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Thread: Are my friends wrong?

  1. #1 Are my friends wrong? 
    Forum Freshman asxz's Avatar
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    Okay, so I was away on a sports tournament, and because everyone knows I'm good at science one team mate asked me a question she had for homework. It was the one where two people jump off a diving board at the same time and land in the water at the same time because of the laws of forces, gravitation, and F=MA.

    I said that they would land at the same time because Force = Mass x Acceleration. That means that, because because we are trying to find out the Accleration of the people to see who goes faster, we use the equation: Acceleration = Force over Mass.
    All right so far?
    Then I said that, because the body mass would be relatively the same [mass, not weight. If it were mass, then we would be close enough, wouldn't we? Give or take a few muscle vs. fat issues] and therefore, they would land at the same time because the Mass and Gravity [force] would be the same, and that means they have the same acceleration, therefore speed and timing.

    So that was my theory.

    Then they said that:
    The mass wouldn't be the same, because Mass is measured in Kg's. I said that they were wrong, because Kg's was a measure of weight, and they rebuted with the 'fact' that weight was actually measured in Newtons.
    I get that, because Mass stays the same, and weight changes due to the forces that act upon it.
    But the person didn't get that I was agreeing with them, and they started to argue for my side [that the weight changes as the forces upon it do] but still proclaimed me wrong. [It happens a lot... I say one thing, the opposition says the same thing in different wording, but makes a mistake, they say I'm wrong, but they've actually proved me right... it's annoying]

    So what I wan't to know is if the mass of the two divers would be the same, and what the proper definition of mass is. I would also want to know why Mass is measured in Kg's and what the Kg measurement is [i.e. kilograms per square meter]

    Thank you!


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    Forum Ph.D. Nevyn's Avatar
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    how fast you fall is actually independant of mass. Newtons second law states that F=ma and because you are falling the downwards force due to gravity = mg.
    So we have F=ma and W=mg, your downwards force equals your weight so ma=mg.
    The masses cancel leaving your acceleration downwards (which essentially controls your velocity) is ALWAYS the same. However the visable effects of this aren't always to because you have take into account the air resistance on the body which will slow people down to different speeds.

    Hope it helped!


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    Forum Freshman asxz's Avatar
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    Quote Originally Posted by Nevyn
    how fast you fall is actually independant of mass. Newtons second law states that F=ma and because you are falling the downwards force due to gravity = mg.
    So we have F=ma and W=mg, your downwards force equals your weight so ma=mg.
    The masses cancel leaving your acceleration downwards (which essentially controls your velocity) is ALWAYS the same. However the visable effects of this aren't always to because you have take into account the air resistance on the body which will slow people down to different speeds.

    Hope it helped!
    Kk, so wait... mg is your weight due to the force of gravity? So does that maen that mass doesn't change even if you weigh different amounts?

    And yes, it did help quite a bit... thanks!
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  5. #4  
    Forum Ph.D. Nevyn's Avatar
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    yes weight is your mass multiplied by the acceleration due to gravity (9.81 m s-2). If your mass changes then your weight will change because on earth gravity is pretty much constant.
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  6. #5  
    Forum Freshman asxz's Avatar
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    But isn't mass a measure of how dense something is? What you just said makes the weight dependent on the mass, so if the mass changes the weight changes. That means that if the weight changes the mass has to change. I was taught that mass was how much of 'something' is packed into 'somewhere'. I think you could calculate the mass by deviding the weight by the area. What that means is that the mass of an object will stay the same, even if it gets bigger, or smaller. I think we did a practical on it, and if the result of the equation was less than 1, then it would be bouyant.

    So what you're meaning to tell me is that that is wrong? [not meaning to sound rude or anything]
    Quote Originally Posted by Scifor Refugee
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    hmm, Density is a measure of how dense something is and that is mass divided by volume (Kg m-3). Mass is just how much of a substance there is without any constraints such as volume or forces such as gravity. if weight changes the mass doesn't nessacarily have to change, for example; something with the same mass on the earth will have a different weight on the moon because weight is mass multiplied by gravity or mg
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    Let's say you have bodies A and B. The force of gravity A experiences is always dependant on the mass of B, so irrespective of the mass of A its acceleration relative to its starting position will always be the same if the mass of B is constant. When B is a vastly more massive body than A, then you get what happens on a planet. The body A still always falls with exactly the same acceleration (disregarding air resistance and buoyancy), but the acceleration B undergoes relative to its starting point is negligible. When you add the two accelerations you get the bigger valued acceleration that each body experiences relative to each other, but again, the difference between this and the acceleration A undergoes relative to its starting position would be negligible when A is, say, a car or a man and B is a planet.

