Newton's 3rd law: action and reaction

[ndriana]

I thought I understood it cause I always had the right answer ever since I learned about it.

But now my friend asked me a question about why does a piece of chalk break if you put a heavy thing on it, say a car.

If we just think about action and reaction, the forces have to be along a vertical. So where are the horizontal forces, that pull the chalk apart, from?

 

[mitch_1211]

I don't there are actually any forces operating in the horizontal direction, the cracking of the chalk comes from either stress or strain (these differ slightly and i can't recall which is which)

obviously there is a certain force that the chalk can withstand, this depends on intrinsic properties such as density, material, and also on length and thickness. When a force is applied that is less that the force required to break the chalk, the normal force simply 'pushes' in the opposite direction and it seems as if the chalk has taken the weight.
If a force is applied that exceeds the breaking force, the normal upwards force can no longer counter the downward weight so the chalk snaps and the 2 new ends (the ones created from the cracking of the chalk)cl will move in the direction of the applied force.

Think of it as a 'tug-of-war' when the normal force can no longer push against the applied force, the applied force wins and so the chalk breaks in that direction (or rather the crack makes its way through the chalk in that direction)

 

[Ken G]

I believe the question is related to one I have pondered-- why do high jumpers run up to the bar instead of just stand at the base and jump? After all, horizontal momentum is not going to help you get higher, you need a vertical force for that and you start with zero vertical speed. But I believe the answer comes from the fact that energy is a scalar quantity (it has no direction), so the goal of the run-up is to generate some kinetic energy, which the muscles can then store, and release in the up-down direction via a vertical action/reaction force on the ground. In short, the kinetic energy helps with the storage of energy (it can be stored faster than it can be dissipated in the muscles). The same thing must hold for a piece of chalk-- the weight pressing down stores some energy in the chalk, such that when the chalk begins to fracture by the effects mitch_1211 described, that energy is released-- but the energy had no direction so can do work via action/reaction pairs in any direction.

Another possible source of the sideways movement doesn't even require energy storage-- just slanted surfaces. Imagine an infinitely rigid cylinder, so it cannot store any energy, but it has a slanted fracture across it. Push down on the top, and that action/reaction pair force between the halves will be perpendicular to the fracture (it's a normal force), so will have a lateral component.

Thus there are several ways that an external force on an object can be connected with internal action/reaction pairs that are not in the same direction as the external force.

 

[Dale]

I thought I understood it cause I always had the right answer ever since I learned about it.

But now my friend asked me a question about why does a piece of chalk break if you put a heavy thing on it, say a car.

If we just think about action and reaction, the forces have to be along a vertical. So where are the horizontal forces, that pull the chalk apart, from?

Actually, this has relatively little to do with Newton's 3rd law and more to do with the transformation properties of tensors. If you "squeeze" chalk along one direction you are loading it in what is called "uniaxial stress". Because of the way the stress tensor transforms, if you look at a plane through the chalk inclined at 45º you will find that the chalk is under shear strain in that direction. In other words, by not applying compression uniformly you are causing shear strains. Chalk is particularly weak in shear (that is why it writes on blackboards) so it fails. It is the very fact that you are not applying the horizontal forces which causes it to fail.

 

[A.T.]

why do high jumpers run up to the bar instead of just stand at the base and jump? After all, horizontal momentum is not going to help you get higher,

You don't only have to reach the height of the bar. You have to fly over it and land on the other side. That alone requires horizontal velocity. The more the better, because it reduces the time you have to spend over the bar.

you need a vertical force for that and you start with zero vertical speed. But I believe the answer comes from the fact that energy is a scalar quantity (it has no direction), so the goal of the run-up is to generate some kinetic energy, which the muscles can then store,

It don't think muscles are storing energy. It is simply kinetic energy that gets converted into potential energy. Just like when you shoot an elastic ball horizontally at an inclined surface, so it bounces upwards. The leg is like an inverted pendulum, that accelerates vertically a mass that initially was moving horizontally. The pendulum here additionally extends during the process.

 

[Ken G]

You don't only have to reach the height of the bar. You have to fly over it and land on the other side. That alone requires horizontal velocity.

Not much though, that's not the reason they run up. I'll bet if you analyze their horizontal speed, you will find that they decelerate dramatically when they jump. So there's a lot of kinetic energy that is disappearing as they "coil" for the leap (as opposed to long jumpers, who of course want to maintain that horizontal speed and really sprint in their runup).

It don't think muscles are storing energy. It is simply kinetic energy that gets converted into potential energy. Just like when you shoot an elastic ball horizontally at an inclined surface, so it bounces upwards.

Yet that's a perfect example of storing energy. That's just what I'm talking about-- though it could be the bones and tendons also that are storing that energy.

