when two objects with different masses are dropped at the same time.....?

Question

does the heavier object have more "momentum" as it hits the ground?

but momentum is not velocity.

Answer 1

Two masses M and m (M > m) are dropped from h height (with zero momentum) at same time. Let V be speed at strike.
Gain in Momentum of heavier mass P = MV so
P^2 = M^2 V^2 = 2M * (1/2) MV^2
= 2 M (gain in kinetic energy)
= 2 M (loss in potential energy = Mgh)

Mgh = P^2 / 2M so P^2 = 2gh M^2 or

P = M sqrt (2gh) like wise for smaller mass “m”
p = m sqrt (2gh)

P – p = (M – m ) sqrt (2gh) here (M – m ) = +ve so

P > p, means momentum of heavier mass M will be more when they hit ground. It is assumed that given heavy objects do not significantly entail any relative air or medium resistance to fall. Though, air resistance is a function of volume of the object, but even a lighter object can entail more volume than the heavier. Here the asker entreats us to ignore it, otherwise it can be inbuilt with some more data for case specific inference.

It may be noted that time taken by both will be same because t is independent of mass and they strike ground with same speed.

Answer 2

Yes, the more massive object will have more momentum.

You see, momentum = (mass) X (velocity)
Now, Galileo had proved that any 2 bodies (irrespective of their masses) experience the same acceleration due to gravity, and so their velocities at the time of impact with the earth will be the same [since, v,final = v,initial + a*t]. Due to this reason, a feather & an iron ball, if left from a height in vacuum, strike the ground exactly at the same time, or you could say, exactly after the the same time interval.

So, the two objects will have the same velocity at the time of impact. Therefore, in the product of mass & velocity, a greater value is possible if a greater mass is considered. So, I think a more massive object will have more momentum as it hits the ground, as momentum = (mass) X (velocity).

Answer 3

If you use V x V = U x U + 2 A S with U = 0, A = 9.8, you find that V (final velocity) will be the same for both the objects.

However, as momentum is defined as mass x velocity, the heavier object will have proportionately more momentum.

Answer 4

The object with the greater mass will certainly have more momentum.

p=mv

(momentum) = (mass) X (velocity)

although the two objects will have the same velocity, one will have the greater mass and therefore have more momentum. If a car and a feather were both dropped in a vacuum, they'd both hit the ground at the same time/speed, but the car would have a much greater momentum. (unless that was one REAL heavy feather)

Answer 5

According to wikipedia, momentum equals mass times velocity. The 2 masses will have the same velocity when they hit the ground, so obviously.......

Answer 6

Yes. Momentum is force and force is mass X velocity. Bigger mass times the same velocity makes a bigger force or a bigger momentum.

If you drop a pea and a rock onto a pane of glass, is one more likely to break the glass?

Answer 7

It will reach the ground at the same time. Just drop a pencil and your pencil case at the same time, same height, you'll prove that it is true (with no air-resistance) the two object with two different weights would land at the same time (in an vacuum).

Answer 8

No, it does not. Gravity still pulls everything at 32 feet per second per second.

Answer 9

no........not momentum............but you should check ........f=ma....that should tell you that force of impact may be affected..........[force = mass / acceleration.