Newton's Force: Same Distance, Different Masses?

[sambarbarian]

hi! i wanted to ask that if all the things fall in the same time from the same distance .. how can the formula for force given by Newton be correct ?

for example . if i take two balls with masses 10:1 .. then by the formula the force/acceleration should be 98 m/s^2 for 1st ball and 9.8 for the other .

i am sure that there is an explanation , or I am wrong :)

this may be a silly question for some people but i would like to know the answer :)

 

[Simon Bridge]

hi! i wanted to ask that if all the things fall in the same time from the same distance .. how can the formula for force given by Newton be correct ?

Because the balls experience different forces. (The heavy ball experiences a stronger force - that's what "heavy" means.)

Newton's law is F = ma
The force due to gravity (close to the Earth's surface) is F = mg where g=9.8N/kg

This becomes mg = ma and the masses cancel out giving you a = g = 9.8m/s/s no matter what the mass is.

It also works with the full formula for gravity:$$F=\frac{GMm}{r^2}=ma$$... again the masses cancel out (comparing little m's).

 

[clm222]

just to add on to that:

calculating the gravitational field strength (it's rate of acceration) if a fairly simple calculation:

g= -GM/d^2
(note the negative sign is due to the fact that gravity is an attractive force)

g=gravitation field strength
G=universal gravitational constant
M=mass of body
d=distance from center of "M"

 

[CWatters]

One way to think of it is that the heavier mass has a greater force acting on it BUT it also needs a greater force to accelerate it. Net result is that acceleration is independent of mass.

 

[Simon Bridge]

... rereading post #1, OP seems to be equating force with acceleration ... easy to do because of the way we commonly talk about gravity. Notice how he has the heavier mass having the greater acceleration?

Taking what was written at face value: force/acceleration = mass (but I don't think OP means the "/" to indicate division.)

 

[sambarbarian]

Taking what was written at face value: force/acceleration = mass (but I don't think OP means the "/" to indicate division.)

yeah , it was just a slash .

 

[Simon Bridge]

force-slash-acceleration doesn't work well either though ... which is why I thought it may have been a pointer to greater understanding. You OK with the acceleration due to gravity being independent of mass now?