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]
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]
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]
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.
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
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)
I can think of better things to argue about 
quote:
Originally posted by vinny1275
The heavy one will accelerate quicker, because the effect of gravity is greater on objects the greater their mass.
quote:
Originally posted by AndyW
I can think of better things to argue about
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
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
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.
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
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
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.
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
building and racing gravity powered toy cars will quickly demonstrate the advantage of mass,...
hth
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.
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.
Looks like an experiment will be needed, featuring 2 ping pong balls one of which is filled to make it heavier...
I built a Gravity car for Goodwood before they banned them for being to fast and dangerous,
Heavy wins every time.
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
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.
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.
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.
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?
I do love how you start with : Lets keep it simples
and end with rotational inertia comes in to play
The simplest way to look into it would be no friction, no air resistance, purely the moving of an object down a plane.
Also when you say the heavier will travel furthest, what are you basing that on? Yes it was more potential energy, but it also has more kinetic when
moving due to both benig a function of mass.
So when a falls x meters, GPE has dropped by some amount, but kinectic energy has increased by the same amount.
Same goes for the other ball.
I still believe that if it was an infinite plane, both balls would be neck and neck the entire way, assuming friction coefficient is low and not the
extreme grass bank.
quote:
Originally posted by 02GF74
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.
Here's my take
2 balls, A=1kg, B=2kg
iniital potential energy =mgh, since g and h are the same B has twice the kinetic energy.
Assume no surface friction, no air friction and no relativistic effects and let the balls roll down the slope.
The potential energy is changed to kinetic energy. Start at 1m high
A has 9.8 joules, so 0.5*m*v*v = mgh = 9.8, actual speed will be approx 4.4m/s (SQRT of 19.6)
B has 19.6 joules, so 0.5*m*v*v =19.6, actual speed will also be 4.4m/s (mass is 2 remember)
In ideal conditions the mass cancels out and they achieve the same speed. There are no frictional losses, so they keep going forever, and will always
have travelled the same distance in the same time.
However, ball B has more kinetic energy and also more momentum. If you are loosing constant energy/second to friction (assuming the frictional forces
are not dependant on normal forces like with a tyre) then the lighter ball will run out of kinetic energy first. The momentum of the heavier ball
means it overcomes the irregularities of the surface easier too. As a coupe of people have mentioned, gravity racers always go for absolute maximum
weight. We did one at belchford last year with 2 drivers in the same kart, but 15kg difference in our driver weights(about 6% of the overall mass),
and the heavier driver was about 2 to 3 seconds quicker down the course.
Regards
Hugh
quote:
Originally posted by Miks15
I do love how you start with : Lets keep it simples
and end with rotational inertia comes in to play
i understand what you meant, just didnt sound simple
Ive just had a rethink (again! ha) and now i reckon the heaviest will be going fastest at the bottom because air resistance is only a function of
velocity and has nothing to do with mass, so both will have the same force applied at the front from the air resistance which will reduce the
acceleration quicker in the lighter ball. The friction is a function of mass so assuming no air resistance and only friction they would be going the
same speed.
If you want a bit of variety...
Take a round ball and a cube - both made of the same material and the same weight. Both are nice and shiny.
Put them at one end of a flat, smooth board, then lift that end slowly.
Which one will get to the bottom first?
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Usually, it will be the cube (if you lift too far, they'll probably arrive together, when gravity has more effect than friction/rotation). The
ball has to convert potential energy into rotational energy, whereas all the cube has to do is slide.
I didn't believe it until I saw a live demo!
^^^ I need to think about that but don't want to.
they may be going same speed when the leave the ramp but I still reckon the lighter one gets there fisrt due to inertia (it will take longer for the
heavier ball to start rolling).... as hinted at by DJs post above.
quote:
Originally posted by 02GF74
^^^ I need to think about that but don't want to.
they may be going same speed when the leave the ramp but I still reckon the lighter one gets there fisrt due to inertia (it will take longer for the heavier ball to start rolling).... as hinted at by DJs post above.