According to Newton's Law of universal Gravitation, the force excerted by the earth on an objest is directly

Question

proprotional to the object's mass. According to his 2nd law of motion, the acceleration of an object is directly proportional to the force being exerted on it. THerefore, it may be concluded that if 2 objects are dropped simultaneously from the same height, the heavier object, having greater acceleartion, will read the ground first.

Use mathematical equations to either verify or refute the above conclusion.

Answer 1

acceleration is inversely proportional to mass (given same force), so mass cancels out and all object fall at same speed.

accelaration = force/mass
force = g*mass

so accelaration = g

Answer 2

Let there be two bodies of masses m and M (m F(m) = mg and F(M) = Mg., g is a constant of proportionality. So F(m) < F(M).
Now by Newton's second law of motion; the accelerations a(m) and a(M) are given by
a(m)=F(m)/m =g & a(M)=F(M)/M =g
In both cases, acceleration for free fall is the same i.e.g.
This is because if F(m) < F(M), m < M in the same ratio, so that
F(m)/m=F(M)/M.
Did the explanation become too tedious.?
II Trial:
Force of gravity exerted by the earth on a material object is proportional to the mass of the object, by the Law of gravitation.
The acceleration produced by this force is inversely proportional to the mass of the object , by the second law of motion. So the mass cancels. So all bodies of whatever mass have the same acceleration due to gravity.

Answer 3

The conclusion is false. Convert Newton's gravitation equation into an acceleration by dividing by the mass of the object. This shows that gravitational acceleration is driven by the mass of the Earth, for smaller masses and is therefore essentially a constant for small masses.

Answer 4

Consider a 1 kg mass on a frictionless plane table.

If a force of is applied on it and if it has an acceleration of 1m/s^2, the force acting on it is 1N as per Newton’s law.

{IF IT HAS AN ACCELERATION OF 10 M/S^2, THE FORCE ACTING ON IT IS 10N}******.

We can by our will change the force and hence change the acceleration on the same mass of 1.kg.

Now simply drop a 1kg mass from certain height. The earth gives or pulls it with a force of 10N.

Read again the sentence given above marked ******.

In the former case we applied force and the force can be changed at our will.

In the case of earth, the earth gives a constant force of 10N on 1kg mass.

This force is always 10 N for that mass of 1kg.

Therefore, the acceleration of mass of 1kg will always be 10m/s^2.


Now consider a 2kg mass made to fall from that height.

The earth gives now double the force; it pulls it with a force of 20N.

The force on 2kg mass will always be 20 N.

The acceleration of the 2kg mass is 20N/ 2kg = 10 m/s^2.

The acceleration is the same as that for 1kg mass.

Hope now you might have understood the basic reason.

In both cases Newton’s law F = ma is applied.

In the former case for a given mass we can change the force on a given mass as per our will.

In the case of earth’s pull, for a given mass, the force is fixed and we cannot change the force at our will.

As the force depends on mass, the acceleration is constant.
The above statement can be said in two ways.

1)
In the case of the pull of the earth, acceleration is constant in the equation F=ma.

Thus F is proportional to the mass.

2)

In the case of the pull of the earth, the force increases or decreases in proportion to the mass of the body. The force is proportional to the mass of the body. Therefore, the acceleration is constant.

Answer 5

Actually acceleration due to gravity works equally on all objects.

It has been proven that a bowling ball and a ball bearing fall at the same rate.

It thing that makes the difference on earth is air resistance, that is why a feather falls less quickly than a brick because the feather has greater air resistance.

http://library.thinkquest.org/03oct/02144/text/basics/accn.htm

Answer 6

Yes, here is what they say trying to baffle you: F = G*M*m/r^2 = m*r’’, now delete m in both parts and show them, that acceleration does not depend on m; thus any m would reach the ground in the same time, with no atmosphere though.

ah! omegared is the first, good boy!

Answer 7

From universal Gravitation law
F=G(mM)/r^2;
where M is the mass of earth,m=mass of the object
@ free fall;
ma=G(mM)/r^2
a=G(M)/r^2

see the acc. is independent from the mass of the object.

Answer 8

Law of gravitation:
F = gm
2nd Law of motion
F = ma
You (should) know that:
F = F
and
m = m
so it follows fairly simply.

Answer 9

f = ma