Relationship between material mass and weight

[The apprentice]

Homework Statement

Newton's second law

Relevant Equations

w=mg

What does it mean that the relationship between material mass and weight is constant and proportional?​

Hi! Yes, another question... I have many doubts. :)
I hope someone can help me with this apparently very basic doubt, but I feel like a stupid monkey trying to join two sticks to reach bananas and without success. My English is not good, I am Mexican and I am still learning it.

I am very new to the world of science, and I have started from the basics. With popular books like "Cosmos" and "History of Time", etc. But I really want to get into this and I started with arithmetic. I have started reading a book on arithmetic, and I found this definition:
Weight

It is not possible to determine directly the amount of matter contained in a body; but it is known that the greater its material mass, the greater the attraction that gravity exerts on it, that is, the greater its weight. This relation between material mass and weight is constant and proportional.

Observing the bodies that appear in Nature and mentally separating all their other qualities, to focus only on the attraction that gravity exerts on them, we arrive at the concept of weight. Because of the constant relation that exists between the material mass of a body and its weight, to the point of being expressed with the same number, we will dispense in this work of speaking in a systematic way about the material mass of bodies, to refer only to their weight. But keep in mind that the concepts of material mass and weight are different.

I tried to understand it, and I started to investigate. I skipped ahead several chapters to see the definition of ratio -also relationship, right?-, and I understand that it is a comparison of quantities to know how much one exceeds the other (arithmetic ratio), and how much one contains the other (geometric ratio), and I wondered then how that fits here. Then I had to dig into other books (very advanced in my current state) like an Algebra book where I found the topic Constants and Variables in which there was something called Direct Variation and a definition that goes as follows.

A is said to vary directly to B or A is directly proportional
to B when multiplying or dividing one of these two variables by a quantity, the other is multiplied or divided by that same quantity. If AA is proportional to BB***,*** AA is equal to BB multiplied by a constant. In general, if AA is proportional to BB*, the relation between* AA and BB is constant; then, designating this constant by kk*, we have* AB=kAB=k and then A=kBA=kB this is quite similar to a=Fma=Fm and to w=mgw=mg

I don't want to write so much so as not to bore you. But the point is that I had to jump to something more advanced, because I also had to go dig into Newton's second law, trying to make sense of it. I found something, but I didn't really understand it, I tried to relate it to what I mentioned before and I thought I understood, but when I kept looking I found more about it

One of the important aspects of physics is the search for relationships between different quantities—that is, determining how one quantity affects another.
So if the relationships are comparisons of quantities as I mentioned before, how does it make sense to say that one quantity affects another? Does this have to do with kilogram-force? Is the relationship between weight and mass constant and proportional because it says so w=mgw=mg? Should I be concerned about understanding this well now, or just settle for an approximation so I don't get confused? Because I just started getting into this.

It's clear that I don't know algebra yet, and also that I'm very confused and I feel stuck on this and I can't learn algebra yet enough to understand it in depth, I think. So I guess there must be something I need to know for now, so I can move forward and then understand in depth this subject.

I really hope someone can help me, I will be very grateful. :)

 

[Stephen Tashi]

Newton's 2nd law is more general that W = mg. The W = mg equation is one particular example of F = ma.

Imagine accelerating a hockey puck horizontally over a lake of ice. You must make some effort to do this regardless of whether you are on Earth or on a planet whose gravitational force is less than that of Earth. So, in a manner of speaking, the mass m of the hockey puck is a measure of how much the puck resists being accelerated. The concept of mass is not the same as the concept of a force. By contrast, weight can be interpreted as a force.

W = mg is an application of F = ma to the case where we have a device that can measure the downward force W on the hockey puck - e.g. we have a scale that can weigh it. If the hockey puck is held above the ice and dropped, the mass m of the hockey puck limits the acceleration it will have. Near the surface of the Earth we make the approximation that W is constant. So we approximate the acceleration of the puck as a constant value g.

