Falling object collision question

[Stellar1]

Hello,
I've been trying to figure out the physica behind a collision of two objects due to the force of gravity. Here's the situation as I'm picturing it:

A massive object A is falling due to gravity which impacts a stationary object B being held up by a structure. In this particular case, the structure is unable to support the impact force of object A and fails, causing the now combined object AB to continue falling.

My difficulty is in picturing how the forces interact during the collision. Object A is falling with a force of F=MaG, which is then applied to Object B. At this instant, object B begins its acceleration... Would a force F be applied, during the collision, to Object A in the opposite direction due to Newtons 3rd law?

 

[tiny-tim]

Hello Stellar1!

Object A is falling with a force of F=MaG, which is then applied to Object B.

That isn't how it works.

M_ag is the force on A (from the Earth).

To find the force on A from B, you find the acceleration of A during the collision, subtract that from g, and multiply by M_a.

The force from A on B is of course the same (Newton's third law).

(that's if you analyse it instantaneously …

the more sensible way would be to use impulse, rather than instantaneous force)

 

[Stellar1]

If object A is on object B, the it is applying the force MaG onto it, no?

 

[Stellar1]

The only way I can reconcile this in my head is if I take compressibility into account. That allows for object B to accelerate and object A to decelerate until a common speed is achieved and gravity accelerates the combined object.

 

[tiny-tim]

If object A is on object B, the it is applying the force MaG onto it, no?

no

the force from A on B (or vice versa) depends on a lot of things

 

[Stellar1]

Let me rewrite this now that I'm not doing 3 things at once and able to think about this with minimal distractions:

I know that A will be falling with a force of F_a=m_ag onto object B, which can only support a force of, say, F_s. The length of time object A is under this acceleration will allow us to determine the velocity of object B at the instant just prior to collision, which we will call v_i

Now, assuming object B is incompressible and, since we assume F_a>F_s, its perfectly consistent to assume that the force during the collision will break the supports and object B will now accelerate from rest under the collision force of object A, as well as gravity.

Since we assume that object B is not very compressible, wouldn't this mean that object A has to essentially come to rest as well, so that object B (now joined to A) will both accelerate from rest (since B is starting from an initially stationary position)? This would then imply that the velocity at the instant just after collision is 0, correct? The force exerted by A on B (and by B on A) would then equal F=m_av_i/t + m_ag, where t is the duration of the collision.

Is there any way to determine how long this collision would take?

 

[tiny-tim]

I know that A will be falling with a force of F_a=m_ag onto object B …

No, that's completely wrong.

Before A hits B, it has an acceleration of g downward, and there is a force on A (from the Earth) of M_ag.

A does not exert a force of M_ag on anything (except of course the Earth).

When A hits B, A will slow down a lot, and will also change shape slightly. B will also change shape slightly, and will start accelerating.

You find the force by finding the acceleration first (on either A or B), and multiplying that by the mass.

You find the acceleration by using Newton's second law, which is about momentum, and also using your knowledge of the elasticity of A and B.

 

[Stellar1]

No, that's completely wrong.

Before A hits B, it has an acceleration of g downward, and there is a force on A (from the Earth) of M_ag.

A does not exert a force of M_ag on anything (except of course the Earth).

When A hits B, A will slow down a lot, and will also change shape slightly. B will also change shape slightly, and will start accelerating.

You find the force by finding the acceleration first (on either A or B), and multiplying that by the mass.

You find the acceleration by using Newton's second law, which is about momentum, and also using your knowledge of the elasticity of A and B.

Ahh, yeah. That's what I meant. Falling onto =>Falling towards with a force of F=m_ag which accelerates it to a certain velocity prior to colliding with B.