Mass for high school students
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The Presentation is about the fundamental physical quantity Mass. The presentation is motivated by my son back from school asked me "if weight is a force, and the unit of force is Newton, why aren't we buying potatoes in Newtons but in Kgs. I didn't answer this question in my presentation. But, I facilitated students to find the answer themselves.
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Mass for high school students
- 3. Newton’s law of Motion Let us start with the Postulate F = ma If a body has a acceleration it needs a force and the relation to acceleration and force is F= Ma.
- 4. Is the Newton’s law Correct How can you verify in this law ? F = ma
- 5. Measuring The mass We don’t know how to measure the mass. we don’t know how to measure the force. A circular argument !!!!
- 6. One Kilogram Mass is Born In 1799, a kilogram, was defined as mass equal to the mass of one cubic decimeter of distilled water at 4°C. The material of the standard kilogram was a platinum cylinder. The First General Conference of Weights and Measures held in 1889 approved this new standard.
- 8. Hooks Law Extension “x” (m) Accelerat ion, “a” (m/s2) Force , “F” (kg m/s2) 0.1 -1 -1 0.2 -2 -2 0.3 -3 -3 -0.1 1 1 -0.2 2 2 -0.3 3 3 Mass = 1 kg here
- 9. Hooks Law F = - K x
- 10. Mass of Anything You can attach a known mass to a spring, see what acceleration it produces. Now attach a unknown mass to the same spring, you now know the mass of the object by the acceleration it produces. This way you can find the mass of anything.
- 12. Another Mass and Another Law
- 13. Another Mass and Another Law • Here again we have more question than answers. • As in laws of motion, what is measurable here?
- 14. Another Mass and Another Law Gm=V2r
- 15. Measuring the Value of “G” Torsion balance
- 16. Mass of Earth Now you are in a position to find the mass of earth, by shooting an object in stable circular orbit, you have all the values except the mass of earth and you compute it as follows. G M1 M2/ r2 = M2V2/r .i.e. equating GRAVITATIONAL FORCE and CENTRIPETAL FORCE. By using the laboratory value for G allows us to deduce the mass of the Earth: 5.98 X 10 24 Kg.
- 17. The Mystery of Two Masses. Inertial mass - measures an object's resistance to being accelerated by a force. Gravitational mass measures the gravitational force exerted and experienced by an object. Although inertial and gravitational mass are conceptually distinct, experiments so far has demonstrated no difference in values.
- 18. More Masses Inertial mass. Active gravitational mass. Passive gravitational mass. Rest Mass Relativistic Mass Quantum Mass E=mc2 m=W/a m= f/a
- 19. Mass in Special Theory of Relativity
- 20. Special relativity "mass" is given two meanings : One is "rest mass“ an invariant quantity which is the same for all observers in all reference frames Other is "relativistic mass" is dependent on the relative velocity between observer and the mass
- 21. Rest Mass Expressed by the relation: E=mc2
- 22. Relativistic Mass Expressed by the relation:
- 23. We understood lot about Mass in the last one hour. what can we do with that?
- 24. What Can We Do Find answers to the questions about mass haunting us:- Underlying cause behind Inertial and Gravitational mass. Force carrier of Gravitational force. Mechanism of Higgs field interaction with matter.
- 25. What Can We Do Einstein worked fruitlessly during his last thirty years of his life to find answers to the questions we were briefly contemplated today.
- 26. What Can We Do Use your early part of your life to find answers to the questions Einstein could not in his last thirty years of his life.
- 28. Questions ?
- 29. Optional Exercise for those Interested in mass Photon is known to be a mass less particle. We know momentum is m x v KE is ½ x m x v2 How does Photon has definitive momentum and energy?
- 30. References: Wikipedia free encyclopedia. The God Particle- Leon Lederman. Beyond God Particle - Leon Lederman Fundamentals of Physics I and II – Yale University Open Course.
- 31. A Glance at Particle Physics
- 32. More Adventure With Mass We know our Universe is made of Hadrons and Leptons at the fundamental level Hadrons forms matter and Leptons forms the force carriers. Forces ..... Force Carriers Strong Nuclear Force ...... Gluon Weak Nuclear Force ...... Z , W Boson Electromagnetic Force ...... Photon Gravitational Force ...... Graviton ?
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- Slide 1: Mass What we know about this fundamental property of nature? What we do not know about this fundamental property of nature? Is the subject of our discussions today.
- Slide 1: Mass What we know about this fundamental property of nature? What we do not know about this fundamental property of nature? Is the subject of our discussions today.