 

[PeroK]

Homework Statement:: Newton's second law
Relevant Equations:: w=mg

What does it mean that the relationship between material mass and weight is constant and proportional?​

Hi! Yes, another question... I have many doubts. :)
I hope someone can help me with this apparently very basic doubt, but I feel like a stupid monkey trying to join two sticks to reach bananas and without success. My English is not good, I am Mexican and I am still learning it.
I am very new to the world of science, and I have started from the basics. With popular books like "Cosmos" and "History of Time", etc. But I really want to get into this and I started with arithmetic. I have started reading a book on arithmetic, and I found this definition:
Weight
It is not possible to determine directly the amount of matter contained in a body; but it is known that the greater its material mass, the greater the attraction that gravity exerts on it, that is, the greater its weight. This relation between material mass and weight is constant and proportional.
Observing the bodies that appear in Nature and mentally separating all their other qualities, to focus only on the attraction that gravity exerts on them, we arrive at the concept of weight. Because of the constant relation that exists between the material mass of a body and its weight, to the point of being expressed with the same number, we will dispense in this work of speaking in a systematic way about the material mass of bodies, to refer only to their weight. But keep in mind that the concepts of material mass and weight are different.
I tried to understand it, and I started to investigate. I skipped ahead several chapters to see the definition of ratio -also relationship, right?-, and I understand that it is a comparison of quantities to know how much one exceeds the other (arithmetic ratio), and how much one contains the other (geometric ratio), and I wondered then how that fits here. Then I had to dig into other books (very advanced in my current state) like an Algebra book where I found the topic Constants and Variables in which there was something called Direct Variation and a definition that goes as follows.
A is said to vary directly to B or A is directly proportional to B when multiplying or dividing one of these two variables by a quantity, the other is multiplied or divided by that same quantity. If AA is proportional to BB***,*** AA is equal to BB multiplied by a constant. In general, if AA is proportional to BB*, the relation between* AA and BB is constant; then, designating this constant by kk*, we have* AB=kAB=k and then A=kBA=kB this is quite similar to a=Fma=Fm and to w=mgw=mg
I don't want to write so much so as not to bore you. But the point is that I had to jump to something more advanced, because I also had to go dig into Newton's second law, trying to make sense of it. I found something, but I didn't really understand it, I tried to relate it to what I mentioned before and I thought I understood, but when I kept looking I found more about it
One of the important aspects of physics is the search for relationships between different quantities—that is, determining how one quantity affects another.
So if the relationships are comparisons of quantities as I mentioned before, how does it make sense to say that one quantity affects another? Does this have to do with kilogram-force? Is the relationship between weight and mass constant and proportional because it says so w=mgw=mg? Should I be concerned about understanding this well now, or just settle for an approximation so I don't get confused? Because I just started getting into this.
It's clear that I don't know algebra yet, and also that I'm very confused and I feel stuck on this and I can't learn algebra yet enough to understand it in depth, I think. So I guess there must be something I need to know for now, so I can move forward and then understand in depth this subject.
I really hope someone can help me, I will be very grateful. :)

One of the fundamental quantities in physics is mass, which is a measure of the amount of matter. The other two are length and time. Other quantities, such as force and energy, are combinations of mass, length and time.

The next important concept is that of force, which is something that accelerates a mass. Force, mass and acceleration are related, as explained above, by Newton's Second Law of motion: $$F = ma$$
One of the basic forces of nature is gravity. Near the surface of the Earth the gravitational force on every object is proportional to its mass and this leads to the same acceleration for all objects, which is denoted by $g$ and is equal to approximately $9.8m/s^2$.

A object's weight is simply the gravitational force on an object: $$W = mg$$

To get an object's weight, you simply multiply its mass by the constant gravitational acceleration $g$. Or, vice versa, to calculate an object's mass, you divide its weight (e.g. the force it exerts on a set of scales or other device for weighing an object) by $g$: $$m = \frac W g$$.

 

[Bandersnatch]

So if the relationships are comparisons of quantities as I mentioned before, how does it make sense to say that one quantity affects another?

It's the same thing. Let's say we compare two quantities, A and B. We find out that B is always twice a large as A. So there's some relationship between them; changing one always changes the other - they're not independent.
For example, let's say we have crowds of able-bodied people. We count the legs (L) and we count the heads (H). When we compare these two quantities, we find that there's always twice as many legs as there are heads. We can write L=2H. The number of heads affects the number of legs, in the sense that adding another head to the crowd necessarily involves adding two legs. The number 2 is the constant of proportionality that relates these two quantities.
Another example can be the radius of a circle, r and its diameter, d. When we compare these two, we notice that d is always twice the r, no matter what circle we pick. We can write d=2r. We can imagine increasing the radius to make a new circle, and the equation tells us that it'll affect the diameter to be twice as large as the new radius.
With W=mg you have the same thing, only the constant is different than 2.

 

[The apprentice]

Homework Statement:: Newton's second law
Relevant Equations:: w=mg

What does it mean that the relationship between material mass and weight is constant and proportional?​

Hi! Yes, another question... I have many doubts. :)
I hope someone can help me with this apparently very basic doubt, but I feel like a stupid monkey trying to join two sticks to reach bananas and without success. My English is not good, I am Mexican and I am still learning it.