    As I understand it, the acceleration is the same for any mass of A relative to its starting position due to the variable inertia of A, which is totally dependent on its mass. Effectively, the increased acceleration one would expect is cancelled by the increase in inertia, so the acceleration of A is always solely dependent of the mass of B.
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    The force (weight) is different because the mass is different. And assuming the diving boards act like ideal springs this means that the displacement on the diving board will also be different but they should still come off the diving boards with a force proportional to their mass and that means that the resulting acceleration will be mostly the same.

    Actually with the diving board involved the equivalence is more clear in terms of energy for they start with potential energy proportional to their mass and the diving board simply stores and returns that energy to the diver. Thus the potential and kinetic energies remains proportional to the mass all the way and thus it divides out when calculating the velocity from the kinetic energy at a particular time.

    Thus the only differences in motion between the different masses will be due to things like friction in the diving board and air resistance, just like in the case of a brick and a feather when they fall.
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    One kilogram is defined (originally) as the mass of 1 liter of water.

    Mass is a measure of the amount of matter, and weight is a measurement of force.

    or, rather,

    The force of gravity where G is a constant, is, say, the mass of the earth and is the mass of you and r is the distance between the centers of your respective masses. F=ma can be rewritten as and, adjusting the equation, we have taking r to be the approximate circumference of the earth at sea level, we have a constant and, with Newtonian mechanics, we have
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  11. #10 Re: Are my friends wrong? 
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    Quote Originally Posted by asxz
    Okay, so I was away on a sports tournament, and because everyone knows I'm good at science one team mate asked me a question she had for homework. It was the one where two people jump off a diving board at the same time and land in the water at the same time because of the laws of forces, gravitation, and F=MA.

    I said that they would land at the same time because Force = Mass x Acceleration. That means that, because because we are trying to find out the Accleration of the people to see who goes faster, we use the equation: Acceleration = Force over Mass.
    All right so far?
    Then I said that, because the body mass would be relatively the same [mass, not weight. If it were mass, then we would be close enough, wouldn't we? Give or take a few muscle vs. fat issues] and therefore, they would land at the same time because the Mass and Gravity [force] would be the same, and that means they have the same acceleration, therefore speed and timing.

    So that was my theory.

    Then they said that:
    The mass wouldn't be the same, because Mass is measured in Kg's. I said that they were wrong, because Kg's was a measure of weight, and they rebuted with the 'fact' that weight was actually measured in Newtons.
    I get that, because Mass stays the same, and weight changes due to the forces that act upon it.
    But the person didn't get that I was agreeing with them, and they started to argue for my side [that the weight changes as the forces upon it do] but still proclaimed me wrong. [It happens a lot... I say one thing, the opposition says the same thing in different wording, but makes a mistake, they say I'm wrong, but they've actually proved me right... it's annoying]

    So what I wan't to know is if the mass of the two divers would be the same, and what the proper definition of mass is. I would also want to know why Mass is measured in Kg's and what the Kg measurement is [i.e. kilograms per square meter]

    Thank you!
    They hit at the same time because gravity is an acceleration. Since they are subject to the same acceleration their trajectories, given the same initial position and belocity will be identical. You don't even need the concepts of mass or force to resolve this piece of the puzzle, it is purely kinematic.

    Weight is the force exerted on a mass by gravity. So, if mass is in kilograms, weight will be in Newtons. Similarly the English lb is a unit of force and the corresponding unit of mass is the slug (which weighs about 32.2 lb). To confuse things a bit, mechanical engineers speak of pounds force (lbf) which is the usual pound, and pounds mass (lbm) which is a mass that has a weight of on lbf.

    Mass is measured in kilograms (or grams) in the metric system and slugs in the English system. It is not Kg per square meter or per anything else.

    The international kilogram is defined to be the mass of a specific object stored in Sevres France. http://en.wikipedia.org/wiki/Kilogram
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    1.) Mass is NOT measured in newtons. Force is.

    2.) Someone who was leaner and more muscular would fall faster because they would have more overall kinetic energy, therefore be able to displace air faster, and also would have to displace less air. ( that also depends on how they are diving. )

    3.) This is being somewhat picky, but the acceleration force of gravitation is SLIGHTLY more along the equator, because the earth is an oblate spheroid, and has a slight bulge there.

