Article status: Draft
Time Estimate for Reading: 20 min
Learning Objectives: Difference between mass, weight and force
Effort Required: Medium
Pedagogy Model: Evolution, Formula Analysis
Prior Physics Concepts: displacement, velocity, acceleration, mass, power, force
Prior Math Tools: Secondary school level Arithmetic, geometry and algebra
Space, Time and Mass. The three fundamental concepts on which the whole of science is built. rather that is how we try to understand nature.
We have discussed on space in the article "Euclid has Point". We are yet to discuss on time. The focus of this article is mass.
Mass, Weight and Force. This a cause of confusion for most beginners of science. And there have been many efforts from different perspectives to give a clear understanding of this. This is one such effort from yet another perspective (after all each one learns from a different perspective).
By definition, weight is perceived gravity and force is a general term referring to the product of mass * acceleration. mass has multiple definitions and are summarized at the end of this article.
Similar to mass and weight, for beginners in electricity, the direction of conventional current, electromotive force (which is not a force. we should not even say work. we should say it is potential difference) etc are some pitfalls to watch out for.
This is one of the simplest examples i could come across to understand the difference between mass and weight. or rather to define weight.
Let us begin with mass. The textbook definition says "amount of matter". What is the matter with that definition?
From our experience, if someone asks us to buy, say "salt", we will ask how many grams or kilograms. depending on the shop, assuming we were living in the days of Galileo, it may be measured with a simple balance or a spring balance. The digital scales are yet to arrive.
The word 'mass' is yet to have a clear definition. The term heaviness and weight were used for comparing quantities. So, we could say the weight or heaviness of salt is 1 kg.
We are also aware of the fact from Galileo's experiments that every object on the surface of earth has the same acceleration; independent of their heaviness.
Newton with his experiments and observation finds that gravitational acceleration is different on earth and moon. If we carry the same quantity of salt to moon and weigh it with spring balance, it will show a different value as the gravitational acceleration of moon is different.
This is not an acceptable situation. Say, for example we weigh gold with a spring balance and carry it to a place which is much higher in altitude, it would show a different value. With increase in altitude, the gravitational acceleration would decrease. you may refer to the graph on this page for variation of gravitational acceleration with altitude. Notice here that the simple balance is a comparison device and can be used to measure weight independent of altitude.
This issue was put to rest by newton. He introduced the concept of force which is equal to mass * acceleration. f= ma.
At this point, for a detailed discussion on f=ma, you may refer to the article http://openneuron.blogspot.in/2016/03/acceleration-bridge-between-space-time.html
On earth, f = m * 9.81 m/s^2.
What if we define the unit of force as 1 Newton which is equal to 1 kg mass * 1 m/s^2. That is 1 Newton of Force.
So, going back to our salt example which we measured with spring balance, it will contain the acceleration component of 9.81 m/s^2.
Try converting this weight into Newtons. We have to multiply 1kg by 9.81m/s^2
which is = 9.81 Newtons.
Now we can say that mass of the object = 1 kg and Weight (or force) of the object is 9.81 Newtons.
This brings us to another question. Is weight and force the same?
No. Weight has been given an new definition. Weight is defined as perceived gravity. What does that mean?
This is where we take help from E M rogers toy. Alternative example is of measuring our weight in a lift.
When the toy is at rest, the weight of the ball (mg) and force exerted by the spring (kx), balance each other. But, when we allow the toy to fall down, the force exerted by the spring will remain the same, but weight of the ball will reduce and the ball will be pulled by the spring to the top. The component of 'g' will have a lesser value and hence the weight becomes lesser. So, we can say that weight of an object changes with accelerated (or decelerated) motion and hence the definition "perceived gravity ".
We have discussed about weight and understood the concept of perceived gravity with the simple toy.
Now, discussing about force, force is a general term. it may be applied to gravitation force, electric force, magnetic force etc. Weight is similar to force but used only in the context of gravitational force.
Having settled the matter with weight, force and mass, the story does not end here.
Almost all practical applications use weight for calculations. So, what is the need for mass? Every object we take for analysis has a gravitational force acting on it which forces us to take ‘weight’ for analysis. So, is mass just a theory?
Imagine in next 100 years, we colonize few galaxies (am I being too optimistic?). You weigh something here and transport them to some planet in Andromeda. Obviously, the gravitational acceleration there would be different which depends on the mass of the planet (Newtons law of gravitation G*(m1*m2) / r^2). That’s a different story. You export gold and they decide not to pay what you ask for, since it weighs way less than in earth. Chaos!
This would force us a generalized term for measurement. Generalization is possible only if we could remove the variable. In this case, acceleration due to gravity. Remove that ‘g’ from weight and we are left with mass.
In order to make life more interesting, Mass has different names or definitions.
mass: density/volume (we would discuss this in fluids)
Gravitational mass: m * g
Inertial Mass: m * a (linear motion): m=f/a.
Inertial Mass: mr^2 * alpha (rotational motion). Here inertial mass is mr^2 and not just m.
Amount of matter: Given a mass m, we can find the number of atoms or molecules present. Avogadro number is the link.
Mass = moles * Atomic Mass Unit (1 mole of a substance will weigh AMU gms)
As much as 1 dozen is 12, 1 mole represents a number which is 6.023 * 10^23
So from our example, we may ask the question, how many molecules of NaCl are present in 1 kg mass of salt.
From the periodic table, we find that the molecular mass of NaCl is 22.989 + 35.453 grams.
These many grams will contain 1 mole or 6.023 * 10^23. From this we can find out the amount of matter or number of molecules contained in 1 kg mass of salt.
