

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

ISP 209 - 2B

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.Newtons laws of motion

ISP 209 - 2B

Newtons third lawWe 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.

ISP 209 - 2B

Example A collision

ISP 209 - 2B

Playing catch with a medicine ballA throws the ball and B catches it. four forcesWhen 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).ABWhen 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). Newtons third law for the throw Newtons 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 Newtons third law.Well consider two examples: The force of universal gravitation The spring force

ISP 209 - 2B

Universal Gravitation --- an example of Newtons third law

ISP 209 - 2B

The Earth pulls the apple down (action).The apple pulls the Earth up (reaction).The two forces are equal (but opposite).

ISP 209 - 2B

When does a scientific theory become accepted as true?

ISP 209 - 2B

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)For a laboratory measurement, the gravitational force is really very weak.Henry Cavendish, 1798 : first measurement of G

ISP 209 - 2B

What makes g?

ISP 209 - 2B

Weighing the EarthCalculate the mass of the Earth.

ISP 209 - 2B

The spring force ---another example of 3rd lawThe forces are equal but opposite.

ISP 209 - 2B

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 NHookes law: The strength of a spring force is proportional to the displacement (extension or compression). F = k x where k is called Hookes constant for the spring.

ISP 209 - 2B

The truck pulls to the right. According to Newtons 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 dont forget that other forces are also acting.

ISP 209 - 2B

Which team will end up in the puddle?But arent the forces equal but opposite !?Resolution: Dont 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

ISP 209 - 2B

Momentum, p = mvNewtons third law implies conservation of momentum.As vectors, p = m v.momentum = mass x velocityTotal momentum is constant.

ISP 209 - 2B

Momentum, p = mvTotal momentum is conserved:Proof

ISP 209 - 2B

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 Newtons third law! equalequal

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 Newtons third law, the third law became an accepted fact: a law of nature not just a hypothesis.

ISP 209 - 2B

Harold Edgertons 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!

ISP 209 - 2B

Quiz QuestionThe planet is pulled toward the moon (and vice versa).Calculate the gravitational force on the planet.

ISP 209 - 2B

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 cant accelerate!

ISP 209 - 2B

Resolution: Consider each part separately, and dont forget that there are other forces acting.So how can they start moving, or accelerate?A puzzleHorse and Cart

ISP 209 - 2B

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 Newtons third law.Nature appears to be complex; but beneath the surface, nature is simple.

ISP 209 - 2B

PREPARE ON THE BLACKBOARDUniversal GravitationF=Gm1m2/r^2, equal but opposite

OUTLINE1/ Introduction (15 min)2/ Universal Gravitation (20 min)3/ Spring force (10 min)4/ Puzzles (15 min)5/ Momentum (20 min)

DEMOs1/ 2 spring scales (2 volunteers)2/ Medicine ball (2 volunteers)3/ Rubber ball of Miles4/ Mass hanging from a spring (Hookes law)5/ Falling meter stick6/ Bottle rocket

Part 1 - Introduction (15 minutes)Todays lecture is about Newtons third law.Newtons third law is a statement about forces. Well see that it is difficult to comprehend. Indeed, it is a puzzling law of nature, not at all simple common sense.Aristotles ancient Physics was based on philosophical assumptions and common sense. Most of Aristotelian physics was wrong, although it seemed like good common sense. It took the genius of Galileo to over-throw the ancient incorrect theories of the Aristotelians.Then Newton developed a complete theory of mechanics. Newtons third law is by no means simple common sense, as well see.Newtons third law concerns interactions --- the forces when two objects are exerting forces on one another.{READ}Most people will answer this question incorrectly.Do you think the answer is obvious? Then you probably have the wrong answer.Well see what Newtons third law says about it.

