Naked Science Forum
General Science => General Science => Topic started by: ukmicky on 17/12/2005 02:35:57

OK i've decided to go back over what i learn't in physics class at school .
and in case ive forgotten something ive started back at the basic's so bare with me
Now Forgetting about air resistance. do two ojects of different weights dropped from the same height at the same time really fall at the same speed and hit the ground at the same time.
Doesn't the mass of the object that falling create it own gravitaional pull on the earth, meaning a large object will fall faster than a small object with less mass because the large object pulls the earth more with it own gravitational pull .
Obviously the difference would be tiny but is it so.
Michael (https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fi11.photobucket.com%2Falbums%2Fa186%2Fukmicky%2Fwallbash.gif&hash=7fbfae96ee4eb666ba3ec22832e5a81f)

F=ma
=> GMm/rr=ma
=> GM/rr=a
=> a not a function of m
QED
(The mathematical explanation is so much simpler than the verbal explanation, don't you think?) [:D]

Newtons law states that the force between two solid objects m1 and m2 is G.m1.m2/dquared where dsquared is the square of the distance between their respective centres of gravity so the mass of the heavier particle and hence its own gravitational field has already been taken into account in the equation. therefore provided they are in the same position they would both fall at the same rate.
Learn, create, test and tell
evolution rules in all things
God says so!

Oh, OK then, here's an explanation in English:
Yes, in the absence of air resistance the two objects will fall at exactly the same speed and hit the ground simultaneously.
There will be a greater force of gravitational attraction between the earth and the heavier object, but that does not lead to faster acceleration.
The reason can be seen by looking at Newton's equation F=ma (i.e. force = mass x acceleration).
In the case of gravity, the force is directly proportional to the mass of the object. So if the mass 'm' on the right hand side of the equation is doubled (say), then the force 'F' on the left hand side is also doubled. So for the equation still to balance, the acceleration 'a' must stay constant.
If you want to be even more specific (and technical) …
The rate of acceleration ‘a’ is calculated as:
a=(G*M)/(r*r)
where ‘G’ is Newton’s “gravitational constant”, ‘M’ is the mass of the earth, and ‘r’ is the distance from the falling object to the centre of the earth.
So ‘a’ does depend on ‘r’ (the distance to the centre of the earth). Of course, ‘r’ doesn’t vary significantly over most of the earth’s surface, so ‘a’ stays fairly constant at about 9.8 m/s/s. However, if you did the experiment at the top of Mount Everest (say), then you would find that the rate of acceleration is a tiny bit lower (because the distance ‘r’ is bigger when your on top of Everest).
I’d better stop there – I can sense you’re falling asleep while reading this Michael. We’ll resume the lesson tomorrow, when I’ll set you some nice problems to do as homework. [}:)]

Oops  didn't realise you'd posted something while I was typing my last entry, Ian.
(Your explanation seems somewhat more succinct then mine.[:)])

Oops  didn't realise you'd posted something while I was typing my last entry, Ian.
(Your explanation seems somewhat more succinct then mine.)
__________________________________________________________
Succinct?[:)] Looks like i need to go over my old English schoolwork as well. Where's my dictionary
Got it Succinct means short and snappy. [:)]ok concise sounds better.
Ian,paul thankyou
Michael (https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fi11.photobucket.com%2Falbums%2Fa186%2Fukmicky%2Fwallbash.gif&hash=7fbfae96ee4eb666ba3ec22832e5a81f)

quote:
Originally posted by ukmicky
OK i've decided to go back over what i learn't in physics class at school .
and in case ive forgotten something ive started back at the basic's so bare with me
Now Forgetting about air resistance. do two ojects of different weights dropped from the same height at the same time really fall at the same speed and hit the ground at the same time.
Doesn't the mass of the object that falling create it own gravitaional pull on the earth, meaning a large object will fall faster than a small object with less mass because the large object pulls the earth more with it own gravitational pull .
Obviously the difference would be tiny but is it so.
Michael (https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fi11.photobucket.com%2Falbums%2Fa186%2Fukmicky%2Fwallbash.gif&hash=7fbfae96ee4eb666ba3ec22832e5a81f)
The two subject objects will fall at exactly the same speed. This is true for the case where the falling object is large enough to disturb the larger object, such as the earth and the moon.
This may sound like the most amazing coincidence, and between the time of Newton and Einstein, it was just that. General Relativity combines the gravitational force of gravity with the inertial properties of matter into a unified treatment. The subject effect here is known as the equivalence principle.
"F = ma, E = mc^2, and you can't push a string."

As a firm believer in empirical study I took one balloon filled with water and one tennis ball and dropped them from the top floor of my house.
I learned two things:
1: They both reached ground level at the same time
2: This experiment is best done outside !!
Men are the same as women.... just inside out !!

quote:
Originally posted by gsmollin
... force of gravity with the inertial properties of ...
This is a common missconception. Gravity is not a force. The force is the product of mass and the strength of the gravitational filed, ie, the quotient of the ratio force/mass.
Big Tim

this is such a universal(get it? sorry) misconception.
its one of those things that goes against human perception... when you consider it... "of COURSE a heavier object will fall faster. its HEAVIER!" i used to think so too.
why is this our initial impression? is it because heavier things make louder noises and more of a dent, so we perceieve it to be moving faster when it hits the ground?
its strange that something most people believe makes sense, like heavier objects fall faster, is totally false!

It's interesting to consider Galileo's reasoning about it:
"Let's suppose the bigger (heavier) body would fall faster than the smaller; so, if you connect the two bodies with a rope, the bigger will accelerate the smaller, and the smaller will slow down the bigger, so the speed will be an intermediate value between the two speeds. But, the two bodies together actually form...another body even bigger, so its speed should be greater than both speeds! So, the initial hypotesis is false, and the two bodies will fall with the same speed!"