graememk
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| posted on 8/4/11 at 11:22 AM |
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help solve an argument please
If you put to balls of the same size on a slope
Which one will accelerate faster the light one or the heavy one?
Which one will be going faster at the bottom of the hill?
Which one will travel further?
[Edited on 8/4/11 by graememk]
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Daddylonglegs
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| posted on 8/4/11 at 11:25 AM |
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Put your balls on a slope and time them 
Oh, and all things being equal (except the weight of course  ) I would say the heavy one would go further because of mementum, but the lighter one
would probably start off quicker?
[Edited on 8/4/11 by Daddylonglegs]
It looks like the Midget is winning at the moment......
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deezee
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| posted on 8/4/11 at 11:30 AM |
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Assuming a perfectly smooth slope at atmospheric pressure and earth gravity, both will travel the same speed and take the same time rolling down the
hill. If you add any friction to the surface of either the slope or the ball, the lighter one will get down faster as the heavier one produce more
friction.
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vinny1275
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| posted on 8/4/11 at 11:34 AM |
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The heavy one will accelerate quicker, because the effect of gravity is greater on objects the greater their mass. Unless you had enough slope to
reach terminal velocity (which is determined by friction - air resistance and friction of the slope service in this case), the heavier ball would be
travelling faster at the end of the slope. The heavier ball will travel further when they get to the bottom of the slope as it will have greater
momentum (which is velocity x mass).
As Daddylonglegs says, all other things need to be (near) equal - particularly the surface of the ball can alter the friction it experiences...
HTH,
Vince
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cliftyhanger
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| posted on 8/4/11 at 11:36 AM |
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the same size, different mass thing IS the biggy here.
As the air resistance is the same on both. Therefore the heavier ball will get there faster. (if NO air, then they will reach the bottom at the same
time) The heavy ball will also travel further as it has the greater kinetc energy at the bottom of the slope.
It all assumes there is zero friction between the ball and slope, which is a very fair assumption for a hard, smooth ball and a smooth slope. (contact
area is tiny)
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AndyW
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| posted on 8/4/11 at 11:37 AM |
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I can think of better things to argue about 
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cliftyhanger
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| posted on 8/4/11 at 11:42 AM |
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quote:
Originally posted by vinny1275
The heavy one will accelerate quicker, because the effect of gravity is greater on objects the greater their mass.
Not true, remember (or seem) the hammer and feather dropped on the moon? both fell at the same rate.
If you take the 2 equations involved
the potential energy at the top of the slope
this becomes Kinetic energy
1/2 mass x velocity squared
so
mass x g x (vertical) height = 1/2 mass x velocity squared
mass cancels from both sides, so plays no part!
(teacher hat now off)
Of course momentum is a different kettle of fish
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cliftyhanger
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| posted on 8/4/11 at 11:42 AM |
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quote:
Originally posted by AndyW
I can think of better things to argue about
Disagree, basic physics is rather important
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Miks15
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| posted on 8/4/11 at 11:47 AM |
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since F=ma,
And the force moving the ball is proportional to the mass of the ball. Acceleration will be the same at the start.
But then friction comes in to play so since we dont live in a perfect world. The heavier one will experience greater friction, which will act against
force accelerating the ball.
So the heavier ball would be going slower at the bottom than the lighter one.
Thats what i think anyway
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speedstar
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| posted on 8/4/11 at 11:49 AM |
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quote:
Originally posted by vinny1275
The heavy one will accelerate quicker, because the effect of gravity is greater on objects the greater their mass. Unless you had enough slope to
reach terminal velocity (which is determined by friction - air resistance and friction of the slope service in this case), the heavier ball would be
travelling faster at the end of the slope. The heavier ball will travel further when they get to the bottom of the slope as it will have greater
momentum (which is velocity x mass).
As Daddylonglegs says, all other things need to be (near) equal - particularly the surface of the ball can alter the friction it experiences...
HTH,
Vince
Errr.... no :S
All things equal (aside from mass) they would accelerate exactly the same.
Friction - Heavier ball will epxerience a greater frictional force due to the reaction from the surface.
Air resistance - if they are the same size, its irrelevant HOWEVER you would need to consider momentum...
Momentum - Heavy ball will have more momentum and more kinetic energy. So it will overcome air resistance mroe easily (or be less affected by it -
however you want to look at it) and will also travel further.
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vinny1275
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| posted on 8/4/11 at 11:51 AM |
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quote:
Originally posted by cliftyhanger
quote:
Originally posted by vinny1275
The heavy one will accelerate quicker, because the effect of gravity is greater on objects the greater their mass.
Not true, remember (or seem) the hammer and feather dropped on the moon? both fell at the same rate.
I was wondering about that as I typed it (it's a fir few years since my last physics lesson...) - I remember now that it's lack of air
resistance that caused that. The greater the mass, the greater the potential energy for the same height, and the more quickly it picks up kinetic
energy though?
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graememk
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| posted on 8/4/11 at 11:53 AM |
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ok here is my view
lighter ball will accelerate faster than heavy ball
heavy ball will be going faster at the bottom
heavy ball will travel further
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Miks15
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| posted on 8/4/11 at 11:56 AM |
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Actually just thought about it again.