Here again are Newtons three laws of motion.{READ}= The third law is a statement about forces rather than a statement about motion. But it is called a law of motion because this property of forces affects the way mechanical systems move.The words action and reaction are Newtons original terminology. These terms are really archaic. In fact, this phraseology may be downright misleading.What did Newton mean by action and reaction?{APPEAR last}Action means a force. Reaction means another force. So in any interaction there are two forces. Which one is called the action and which one is called the reaction is very arbitrary.The archaic terminology of action and reaction suggests, wrongly, that one occurs first and then the other occurs. On the contrary, the two forces occur simultaneously. Either one can be considered the reaction force of the other.= We need to restate Newtons third law in a modern and more clear way.{READ first line}But here is a more modern statement{READ purple}The figure shows attractive forces between two objects, as a specific illustration. The blue object A exerts a force on the red object B and B exerts an equal (but opposite) force on A. In this example, the objects attract each other. It would be the same for repulsion.{READ: Forces always occur like this, in pairs. Etc}

DEMO [1/4]Two spring balances; need two volunteers a big hulk and a little coed. Each pulls on one of the spring balances and they both register the same force. Ask the girl to hold still while the big guy pulls harder. But the forces are always measured to be equal!Lets work through an example that depends on Newtons third law.{READ}Maybe the final answer seems obvious. But the detailed explanation shows how Newtons third law is involved.DEMO [2/4]= Playing catch with a medicine ball.Need two volunteers people with good coordination and pretty strong and not too large.{READ}Common sense would probably tell you that the truck exerts a larger force than the car. After all,1/ The truck is much larger than the car;2/ The truck is in gear with the engine engaged, whereas the car is in neutral with the engine off;3/ The truck and car are going to move in the direction that the truck is pulling. The car pulls backward not the direction of motion. For all these reasons, most people will say that the truck exerts a greater force than the car.Common sense is wrong.The interaction is governed by Newtons third law: The reaction (the pull of the car) is equal to the action (the pull of the truck). The two vehicles exert equal forces (but opposite in direction).{READ}Part 2 Universal Gravitation (20 minutes)Newtons third law is a statement about forces. Here is a specific example gravity.Newtons Law of Universal Gravitation states that any two of masses in the universe attract each other. The Earth pulls an apple down to the ground; anyone could see that. The apple pulls the Earth upward toward the apple; it took a great genius like Newton to see that.{READ slide; inverse square law; youll need the equation for CAPA; man and earth gravity obeys the third law}So this theory of universal gravitation was another remarkable discovery of Isaac Newton. But how could such a sweeping statement be accepted as a scientific truth?(next slide!)How could Newtons theory of Universal Gravitation become accepted as scientific truth?Well, for one thing, Newton explained the motion of the planets based on this theory. No one else could explain planetary motions by any competing theory. Newton explained certain other natural phenomena based on this theory comets and the tides. No other theory could explain those phenomena. So Newtons theory of universal gravitation became accepted as true in his time.But this is a general question: When does a theory become a fact? Can a theory ever be accepted as a fact. Is the theory of evolution in biology a theory or a fact? Obviously its a theory. But when can you say the theory is true?In physics, a theory can be tested in the laboratory, to test whether it is true. Can the Law of Universal Gravitation be tested in the laboratory?

{READ the first line}We tend to think of gravity as a strong force but that is because we experience the force exerted by an entire planet Earth. But the force between laboratory masses is very weak.{Read }{Blackboard: F = G m1 m2 /r2 equal but opposite}The first measurement of Newtons constant G was by Henry Cavendish in 1798, long after the death of Isaac Newton (71 years later). Why was the measurement so difficult? You can see from the value that the force is very weak.The Cavendish experiment provides a direct laboratory test of Newtonian gravitation.

As long as we are considering gravity, lets take a little detour and learn something more about gravity. Well come back to Newtons third law in a few minutes. But first, what makes g?Newtons law of universal gravitation is a fundamental theory.How does it determine little g, the acceleration due to Earths gravity?DEMO [3/4] Drop a ball

What makes g?{READ}

Lets do an example problem: Calculate the mass of the Earth.How can we determine the mass of he Earth? You cant put it on scales its too big. So, how do we know the mass of the Earth? We know it from Cavendishs measurement of G.EXAMPLE # 1Calculate the mass of the Earth.Blackboard: GMm/R^2 = mg implies M = gR^2/GHenry Cavendish did this very calculation, and deduced that the average density of the Earth is 5.5 times greater than the density of water, i.e., 5.5 g/cc.This is interesting, because the density of various common rocks ranges from 2.5 to 4.5 g/cc. Evidently the Earth is not just made of rock. The density of iron is 7.87 g/cc. We can conclude that the Earth has a large iron core. We cant go to the center of the earth, but we can know that the iron core exists from the calculation.

Part 3 - Spring force (10 minutes)

Another example of a force is the spring force.{READ}So the spring force obeys Newtons third law.