- Slide 2: Newton’s law of Motion Newton’s law says that if a body has a acceleration it needs a force and the relation to acceleration and force is F= Ma. With “a” measured in m/s2, “m” measured in Kg and “Force” measured in Kg.m/s. Later people got tired of saying this unit that and called it a Newton “N” in his honour. Why do we start from Newton’s Postulate?. The first definition of mass and also the first definition of force was given by Newton in this postulate. For clarity, Postulate is one which is not derived from already known laws of physics but a statement ab-initio. Postulate can only be verified by observation or experiment. This postulate can become a law only if it is proved. In the normal course of invention in science, a idea is treated as a Hypothesis, If the Hypothesis is true for 95% of the observation done for adequate no times, the hypothesis can be investigated further before accepting the same as a Theory. Postulate will be accepted as a Theory if it is true most of the time and can become law only when it is true all the time. In your school some one tells you a Force of 20 Newton acts on a 4 kilogram mass, and asks you what is the acceleration you divide force by mass and tell the acceleration is 5 m/s2, and you say you know what to do with Newton’s law. Here I want to tell you that it is actually more complicated than that, which I realised much later after my formal education. To understand the whole concept in right perspective; ……………. Take yourself back to 1600s when Newton gave the Law. At that time people had only a intuitive understanding of force and mass, and suddenly Newton tells you here is a law F=ma. Are you better off with this law. What can you do with this law?
- Slide 3: Is the Newton’s law Correct Before using the law given by Newton, How de we even know if this law is correct. How can we verify if it is true? Here is a body which is in motion, I what you to tell me if Newton is right. (allow students to answer the question) You can measure the LHS and measure RHS and if they are equal, you can say Newton was right. What can you measure in this equation? Acceleration can be measured with a clock and a meter stick, as time in seconds and distance in meter has been defined before Newton’s days. (A metre, being defined earlier as I / 1O millionth part of the meridian quadrant passing through Paris. Now it is the length of the path travelled by light in a vacuum during a time interval of 1/299 792 458 of a second). An object is in motion, you make a measurement of position and time now, and again do a measurement a little later, and again little- little later. First two measurement gives you first velocity; the second and third measurement gives you the next velocity; now divide the change in velocity with the corresponding change in time and you get acceleration. So what is the acceleration right now? Make the difference between the measurements quicker and quicker you get the acceleration right now. (Mathematically you can make this difference nearly zero. Newton’s infinitesimal calculus helps here). So you have measured the acceleration.
- Slide 4: Measuring The mass We don’t know mass and we don’t know force. This looks like a circular definition. How are we going to find the mass of anything? We have not measured mass and we have not measured force either.
- Slide 5: One Kilogram Mass is Born Some clever people took a blob of metal of handle-able size kept at Bureau of standard at Paris and declared it as one kilogram. Instead of a arbitrary quantity, they made the blob of metal equivalent to mass of a litre of pure water. This 1 kg mass is nether right or wrong but is just a convention. Now we have one Kg mass, to start an experiment to find the force. (what experiment can you do to find the force?) You should know at all times how you are going to measure anything. If you don't know how to measure anything, you are doing algebra or trigonometry. You are not doing PHYSICS.
- Slide 6: Hook’s Law British physicist Robert Hooke did an experiment to see if Newton’s law was true. Here is how we can experiment:- We can take a spring and we want to know how much force it exerts when it is pulled by a certain amount. Now to measure that force, we can pull it by one centimetre and find the acceleration it exerts on a known mass. That “m” times “a” is the force the spring is exerting. Then we pull it by 1.1 cm, and I find “ma”. We then pull it by 1.2 cm and so on. We then can draw a graph here of the amount by which we pull the spring versus the force it exerts. It will typically look like that shown in the slide and the formula we get is F = -kx, where k is called "the force constant.“ or spring constant. F= -Kx is the Hook’s law. You got to understand what the minus sign is doing here. This is the force exerted by the spring on the mass. It says, if you pull it to the right, x is positive, the spring will exert a force which is in the negative direction; that's why you have a minus sign. I want you to think for a second about two equations. One equation says F = ma. Other equation says F=-kx. If one of them is Newton's law? What's the other one? What's the difference between saying F = -kx and F = ma? Do they are say a different things? (Any one want to try? class to try) F = ma is a universal law. F = -kx is a law only describing how the spring works.
- Slide 6: Hook’s Law British physicist Robert Hooke did an experiment to see if Newton’s law was true. Here is how we can experiment:- We can take a spring and we want to know how much force it exerts when it is pulled by a certain amount. Now to measure that force, we can pull it by one centimetre and find the acceleration it exerts on a known mass. That “m” times “a” is the force the spring is exerting. Then we pull it by 1.1 cm, and I find “ma”. We then pull it by 1.2 cm and so on. We then can draw a graph here of the amount by which we pull the spring versus the force it exerts. It will typically look like that shown in the slide and the formula we get is F = -kx, where k is called "the force constant.“ or spring constant. F= -Kx is the Hook’s law. You got to understand what the minus sign is doing here. This is the force exerted by the spring on the mass. It says, if you pull it to the right, x is positive, the spring will exert a force which is in the negative direction; that's why you have a minus sign. I want you to think for a second about two equations. One equation says F = ma. Other equation says F=-kx. If one of them is Newton's law? What's the other one? What's the difference between saying F = -kx and F = ma? Do they are say a different things? (Any one want to try? class to try) F = ma is a universal law. F = -kx is a law only describing how the spring works.