The frictional force is proportional to the normal force on the slope, and therefore the mass of the object.
This will therefore have a greater effect on the heavier ball.
BUT in proportion it will have the same effect on both.
So if the heavier is twice as heavy:
The mass is double, therefore the force accelerating is double and therefore same acceleration on both.
Friction force on the heavier is also double that on the lighter ball as the normal force is double.
SO acceleration will still be the same.
So my new answer is both exactly the same
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cliftyhanger
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| posted on 8/4/11 at 12:15 PM |
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As another "ad hoc" approach to the friction issue try this as an idea.....
a golf ball and a pingpong ball, same size, diffeent mass.
Stick them on a grass covered bank. Which one moves......
the physics is clear, acceleration is independant of mass (no matter what people think ) as long as friction is negligable.
The friction issue is a different matter, and can be very complex, and needs to consider speed as well as surface.
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MikeRJ
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| posted on 8/4/11 at 12:26 PM |
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quote:
Originally posted by graememk
ok here is my view
lighter ball will accelerate faster than heavy ball
heavy ball will be going faster at the bottom
heavy ball will travel further
This is really basic physics, not even GCSE level. The balls will accelerate at the same rate. The heavier ball experiences a greater force due to
gravity, but this is exactly cancelled by it's greater mass so they have the same acceleration.
The heavier ball starts with more potential energy (mgh), and obviously ends up with more kinetic energy (0.5mv^2) than the lighter ball.
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HowardB
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| posted on 8/4/11 at 12:26 PM |
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building and racing gravity powered toy cars will quickly demonstrate the advantage of mass,...
hth
Howard
Fisher Fury was 2000 Zetec - now a 1600 (it Lives again and goes zoom)
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Miks15
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| posted on 8/4/11 at 12:27 PM |
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you can hardly considering a grass covered bank as a surface unless it is cut very short and the blades will pose no physical restriction to the
balls. If it was cut short enough, both balls would roll down the bank.
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scudderfish
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| posted on 8/4/11 at 12:27 PM |
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It also gets more interesting if you don't assume constant density and the mass is allowed to be concentrated either at the centre or to the
outside.
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Ninehigh
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| posted on 8/4/11 at 12:34 PM |
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Looks like an experiment will be needed, featuring 2 ping pong balls one of which is filled to make it heavier...
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mikeb
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| posted on 8/4/11 at 12:35 PM |
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I built a Gravity car for Goodwood before they banned them for being to fast and dangerous,
Heavy wins every time.
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balidey
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| posted on 8/4/11 at 12:38 PM |
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Three balls.
Light one must be the BEB (bike engined Ball)
Heavy one must have the Pinto.
Third ball not yet ready to test as Darren was supposed to have supplied it 18 months ago.
I think thats covered all bases
Dutch bears have terrible skin due to their clogged paws
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cliftyhanger
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| posted on 8/4/11 at 12:40 PM |
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quote:
Originally posted by Miks15
you can hardly considering a grass covered bank as a surface unless it is cut very short and the blades will pose no physical restriction to the
balls. If it was cut short enough, both balls would roll down the bank.
Of course it is a surface, but a high friction one. When using ideas as models, it is always good to start at extremes, even if they are not
realistic. The blades of grass provide a visible form of friction, easier to work with than microscopic ideas
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Miks15
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| posted on 8/4/11 at 12:58 PM |
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i see your point but i think that is too extreme, the blades of grass themselves are like posts sticking up infront of the balss which need to be
flattened down to a flat surface.
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morcus
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| posted on 8/4/11 at 07:31 PM |
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Just going back to something someone said about the hammer thing on the moon, that was about air resistance but the mass of something on the moon IS
EXACTLY THE SAME AS ON EARTH, there for if you dropped two things the same shape but different weights on earth they would land at the same time.
The biggest problem we have here is that experimental results will most likely be different from the theoretical by some margin, but I think should
travel at the same speed in a perfect situation mostly because acceleration is constant as it's just gravity, the force of the heavier ball at
the bottom will be greater but it will be traveling at the same speed.
I can't clearly remember the specifics but this is pure newtonian mechanics and I'm sure the answer lies in the equation v=u+at which is
Final velocity (v) is equal to initial velocity (u, in this case 0) plus acceleration times time. If we assume 0 friction a can be calculated by
trigonometry (I think, it was a long time ago) as a fraction of g (Gravity). If I'm thinking on the right lines then a perfect situation of this
doesn't involve mass.
In a White Room, With Black Curtains, By the Station.
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02GF74
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| posted on 11/4/11 at 11:47 AM |
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quote:
Originally posted by graememk
If you put to balls of the same size on a slope
1. Which one will accelerate faster the light one or the heavy one?
2. Which one will be going faster at the bottom of the hill?
3. Which one will travel further?
let's not get bogged down with blades of grass, friction, air resistance, densitiy distribtion etc. but keep it simples.
1. both should experience same accelerating force = gravity *
2. same speed due to 1
3. heavier one will travel further due to having more poential energy
* That is certainly true when in free fall but I am wondering about this since balls rotate when rolling along a surface so rotational inertia
comes into play.
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