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Thread: Different masses moving down a hill at different speeds?

  1. #1 Different masses moving down a hill at different speeds? 
    Junior Member
    Join Date
    May 2013
    When dropping two objects their mass does not affect their speed because the greater force of the weight of the higher mass is balanced by its greater inertia. Therefore the reason that objects fall at different speeds is entirely due to the friction from the air. Therefore the object with the larger surface area exposed to air resistence is the one that falls slowest.
    Is this the same when you roll or slide two different masses down a hill? (And I am fully aware that the distinction between rolling and sliding may be an important one).
    This question posed itself when I realised that my dad (who is more massive than me) always beats me when going down a hill on skis, on sledges and also on roller skates. I am smaller and therefore have less air resistence acting on me and so expect to go faster but it's become apparent that I don't. Is there a reason why my dad always goes faster down a hill other than him being more skilled?
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  2. #2  
    Senior Member
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    Jan 2014
    out there
    In a vertical short fall of different sized objects of similar high density there will be a slight affect of air resistance. It becomes evident as terminal velocity is reached. A mouse can be dropped from ten stories and survive. A man is smashed. A horse is splattered.
    A bowling ball and a billiard ball off a table... the difference will be only evident in a precise experiment, to the eye no difference is pereceptible.
    In ballistics for examples pistols, rifles and cannons. Denser projectiles are more efficient. Thus lead or tungsten shot are more efficient than steel. Larger projectiles are more efficient. Thus a 16 inch diameter naval cannon with 2000 pound projectiles will shoot farther than a a high powered rifle shooting 200 grain bullets.

    You cannot ignore air resistance when skiing. Downhill skiers wear skin tight suits and tighten up in order to streamline themselves and reduce surface area to mass ratios to attain higher velocities (and reduce loss of velocity).

    Your father and you have different surface to mass ratios. An elephant on skis would beat a mouse on skies. A clay brick will have a lethal terminal velocity but clay dust will blow away with a breeze.

    Although simple friction of the skis on the snow is proportional to mass via the normal force (cosine of the angle of the slope here) multiplied by friction coefficient this is compensated by gravity x mass resolved along the plane of the slope (sine of the angle here). So both you and your father are on an equal basis here. The same argument as curve banking, whereby what is good for one is good for all.
    Last edited by pikpobedy; 02-21-2014 at 11:55 PM.
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  3. #3  
    KJW is offline
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    Jun 2013
    Quote Originally Posted by MaxH View Post
    And I am fully aware that the distinction between rolling and sliding may be an important one
    Yes, it is. For rolling, part of the total kinetic energy is rotational kinetic energy so that there is less kinetic energy for the translational motion down the hill.
    A tensor equation that is valid in any coordinate system is valid in every coordinate system.
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