- Slide 6: Hook’s Law British physicist Robert Hooke did an experiment to see if Newton’s law was true. Here is how we can experiment:- We can take a spring and we want to know how much force it exerts when it is pulled by a certain amount. Now to measure that force, we can pull it by one centimetre and find the acceleration it exerts on a known mass. That “m” times “a” is the force the spring is exerting. Then we pull it by 1.1 cm, and I find “ma”. We then pull it by 1.2 cm and so on. We then can draw a graph here of the amount by which we pull the spring versus the force it exerts. It will typically look like that shown in the slide and the formula we get is F = -kx, where k is called "the force constant.“ or spring constant. F= -Kx is the Hook’s law. You got to understand what the minus sign is doing here. This is the force exerted by the spring on the mass. It says, if you pull it to the right, x is positive, the spring will exert a force which is in the negative direction; that's why you have a minus sign. I want you to think for a second about two equations. One equation says F = ma. Other equation says F=-kx. If one of them is Newton's law? What's the other one? What's the difference between saying F = -kx and F = ma? Do they are say a different things? (Any one want to try? class to try) F = ma is a universal law. F = -kx is a law only describing how the spring works.
- Slide 7: Mass of Anything Ok now you can attach a known mass to a spring, see what is the acceleration it produces. Attach a unknown mass (an elephant , a potato or anything) to the same spring experimented with to know the force. You will know the mass of that object by the acceleration it produces. (remember that a spring will give the same force when extended by a sensible distance and not used too many times like the shock absorbers of the car where it loses its property of exerting the same force over a long period of time.) You got to ensure that the spring exerts the same force every time for your experiment.
- Slide 1: Mass What we know about this fundamental property of nature? What we do not know about this fundamental property of nature? Is the subject of our discussions today.
- Slide 8 and 9 : Another Mass and Another Law Now we will go to the next law Newton gave us in 1687, “ The law of universal gravitation” It Says F = Gm1m2/r2 Here again we have more question than answers. As in laws of motion, what is measurable here? We know mass, we know length (for radius of celestial objects) We do not know “g ” the gravitational constant” and we do not know Force “F ” due to gravitation. Again measurement is essential to establish the equality of the law, before we can plug in the known and find the unknown. How do we check if this law is true? What experiment can we do? Measurements of planets orbits provide a value for the product “G*M” of Sun, Similarly, earthbound satellites and the Moon's orbit provide a value for “G*M” of Earth. To determine a value for G alone requires an a priori knowledge of both masses involved in the gravitational attraction.
- Slide 8 and 9 : Another Mass and Another Law Now we will go to the next law Newton gave us in 1687, “ The law of universal gravitation” It Says F = Gm1m2/r2 Here again we have more question than answers. As in laws of motion, what is measurable here? We know mass, we know length (for radius of celestial objects) We do not know “g ” the gravitational constant” and we do not know Force “F ” due to gravitation. Again measurement is essential to establish the equality of the law, before we can plug in the known and find the unknown. How do we check if this law is true? What experiment can we do? Measurements of planets orbits provide a value for the product “G*M” of Sun, Similarly, earthbound satellites and the Moon's orbit provide a value for “G*M” of Earth. To determine a value for G alone requires an a priori knowledge of both masses involved in the gravitational attraction.
- Slide 8 and 9 : Another Mass and Another Law Now we will go to the next law Newton gave us in 1687, “ The law of universal gravitation” It Says F = Gm1m2/r2 Here again we have more question than answers. As in laws of motion, what is measurable here? We know mass, we know length (for radius of celestial objects) We do not know “g ” the gravitational constant” and we do not know Force “F ” due to gravitation. Again measurement is essential to establish the equality of the law, before we can plug in the known and find the unknown. How do we check if this law is true? What experiment can we do? Measurements of planets orbits provide a value for the product “G*M” of Sun, Similarly, earthbound satellites and the Moon's orbit provide a value for “G*M” of Earth. To determine a value for G alone requires an a priori knowledge of both masses involved in the gravitational attraction.
