Question about collisions -- Knife point piercing a ball of clay

[Decaff]

I have a question regarding the collision of two objects, specifically something heavy falling on something with a point. For example, if a 50lb ball of clay fell from 10 meters onto the point of a knife, would the knife's point have to withstand the entire force of the clay before the blade could plunge into the clay?

 

[berkeman]

Welcome to PF.

What are your thoughts so far? What do you know about collisions between deformable materials?

 

[Dale]

withstand the entire force of the clay

What does this mean?

 

[Decaff]

What does this mean?

I don't know a whole about physics, so bear with me.
F = M*A, so the falling clay has force. My question is, would the tip of the knife be subject to all of that force or just a portion of it before the knife dug into the clay.

 

[berkeman]

I don't know a whole about physics, so bear with me.
F = M*A, so the falling clay has force. My question is, would the tip of the knife be subject to all of that force or just a portion of it before the knife dug into the clay.

What if the ball were made of high strength steel instead of clay? Can you say what you think that difference would make?

 

[Decaff]

Welcome to PF.

What are your thoughts so far? What do you know about collisions between deformable materials?

Well, I'm not very experienced with physics, and this topic comes from a conversation I had with a friend. I know F = M*A, so the falling clay has Force. My friend thinks the knife point would be hit by all that force, while I thought the smaller area of the knife point would only subject it to some of the force before it digs into the clay.

 

[Decaff]

What if the ball were made of high strength steel instead of clay? Can you say what you think that difference would make?

I think the hardness and density of the steel ball would be too much for the knife to handle.

 

[berkeman]

Exactly! Why? What is the difference between the steel ball and the clay ball?

Also, have a look at this information from Wikipedia about the most relevant consideration, which is "impulse", not just "force". The impulse involves the force exerted over time (shorter time means higher impulse):

https://en.wikipedia.org/wiki/Impulse_(physics)

 

[Decaff]

Exactly! Why? What is the difference between the steel ball and the clay ball?

Also, have a look at this information from Wikipedia about the most relevant consideration, which is "impulse", not just "force". The impulse involves the force exerted over time (shorter time means higher impulse):

https://en.wikipedia.org/wiki/Impulse_(physics)

I assume the knife fairs worse against the steel ball because it's heavier, which increases the force. As for the impulse, from my understanding, the steel ball would have a high impulse while the clay ball might have a lower impulse.

 

[berkeman]

I assume the knife fairs worse against the steel ball because it's heavier, which increases the force.

I was assuming clay and steel balls of equal mass, since your question seems to be about the deformability of the falling mass.

As for the impulse, from my understanding, the steel ball would have a high impulse while the clay ball might have a lower impulse.

Yes. When one or both of the masses in a collision can deform, that spreads the impact time over a wider time interval, which lessens the impulse and the severity of the collision. That's why cars are designed with "crush zones", to lower the peak forces felt by occupants of the vehicle during collisions. Lower peak forces translate directly into less severe injuries for vehicle occupants, and similarly, into less severe crush forces on the knife in your falling clay ball scenario.

Does that make sense?

 

[Decaff]

I was assuming clay and steel balls of equal mass, since your question seems to be about the deformability of the falling mass.Yes. When one or both of the masses in a collision can deform, that spreads the impact time over a wider time interval, which lessens the impulse and the severity of the collision. That's why cars are designed with "crush zones", to lower the peak forces felt by occupants of the vehicle during collisions. Lower peak forces translate directly into less severe injuries for vehicle occupants, and similarly, into less severe crush forces on the knife in your falling clay ball scenario.

Does that make sense?

If the balls are equal mass, then the steel ball would deform less, causing more force in the collision due to the objects not giving any "leeway," similar to the "Crush Zones" of cars. But the Clay ball being softer, gives way to the knife, which means less force is applied?

 

[berkeman]

Force over time. Impulse...

 

[Decaff]

Thanks, I think I have it down now.
Impulse affects the peak forces.

 

[Dale]

F = M*A, so the falling clay has force. My question is, would the tip of the knife be subject to all of that force or just a portion of it before the knife dug into the clay

The $F$ in $F=ma$ is not a single force. It is the net force. The net force on the clay will almost always be different from the force on the tip of the knife.

 

[nasu]

F = M*A, so the falling clay has force.

You have the wrong idea about force. Force is not something that an object has. Actually there is no force if you have only one object. The force is describing the interaction between two objects. The falling ball, before touching the knife, only interacts with the Earth so there is a force describing this, the weight of the ball. And an equal and opposite force acting in the Earth. If we neglect the interaction with te air, this weight is the net force and will determine the ball's acceleration.

As the ball touches the knife it interacts with the knife so there will be another force acting on the ball (and on the knife) due to this interaction. This force may increase and decrease during the interaction but it is not something that the ball had before the interaction and is now applying it to the knife. The net force on the ball will now be composed from the weight and the contact force with the knife and this will determine the acceleration of the ball by Newton's second law.

The quantities that may work closer to your idea are kinetic energy and momentum. Those can be associated with a single object so it make sense to say "the ball has kinetic energy" or "the ball has momentum". But not "the ball has a force".