Understanding Momentum and Gravity on the Moon

[Ash17]

Firstly, please could you forgive me if what I'm asking is stupid; I'm only just starting out on A-level Physics/Maths so I'm hardly anything of a scientist yet.

I've seen video clips in class of a NASA experiment on the moon which involved dropping a feather and a hammer. Of course, there's no air resistance there, so they both fall at the same rate, Newton's second law gives that. But then there's momentum, which is the product of mass and velocity. If the masses of the two objects are obviously different, then mv will too be obviously different (v = velocity, m = mass). I just can't get my head around the fact that the objects hit the lunar surface with different momenta, given the conditions.

Whilst typing this I thought about the Moon moving more towards the heavier object - just an exceptionally small distance, femto- maybe even zeptometres (10^-21m). Is this true?

Thanks a lot
Ash

 

[berkeman]

The acceleration of gravity is a constant on the surface of the moon or any planet. F=ma is the fundamental equation to apply here. Since the accelerations are equal, the resulting velocities will be equal (acceleration is the change of velocity per unit time).

 

[Ash17]

That makes sense. What I found odd was two objects having the same speed but different masses so their momenta can't be equal, yet they cover the same distance in exactly the same time.

 

[russ_watters]

I'm not sure why you find that odd. The momentum is the product of two completely separate quantities, the mass and the velocity. So if the velocities are the same and masses are different, the momenta will be different.

Their energy is also different, for the same reason.

 

[robphy]

Sometimes its useful to distinguish the notions of dynamics (which involves mass m and F=ma; loosely speaking... "why it moves") and kinematics (which doesn't involve F=ma; loosely speaking... "how it moves").

Velocity is a kinematical quantity...and so is position, acceleration,...
Momentum is a dynamical quantity... and so is kinetic energy, ...

Considering a variant of your experiment...
would you rather get hit with a marble or a bowling ball dropped from the same height? [don't try this at home!] They'll certainly have different momenta upon impact.

 

[dst]

Another way to look at it from is through energy.

Even though they have different momenta, it doesn't matter. The feather needs less energy compared to the bowling ball to drop at any given rate. Since acceleration and everything else is constant, then the feather has less energy, and less momentum. In other words, it takes less "push" to get the feather moving the same distance.

And yes, the moon would have accelerated in the opposite direction ever so slightly.

 

[Ash17]

Thanks, people. This is all good stuff =)

 

[Narf the Mouse]

To put it simply, my understanding is the increased mass of the object does mean more energy pulls on the object, but that energy is absorbed moving the increased mass of the object.

Of course, I could be wrong.