- Slide 10: Measuring the Value of G In 1798 Henry Cavendish, did an experiment to measure the force of gravity between masses in the laboratory by using an instrument called a "torsion balance,". This consists of a mass distribution suspended by a long thin fibre. Unbalanced forces that act on the precisely weighed suspended masses can rotate the masses (all enclosed within a vacuum vessel). The reflection of a light beam from a mirror attached to the pendulum measures the twist angle. Since a very weak force can twist a long thin fiber, even the tiny torques created by gravitational forces lead to measurable twist angles. We can get some value for “G” by this experiment. The proportionality of the law is still not proved. You repeat the experiment with different weights and if you get the same value for “G” then the proportionality postulated by Newton in the law of Universal Gravitation is proved. Now you are free to plug-in the known values in your astronomical observation and find the unknown. The gravitational constant was measured seventy-one years after Newton's death. Cavendish's aim was not actually to measure the gravitational constant, but rather to measure the Earth's density relative to water, but any way he computed the value of “G ” Cavendish experiment implies a value for G as 6.754 × 10−11 m3 kg−1 s−2. The currently accepted value of G is 6.674280.00067 x 10-11 N-m2/kg2 by more advanced experiments.
- Slide 11: Mass of Earth Now you are in a position to find the mass of earth, by shooting an object in stable circular orbit, you have all the values except the mass of earth and you compute it as follows. GM1xM2/r2 = M2V2/r .i.e. equating Gravitational Force and Centripetal Force. Alternately, dividing GMEarth found from observing lunar orbits by the laboratory value for G allows us to deduce the mass of the Earth: 5.98 X 1024kilograms. What else can we do with the law of universal gravitation. We can find the escape velocity of an object. How? For this equate the Gravitational Potential Energy to the Kinetic Energy of the object in orbit. Since Force times Distance (.i.e. how far the force has been acting) is energy, and rate of change of energy is force. To know the gravitational energy you need to guess if the derivative of energy (u) that is if - du/dr is –gMm/r2 then what is “u”. Since we know derivative of –i/x is –i/x2 . Therefore the gravitational Potential energy is –gMm/r. Equating this to the Kinetic energy ½ mv2 We get v 2 = 2gM/r .i.e. is the escape velocity. So we are able put the law of universal gravitation to some use in prediction of celestial bodies and manmade objects. I am done with the concept of mass in Newton’s second law and Newton’s law of Universal gravitation to the extent what you will be taught and learn in school and college. Since I am here to teach and understand mass in its completeness, Let us get further.
- Slide 13 to 15: Mystery of Two Masses Inertial mass (in Newton’s law of Motion) measures an object's resistance to being accelerated by a force. Active Gravitational mass measures the gravitational force exerted by an object. Passive Gravitational mass (another of the “m” in Newton’s Law of Universal Gravitation) measures the gravitational force experienced by an object in a known gravitational field. We take it for granted that both the masses are equivalent. Although Inertial mass and Gravitational masses are conceptually distinct, no experiment has demonstrated any difference between them. Newton's third law implies that gravitational mass and inertial mass are identical, but offers us no reason. Newton realised that both the masses are equivalent till second decimal with his own experiment. Both the masses are proved to be equivalent till the fifth decimal by the early 2000. Now, we know that, both the masses are equivalent till 12th decimal with most advanced experiment. But WHY? are the values of these two disparate properties of masses same? It is like realising that the atmospheric pressures of earth and a planet on the other end of our galaxy is same. The values of the pressures can be nearly same, but you measure the values till the nth decimal and you see it as equivalent, you realise the equality is not just a coincidence but due to some underlying principle connecting the two parts of the universe. Is there an underlying relation between the two masses? We do not know. I am not elaborating on the other masses namely “Rest mass” which measures the total amount of energy contained within a body, using E=mc² “Relativistic Mass” and “Quantum Mass”
- Slide 12: Mystery of Many masses I am done with what we know about the mass. Now on I am going discuss what we do not know about the mass. So, right now only I am ignorant about some aspects of the mass; at the end of the lecture we all will be ignorant. The pressure is off you, relax and listen further. Out of the many confusion about the masses I will deliberate on the confusion arising out of the masses we have discussed so far .i.e. Inertial and Gravitational masses.
- Slide 16: A Glance at Particle Physics A cursory look at standard model of particle physics is necessary to take the discussion on the mass further.
- Slide 17: More Adventure With MASS What is our Universe made of? It is Hadrons and Leptons ‘Hadrons’ forms matter and ‘Leptons’ forms the force carriers. There are four forces in nature, Strong Nuclear Force, Weak Nuclear Force, Electromagnetic Force Gravitational Force. Force carriers are: Gluons for strong nuclear force, “Z” and “W” bosons for weak nuclear force, Photons for electromagnetic force, Gravitons ? for Gravitational Force. Except Gravitons other force carriers are known and proved conclusively by experiments. The Standard Model of Particle physics is incomplete due to incomplete understanding about the property called Mass and the Force it generates called Gravitational Force at the fundamental level.