I am very new to the world of science, and I have started from the basics. With popular books like "Cosmos" and "History of Time", etc. But I really want to get into this and I started with arithmetic. I have started reading a book on arithmetic, and I found this definition:
Weight

It is not possible to determine directly the amount of matter contained in a body; but it is known that the greater its material mass, the greater the attraction that gravity exerts on it, that is, the greater its weight. This relation between material mass and weight is constant and proportional.

Observing the bodies that appear in Nature and mentally separating all their other qualities, to focus only on the attraction that gravity exerts on them, we arrive at the concept of weight. Because of the constant relation that exists between the material mass of a body and its weight, to the point of being expressed with the same number, we will dispense in this work of speaking in a systematic way about the material mass of bodies, to refer only to their weight. But keep in mind that the concepts of material mass and weight are different.

I tried to understand it, and I started to investigate. I skipped ahead several chapters to see the definition of ratio -also relationship, right?-, and I understand that it is a comparison of quantities to know how much one exceeds the other (arithmetic ratio), and how much one contains the other (geometric ratio), and I wondered then how that fits here. Then I had to dig into other books (very advanced in my current state) like an Algebra book where I found the topic Constants and Variables in which there was something called Direct Variation and a definition that goes as follows.

A is said to vary directly to B or A is directly proportional
to B when multiplying or dividing one of these two variables by a quantity, the other is multiplied or divided by that same quantity. If AA is proportional to BB***,*** AA is equal to BB multiplied by a constant. In general, if AA is proportional to BB*, the relation between* AA and BB is constant; then, designating this constant by kk*, we have* AB=kAB=k and then A=kBA=kB this is quite similar to a=Fma=Fm and to w=mgw=mg

I don't want to write so much so as not to bore you. But the point is that I had to jump to something more advanced, because I also had to go dig into Newton's second law, trying to make sense of it. I found something, but I didn't really understand it, I tried to relate it to what I mentioned before and I thought I understood, but when I kept looking I found more about it

One of the important aspects of physics is the search for relationships between different quantities—that is, determining how one quantity affects another.
So if the relationships are comparisons of quantities as I mentioned before, how does it make sense to say that one quantity affects another? Does this have to do with kilogram-force? Is the relationship between weight and mass constant and proportional because it says so w=mgw=mg? Should I be concerned about understanding this well now, or just settle for an approximation so I don't get confused? Because I just started getting into this.

It's clear that I don't know algebra yet, and also that I'm very confused and I feel stuck on this and I can't learn algebra yet enough to understand it in depth, I think. So I guess there must be something I need to know for now, so I can move forward and then understand in depth this subject.

I really hope someone can help me, I will be very grateful. :)

Thank you all so much for responding. I'm sorry for taking so long to respond, and being kind of a dummy because it still wasn't clear to me, and I feel like I'm missing more information and need to go back to even more basic things. I am very confused by the use of the word "relationship". I don't know if they use it to refer to these relationships as in my post, or as it is used everyday, among other doubts like where does 9.81 come from? Who calculated irt? How did they know which structure to use for F=ma? How did they determine 9.81? Sorry, I will try to do more research to someday understand this. I have been trying to understand for months because I have very little time for this, and honestly I don't know if I will ever be able to do it... Thank you, really.

 

[jbriggs444]

where does 9.81 come from?

Force is how hard you are pushing on something. Acceleration is how fast a thing changes its velocity as a result [if no other forces interfere].

The more mass an object has, the more force it takes to give it a particular acceleration. If you have two bricks, it takes twice as much force to give them the same acceleration as it takes for one brick.

We have standardized on a unit of mass -- the kilogram. We have standardized on a unit of acceleration -- a change in velocity of one meter per second every second.

We use these two standards to define a standard unit of force -- the Newton. One Newton is the force it takes to accelerate a one kilogram mass at a rate of one meter per second per second.

1. If you want to support a one kilogram mass against the downward force of gravity, it takes approximately 9.81 Newtons of force to do so.

2. If you stop providing that force, the mass will fall with an acceleration of 9.81 meters per second per second.

We can say that the "acceleration of gravity" is 9.81 meters per second per second.

This 9.81 is an average over the surface of the Earth. There is some slight variation (about 0.5%) between places where [apparent] gravity is exceptionally strong (deep valleys close to the north or south poles) and places where it is exceptionally weak (high mountains close to the equator).

https://en.wikipedia.org/wiki/Gravity_of_Earth