    4.) Mass is the measurement of how much force is required to move an object. M=F/A.
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  13. #12  
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    Quote Originally Posted by asxz
    But isn't mass a measure of how dense something is? What you just said makes the weight dependent on the mass, so if the mass changes the weight changes. That means that if the weight changes the mass has to change. I was taught that mass was how much of 'something' is packed into 'somewhere'. I think you could calculate the mass by deviding the weight by the area. What that means is that the mass of an object will stay the same, even if it gets bigger, or smaller. I think we did a practical on it, and if the result of the equation was less than 1, then it would be bouyant.

    So what you're meaning to tell me is that that is wrong? [not meaning to sound rude or anything]
    Gravity is an interesting thing. On Earth, it always adds however much force it takes to accelerate you by 9.8 meters per second per second. It doesn't matter how much that is, it will add it. If your mass is 10 trillion KG, gravity will add 98 trillion Newtons of force to make you accelerate at exactly 9.8 meters per second per second.

    You are right that "weight" is measured in Newtons, but the amount of Newtons you weigh is pretty much always your mass * 9.8 (Because 9.8 Newtons is how much force gravity imparts to 1 KG of mass)

    The only thing that could cause one diver to fall more slowly than the other is if one of them is more aerodynamic. If one of them is fat or something, so he's really wide, he'll have more air drag, and the skinnier one will fall faster.
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    Quote Originally Posted by kojax
    The only thing that could cause one diver to fall more slowly than the other is if one of them is more aerodynamic. If one of them is fat or something, so he's really wide, he'll have more air drag, and the skinnier one will fall faster.
    No, the skinny one falls slower because mass increases as the cube of the dimensions but cross-sectional area (which is proportional to the drag) only increases as the square.
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  15. #14  
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    Think you would be hard pressed to measure the micro seconds difference at these velocities.
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    Quote Originally Posted by Harold14370
    Quote Originally Posted by kojax
    The only thing that could cause one diver to fall more slowly than the other is if one of them is more aerodynamic. If one of them is fat or something, so he's really wide, he'll have more air drag, and the skinnier one will fall faster.
    No, the skinny one falls slower because mass increases as the cube of the dimensions but cross-sectional area (which is proportional to the drag) only increases as the square.
    Oh yeah. I was forgetting that your mass does determine how much of an effect the air has on you.

    So, the deceleration from air resistance would be (drag coefficient of the air) * Area/Mass. And you're right. Mass grows faster than area, so I was definitely wrong about who would fall slower.
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  17. #16  
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    Quote Originally Posted by Harold14370
    Quote Originally Posted by kojax
    The only thing that could cause one diver to fall more slowly than the other is if one of them is more aerodynamic. If one of them is fat or something, so he's really wide, he'll have more air drag, and the skinnier one will fall faster.
    No, the skinny one falls slower because mass increases as the cube of the dimensions but cross-sectional area (which is proportional to the drag) only increases as the square.
    You are assuming that the fat one and the skinny one are both spherical. Unlikely.
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  18. #17  
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    Quote Originally Posted by DrRocket
    Quote Originally Posted by Harold14370
    Quote Originally Posted by kojax
    The only thing that could cause one diver to fall more slowly than the other is if one of them is more aerodynamic. If one of them is fat or something, so he's really wide, he'll have more air drag, and the skinnier one will fall faster.
    No, the skinny one falls slower because mass increases as the cube of the dimensions but cross-sectional area (which is proportional to the drag) only increases as the square.
    You are assuming that the fat one and the skinny one are both spherical. Unlikely.
    If we really want to make it interesting, let's say the fat guy is wearing a speedo. (For your own sanity, I would advise you not to try to visualize it.)
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  19. #18 food for thought 
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    the notion that all objects fall to the earth was calculated by dropping two different weights in a vacuum. they appeared to both land at relatively the same time. i say relatively because there is always a tolerance. you cant drop two things at exactly the same time. its physicly impossible. what if the difference in weight wasnt great enough to see a difference. meaning that a 1kg weight proportional to the earths mass would be almost identical to a 10 kg weight proportional to the earth. maybe the experiment would be better measured in space with 3 weights. the one both travel towards is 100 kg. the others are 10kg and 1kg. than the proportions would be more drastic in difference and any difference in calculations wouldnt be written off as tolerance differences
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    i got it. the more mass an object has the more force it takes to accelerate but the more force it has to accelerate. they are inverse of each other. if it has twice the mass it takes twice the force to accelerate it and it has twice the gravitational force. the proportion is still 1 to 1. so yes things do fall at the same speed.
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