Relativistic Mass: The change is mass at higher velocities
The story of mass has is yet to see its end. It seems to make a beginning. Einstein comes in and says that mass and energy are convertible and related by the most famous equation E = mc^2. The Mass energy equivalence.
Time Estimate for Reading: 20 min
Learning Objectives: Difference between mass, weight and force
Effort Required: Medium
Pedagogy Model: Evolution, Formula Analysis
Prior Physics Concepts: displacement, velocity, acceleration, mass, power, force
Prior Math Tools: Secondary school level Arithmetic, geometry and algebra
Space, Time and Mass. The three fundamental concepts on which the whole of science is built. rather that is how we try to understand nature.
We have discussed on space in the article "Euclid has Point". We are yet to discuss on time. The focus of this article is mass.
Mass, Weight and Force. This a cause of confusion for most beginners of science. And there have been many efforts from different perspectives to give a clear understanding of this. This is one such effort from yet another perspective (after all each one learns from a different perspective).
By definition, weight is perceived gravity and force is a general term referring to the product of mass * acceleration. mass has multiple definitions and are summarized at the end of this article.
Similar to mass and weight, for beginners in electricity, the direction of conventional current, electromotive force (which is not a force. we should not even say work. we should say it is potential difference) etc are some pitfalls to watch out for.
This is one of the simplest examples i could come across to understand the difference between mass and weight. or rather to define weight.
By now, you should have got it. if not, continue reading.
Let us begin with mass. The textbook definition says "amount of matter". What is the matter with that definition?
The word 'mass' is yet to have a clear definition. The term heaviness and weight were used for comparing quantities. So, we could say the weight or heaviness of salt is 1 kg.
We are also aware of the fact from Galileo's experiments that every object on the surface of earth has the same acceleration; independent of their heaviness.
Newton with his experiments and observation finds that gravitational acceleration is different on earth and moon. If we carry the same quantity of salt to moon and weigh it with spring balance, it will show a different value as the gravitational acceleration of moon is different.
This issue was put to rest by newton. He introduced the concept of force which is equal to mass * acceleration. f= ma.
At this point, for a detailed discussion on f=ma, you may refer to the article http://openneuron.blogspot.in/2016/03/acceleration-bridge-between-space-time.html
On earth, f = m * 9.81 m/s^2.
What if we define the unit of force as 1 Newton which is equal to 1 kg mass * 1 m/s^2. That is 1 Newton of Force.
So, going back to our salt example which we measured with spring balance, it will contain the acceleration component of 9.81 m/s^2.
Try converting this weight into Newtons. We have to multiply 1kg by 9.81m/s^2
which is = 9.81 Newtons.
Now we can say that mass of the object = 1 kg and Weight (or force) of the object is 9.81 Newtons.
This brings us to another question. Is weight and force the same?
No. Weight has been given an new definition. Weight is defined as perceived gravity. What does that mean?
This is where we take help from E M rogers toy. Alternative example is of measuring our weight in a lift.
When the toy is at rest, the weight of the ball (mg) and force exerted by the spring (kx), balance each other. But, when we allow the toy to fall down, the force exerted by the spring will remain the same, but weight of the ball will reduce and the ball will be pulled by the spring to the top. The component of 'g' will have a lesser value and hence the weight becomes lesser. So, we can say that weight of an object changes with accelerated (or decelerated) motion and hence the definition "perceived gravity ".
We have discussed about weight and understood the concept of perceived gravity with the simple toy.
Now, discussing about force, force is a general term. it may be applied to gravitation force, electric force, magnetic force etc. Weight is similar to force but used only in the context of gravitational force.
Having settled the matter with weight, force and mass, the story does not end here.
Almost all practical applications use weight for calculations. So, what is the need for mass? Every object we take for analysis has a gravitational force acting on it which forces us to take ‘weight’ for analysis. So, is mass just a theory?
Imagine in next 100 years, we colonize few galaxies (am I being too optimistic?). You weigh something here and transport them to some planet in Andromeda. Obviously, the gravitational acceleration there would be different which depends on the mass of the planet (Newtons law of gravitation G*(m1*m2) / r^2). That’s a different story. You export gold and they decide not to pay what you ask for, since it weighs way less than in earth. Chaos!
This would force us a generalized term for measurement. Generalization is possible only if we could remove the variable. In this case, acceleration due to gravity. Remove that ‘g’ from weight and we are left with mass.
mass: density/volume (we would discuss this in fluids)
Gravitational mass: m * g
Inertial Mass: m * a (linear motion): m=f/a.
Inertial Mass: mr^2 * alpha (rotational motion). Here inertial mass is mr^2 and not just m.
Amount of matter: Given a mass m, we can find the number of atoms or molecules present. Avogadro number is the link.
Mass = moles * Atomic Mass Unit (1 mole of a substance will weigh AMU gms)
As much as 1 dozen is 12, 1 mole represents a number which is 6.023 * 10^23
So from our example, we may ask the question, how many molecules of NaCl are present in 1 kg mass of salt.
From the periodic table, we find that the molecular mass of NaCl is 22.989 + 35.453 grams.
These many grams will contain 1 mole or 6.023 * 10^23. From this we can find out the amount of matter or number of molecules contained in 1 kg mass of salt.
Relativistic Mass: The change is mass at higher velocitiesThe story of mass has is yet to see its end. It seems to make a beginning. Einstein comes in and says that mass and energy are convertible and related by the most famous equation E = mc^2. The Mass energy equivalence.
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