Question for Blogmaster


Dear David,

If a person weighs 80kg-f, what is his mass? I want this for my new novel. I’d like someone with a science/maths background to take me through the answer, as I have always been rather hazy about the relationship between mass and weight.

Of course, my manner of asking this question makes it one not merely for David, but for the whole world.

Sean

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14 responses to “Question for Blogmaster

  1. Mass and Weight

    The mass of an object is a fundamental property of the object; a numerical measure of its inertia; a fundamental measure of the amount of matter in the object. Definitions of mass often seem circular because it is such a fundamental quantity that it is hard to define in terms of something else. All mechanical quantities can be defined in terms of mass, length, and time. The usual symbol for mass is m and its SI unit is the kilogram. While the mass is normally considered to be an unchanging property of an object, at speeds approaching the speed of light one must consider the increase in the relativistic mass.

    The weight of an object is the force of gravity on the object and may be defined as the mass times the acceleration of gravity, w = mg. Since the weight is a force, its SI unit is the newton. Density is mass/volume.

  2. Weight or Mass?

    Q: Aren’t “weight” and “mass” the same?

    A: Not really.

    An object has mass (say 100 kg).

    This makes it heavy enough to weigh 100 kg
    Gravity causes Weight
    gravity

    An objects weight is how hard gravity is pulling on it.

    We think the weight is the same everywhere … because we all live on the surface of the planet Earth!

    But if the object were far out in space it would just float around, exerting no force on the scales.

    The scales would show 0 kg … but the mass is still 100 kg !
    freefall weight is zero

    An object’s mass doesn’t change (unless you remove some!), but its weight can change.

    So Why Do People Say Weight instead of Mass?

    People often use “weight” to mean “mass”, and vice versa.

    Because gravity is pretty much the same everywhere on Earth, we don’t notice a difference.

    But remember .. they do not mean the same thing,
    and they can have different measurements.

    Here are some conditions where the Weight might change:

    in space (can be weightless!)
    on the moon (a 100 kg mass would weigh 16.6 kg)
    you can even get very slight differences in weight in different locations on earth!

    Weight is a Force

    So … if weight and mass are different, why are they both in kilograms?

    Well, weight should not really be in kilograms!

    I have used “kilogram” so far because that is what you would see on a pair of scales, but it is technically wrong to talk about weight in kilograms …

    … so sometimes people say “kilogram force” (kgf) or “pound force” (lbf) to show that they are talking about the force that the mass exerts because gravity is pulling down on it.

    But there is a better measurement … Newtons
    Newtons

    The correct unit for force is the Newton (=1 kg·m/s2) which is abbreviated N.
    down Gravity makes a 1 kilogram mass exert about 9.8 Newtons of force

    So a 100kg mass really weighs about 980 Newtons.
    scales in newtons
    Why Scales Show Kilograms or Pounds

    But scales show Kilograms or Pounds because that is what people understand best …

    … but it is really just an estimate of the mass above them.

    Scales should really show Newtons, but that might confuse people!

    Question: how many Newtons should the scales show when you stand on them (hint: multiply kg by 9.8)?

    So the scales show an estimate of your mass based on the force your body exerts on it.
    And to find out how much force your body is exerting on the scales, multiply by 9.8 (to convert kg into Newtons).

    Apparent Weight

    But Scales can be fooled … because they measure a “downwards force” and don’t know if it is gravity or some other force!

    Just jump up and down (gently!) on your scales at home to see your apparent weight change, while your mass stays the same.

    So your mass is the same, and your weight is the same (because the force of gravity hasn’t changed), but your “apparent” weight changes. Read more at Apparent Weight
    Conclusion

    Mass is a measure of how much matter something contains
    Weight is a measure of how strongly gravity pulls downwards
    Apparent Weight is a measure of downwards force
    Force is measured in Newtons, not kilograms or pounds
    When scales show “kg” or “lb” it is just an estimate of the mass above them

  3. Yes, but if an object weighs 80kg on this planet, what is its mass, expressed in the units of your choice?

  4. Sean

    The answer is that the object’s mass is 80kg.
    Such an object’s weight on Earth would be 784.560 Newtons

    Kilograms are a measure of mass, not weight and an object’s mass is fundamental and unaltered by gravity. Newtons are the correct measure of weight. Weight is the gravitational force acting on a mass.

    The relevant equation is a derivation of Newton’s Second Law:

    F = MA
    or
    force = mass * acceleration
    or
    weight = mass * acceleration of gravity
    or
    w = mg

    In your example:
    w = 80kg * 9.807m/s^2
    = 784.560N

    Charles

  5. Thanks for that. However, I’ve decided to make the closing apocalypse in my novel a function of volume not of mass.

  6. Peter and Charles are of course correct for the general case. I might have a mass of 180lbs, and weigh 180lbs on Earth. On the moon, I’d weigh around 30lbs (me diet? why ever!), since the force of gravity there is about 1/6 that of Earth. Simply put, mass can be thought of as either the amount of matter in an object, or a measure of the object’s resistance to having its velocity changed by the application of a force. Weight, on the other hand, is usually thought of as the force exerted on an object via the influence of gravity, and we’ve convenienced ourselves by normalizing 1kg (mass) = 1kg (weight on Earth [at mean sea level or something like that]). (We also tend to ignore the “weight” of the Earth in this case, since although even people exert a gravitational influence upon the earth, its magnitude is infinitesimal compared to that which the Earth exerts on the person.)

