Qualitative collisions questions

[goobertron]

Hello all. I have what seems to be a fairly simple problem but I need a bit of help on the reasoning and what happens in a qualitative sense if some factors change.

The problem is of e.g. a larger spherical type thing happily traveling along at a fixed velocity but with a smaller (e.g. 10x smaller by diameter) sphere adhered to the surface. This large/small pair now hits a surface.

What is the likelihood of detachment based on? I am thinking it is a function of the mass of the smaller particle and the deceleration of the combo pair as it hits the wall (i.e. if the F=ma in this scenario exceeds the adhesion force then the smaller thing detaches?)

Now, keep the smaller sphere the same size but increase the larger sphere (lets assume the same force of adhesion between the pair to keep it simple). If traveling at the same velocity as before it seems like there should be a greater chance of detachment, but is this because of momentum exchange? As you can see my Physics here is shocking!

If someone could sort out this basic issue first I'd then like to expand slightly.

Thanks!

 

[Hia Hasmut]

I doubt they'll detach if they're glued.

 

[chrisbaird]

If I understand correctly, the smaller ball is attached to the back of the larger ball and the larger ball hits the wall. In this case, yes the smaller ball will feel a greater force upon impact the more massive the larger ball because of momentum transfer. You can do this experiment very easily. Hold a large exercise ball a few inches off the ground with a tennis ball resting on top and let go. When they both fall due to gravity and hit the ground, the tennis ball with go rocketing up into the air at a surprisingly high speed. This is a fun demonstration because the balls don't pick up much speed before they hit the ground, yet the tennis ball gains a great speed on impact. It demonstrates that total velocity is not conversed, only total momentum. When a high-mass, low-velocity object transfers its momentum to a low-mass object you get high velocity!

 

[goobertron]

Thanks Chris - what about if it was stuck to the side? Does a larger or smaller parent ball give a more likely qualitative detachment force?

 

[PJC01]

I would approach this problem by first defining the variables and factors involved. In this case, we have the mass of the smaller particle, the deceleration of the combo pair, and the force of adhesion between the pair. These factors will determine the likelihood of detachment when the pair hits a surface.

Based on the concept of Newton's second law of motion (F=ma), it is likely that if the deceleration of the pair exceeds the adhesion force, the smaller particle will detach from the larger one. This is because the force of deceleration will be greater than the force of adhesion, causing the smaller particle to overcome the attraction and detach.

When we increase the size of the larger sphere while keeping the smaller one the same, the mass of the combo pair will increase. This means that the force of deceleration will also increase, making it more likely for the smaller particle to detach upon impact with the surface. This is due to the principle of momentum exchange, where the larger mass will transfer more momentum to the smaller particle upon impact.

To expand on this problem, we could also consider the surface properties of the larger sphere and the surface it is impacting. For example, if the surface is rougher, the force of adhesion may be stronger, making it less likely for the smaller particle to detach. Additionally, we could also consider the speed and angle of impact, as these factors can also affect the likelihood of detachment.

In conclusion, the likelihood of detachment in this scenario is dependent on multiple factors such as mass, deceleration, and force of adhesion. By understanding these factors and their relationship, we can better predict and explain the outcome of this qualitative collision.