Lets do an example problem.{READ the problem; READ Hookes law}

EXAMPLE # 2F = k xFrom the information, k = F/x = (50 N) / (3 cm) = 16.67 N/cm.Now calculate the force for the larger displacement,F = k x = (16.67 N/cm) * (5.5 cm) = 91.7 N.

DEMO [4/4]A mass hanging from a spring. What happens as I add mass?

Part 4 Puzzles (15 minutes)Newtons third law is not plain common sense. On the contrary, it can be very puzzling its a mystery of the physical world.{READ}Start with the car {appear the force on the car}.Now, what about the truck?{Appear the two forces on the truck.}The idea that the road exerts a force on the tires of the truck, to cause the two vehicles to accelerate forward, is hard to visualize; because the road is at rest. But it is obviously correct: What if the truck were located on a patch of very slippery ice; then the vehicles would not be able to accelerate forward. The force of the road would be zero in that case.

Heres another puzzle.{READ all}The weightlifters win because of the frictional force of the ground, which is greater on the weightlifters than on the gymnasts.The net force on the weightlifters is toward the left, because the friction of the ground is stronger than the tension of the rope.The net force on the gymnasts is toward the left, because the friction of the ground is less than the tension of the rope.By Newtons third law the force of the rope is the same on both teams (equal but opposite). The frictional forces of the ground are different thats why the weightlifters win the tug of war.Who would win if you put the weightlifters on slippery ice but the gymnasts on hard ground? Then the frictional force of the ground would put the weightlifters in the puddle.Part 5 - Momentum and collisions (20 minutes)Another important concept in mechanics is momentum.It is related to Newtons third law, as well see.The momentum of an object, usually denoted by the letter p, is defined as the product of mass times velocity. What is so important about that mathematical combination? It is very special!{READ}You need to use conservation of momentum for one of the LON-CAPA problems (the man and box problem).The idea of a conservation law is an important idea in science. Well see it again in this course.

Proof of the conservation of momentum.

{READ}

Note from the proof, that the conservation of momentum is equivalent to Newtons third law.{READ up to the blue text}Is this common sense? You mean, The little Cooper Mini exerts just as strong a force as the huge Mack truck during the collision!?Yet that is exactly what Newtons third law says. I don't think this is just common sense at all. It took a genius like Newton to see this relationship. This is why Newton was so great he could see things that the rest of us would not see.Of course now that he has explained it, the rest of us can see that it is true. But he was the first to get the law of action and reaction. That is an example of the genius of Isaac Newton.

Now, how do we know it is true? Well, by experiments.Because of the third law, the momentum is conserved (etc).{READ the rest; this can be observed.}

{READ}

Is this common sense? You can see the big force on the ball by the fact that the ball is significantly deformed at the instant of the kick. This is not an under-inflated ball, or a ball with no air pressure. It is a normally pressurized football. But in the instant of the kick it is very much deformed by the force of the foot. (You cant see this with your eye your eye is too slow.)

Now, at that instant there is an equal force (in the other direction) exerted by the ball on the toe!

In this, and all the examples, the action-reaction forces are equal. [lead in to next slide]

{READ it all}

This idea that the Earth pushes you forward when you walk (or, rather, when you accelerate while walking) is really hard to comprehend. I guess the reason it is so difficult to see is that the Earth does not move, at least not perceptibly. How can you be pushed forward by something that does not move?

DEMOA meter stick. (1) Stand it up and let it fall. Because of the frictional force, the center of mass moves forward. (2) Now put some soapy water on the bench and stand up the meter stick. When it falls, it falls straight down.{Blackboard:The horse: F1 = - A + friction = m_horse aThe cart: F2 = +A = m_cart a

The accelerations are the same.The directions of the net forces are the same, toward the right.The magnitudes of the net forces are different.The action/reaction pair are equal but opposite.

The idea that the Earth exerts a force on the horses hooves is hard to visualize, because the Earth is at rest. But it is obviously correct: What if the horse were standing on slippery ice; then he would not be able to pull the cart.

Newtons third law is a universal statement about forces.We know it is true by experimental tests.But WHY is it true?Below the surface, nature is simple. {[Einstein: Nature is simple but subtle.]} There are only four fundamental forces in nature. All forces in the physical world trace back to one of these fundamental forces.{READ}All of these fundamental forces obey conservation of momentum, which is equivalent to Newtons third law.