    However, gravity is an accelerative force, and any acceleration — not only gravity — imparts weight to objects with mass. If I, with my 180lbs of mass, were to board a rocket ship which then began accelerating at 98 m/s^2 (roughly 10 times g, earth gravity), I would feel an apparent weight of 1,800lbs, an unpleasant experience to be sure.

    Things get even more interesting in Einstein’s special relativity. In one formalism (which I understand is now somewhat in disfavor), the mass of an object, as its velocity approaches (but never reaches) that of light, can be said to increase toward infinity. Put a different way, the incremental amount of energy needed to achieve each increment in velocity becomes infinite, and thus the speed of light can never been reached by an object with mass.

  7. Well, I suppose that’s all the answer I could ever need. I’ve decided to do volume now instead of mass.

  8. Anirudh Kumar Satsangi

    This has long been proved since the time of discovery of black holes that the speed of light is not the fastest. Black holes do not allow even light to escape. It means the escape velocity at the black holes is much higher than the speed of light. Black holes are the infinitely dense ball of gravitation force. All creational forces of the universe have originated from the gravitational force field and will end up in it. The speed of light is no doubt fastest in our solar system. The source of light is Sun in our solar system. But how this light is originated? We should study the various stages involved in the formation of a star. Our Sun is also a star.

    The starting material for the formation of a star is mainly hydrogen gas and helium gas. If the hydrogen cloud contains a very large number of atoms, each atom feels the gravitational pull of all the atoms in the hydrogen cloud. (Here is NO LIGHT)

    The gas cloud becomes a permanent entity, held together by the mutual attraction of all the atoms present in it. The cloud then begins to contract under its own gravity setting off the process which will convert this huge condensed gas cloud into a star. Such a tight contracting cluster of atoms held in the grip of its own gravity, is called a protostar. The protostar is not yet a star and does NOT emit LIGHT. The temperature of this star is as low as -173 degree C.

    The force of gravity acting on different atoms in the protostar draws every atom towards centre. As a result, the protostar shrinks in size and its density increases. As the atoms in the protostar fall towards the centre, they pick up speed. Because of the high speed and greater density of atoms, the atoms in the gas cloud collide with one another more frequently, thereby raising its temperature from -173 degree C to about 10 ^7 degree C. At these extremely high temperatures the proton (hydrogen nuclei) at the centre of the protostar collide together and undergo a nuclear fusion to form helium nuclei. In this reaction a tremendous amount of energy is released. This further raises the temperature and pressure. The release of nuclear energy marks the birth of the star. The protostar now beings to GLOW and becomes a STAR. Here at this stage LIGHT is ORIGINATED. Thus light is NOT ETERNAL. It has a beginning and an end. So LIGHT cannot be claimed as Cosmic Constant. However, Gravitation Force is eternal.

    It is evident from the above description that light is latent before the birth of star. Light originates and become kinetic only after the action of gravitation force. So the speed of light can never exceed the speed of gravitation force. It cannot be ruled out that the speed of gravitation force is infinitely greater than the speed of light at black holes.
    1. Gravitation Force is the Ultimate Creator
    2. In Scientific Terminology Source of Gravitational Wave is God

    • Anirudh, you’ve got a strange understanding of of physics, easily remedied by carefully reading elementary texts.

      For example, there’s no such thing as the “speed” of the gravitational force. It has a magnitude, which produces an acceleration. A wee bit of differential calculus will show why this distinction is critical.

      Also, consider an LED. There’s no “latent light” phenomenon going on there, nor is there stellar nuclear fusion, yet the LED emits light. It does so by virtue of electrical current passing through certain types of materials. The phenomenon is called electroluminescence (http://en.wikipedia.org/wiki/Electroluminescence).

      As for the rest of your claims, if you’d like to find God there, go ahead. Before doing so, though, you might devote a bit of energy to the study of His rules.

  9. Sorry I didn’t get to this in time Sean. Seems like the others have sorted you out!

  10. Well, am I right in concluding that, when it weighs 80kg on this planet, an object may be said to have 80kg of mass?

  11. That’s exactly right Sean. “Weight” only comes into the thinking when you try to lift the thing here, or on different planets or other places. On Jupiter, you’d need to use 3-4 times a much effort. On the sirface of the Sun, if you could get there, about 36 times the effort. On the moon, only about one sixth of what you’d have to do here, but in all the places it is still 80 kg.

  12. Thanks. I don’t wish in any way to denigrate the very interesting reams of hard sums that people have taken the trouble to explain to me. But that really was all I wanted!!!