The leg is like an inverted pendulum, that accelerates vertically a mass that initially was moving horizontally. The pendulum here additionally extends during the process.

The pendulum maintains a fixed kinetic energy. I'm pretty confident the kinetic energy of a high jumper, at maximum flex beneath the bar, is almost zero.

Anyway, I think DaleSpam's answer is better-- the non-isotropic stress actually generates internal forces in the lateral direction even without any internal energy storage. It bothered me that chalk is not much like a spring. My answer would apply better to the way a grape splatters when you step on it, there's first storage of energy and then conversion to kinetic energy by action/reaction pairs that appear because of the internal stresses, but don't have to line up with the external forces.

 

[A.T.]

- though it could be the bones and tendons also that are storing that energy.

I don't think this is possible to any relevant extend. They are not elastic springs. They will convert it all to heat.

The pendulum maintains a fixed kinetic energy.

Nor really. A pendulum converts kinetic & potential energy back and forth.

 

[Ken G]

I don't think this is possible to any relevant extend. They are not elastic springs. They will convert it all to heat.

Google a photo of a pitcher just about to release a baseball. I think it's a pretty clear image of the kind of storage I'm talking about.

Nor really. A pendulum converts kinetic & potential energy back and forth.

I was referring only to the way the arm forces the bottom to trace an arc. If one wants to include potential energy in the analogy, the situation only becomes even more like what I am talking about-- storage and release of energy.

 

[A.T.]

Google a photo of a pitcher just about to release a baseball. I think it's a pretty clear image of the kind of storage I'm talking about.

No, it's not clear.

 

[Ken G]

Well, I'm sorry, but it's perfectly clear to me. The thing the pitcher is attempting to accomplish is a very cocked arm, which then snaps back and delivers a high velocity pitch. It's an obvlous case of potential energy storage.

 

[dydxforsn]

I always thought it was because although you can reach the same height by just jumping from a standstill, you need a lot of velocity to maintain that height for some set distance so that you can move over an object that you're trying to jump over.

In the case of the pole vault I'm pretty sure that the kinetic energy of the runner is compressed into the pole (the static friction of the pole keeps it from sliding on the ground as it is "loaded up" with energy) and then that potential energy is converted into vertical kinetic energy when the runner used the pole to propel off the ground. I guess this could also apply to the runner's legs in the case of the standard high jump as well.

 

[rcgldr]

chalk breaking

When chalk or any reasonably long object has a side load placed on it there is a bending force on the object, which results in compression on the concave side, and tension on the convex side, and these are forces perpendicular to the load at the point of contact.

high jumper

A high jumper uses his leg similar what would occur if a pole vaulter used a stiff pole with almost no flex (bending). The run up generates kinetic energy, and then the high jumper plants his leg almost straight, if there's any elastic flexing going on, then almost all of it is at the ankle, not at the knee. There's some bending at the hip, but I don't think that generates much height.

 

[A.T.]

A high jumper uses his leg similar what would occur if a pole vaulter used a stiff pole with almost no flex (bending).

Exactly. An inverted pendulum.

 

[Studiot]

The failure mode of the chalk specimen depends upon its shape.

Chalk is a brittle material and a square cross section does indeed fail in diagonal shear under a crushing load.

However if a round piece of blackboard chalk is meant this fails in horizontal tension, not diagonal shear as shown in the attachment.

 

[Drakkith]

For the pole vault questions, this is from wikipedia on pole vaulting:

The goal of this phase [The plant and take-off] is to efficiently translate the kinetic energy accumulated from the approach into potential energy stored by the elasticity of the pole, and to gain as much initial vertical height as possible by jumping off the ground.

See the following link for more: http://en.wikipedia.org/wiki/Pole_vault

In the case of the pole vault I'm pretty sure that the kinetic energy of the runner is compressed into the pole (the static friction of the pole keeps it from sliding on the ground as it is "loaded up" with energy) and then that potential energy is converted into vertical kinetic energy when the runner used the pole to propel off the ground. I guess this could also apply to the runner's legs in the case of the standard high jump as well.

It looks like the energy of the run is converted to potential energy in the pole, while the jump is to get as high off the ground so that the pole can use that stored energy to launch you upwards as far as possible. Also, the pole fits into a sloped "box" that is about 8 inches in depth at the rear wall, which is vertical to stop the pole from moving.

 

[jishitha]

In circular motion of any vehicles or any other particles, which experiences both centripetal and centrifugal forces... Why these two not cancelling?these are in equal and opposite.

 

[Dale]

In circular motion of any vehicles or any other particles, which experiences both centripetal and centrifugal forces... Why these two not cancelling?these are in equal and opposite.

They do cancel in the co rotating reference frame. The centrifugal force does not exist in an inertial frame.

 

[Ken G]

I always thought it was because although you can reach the same height by just jumping from a standstill, you need a lot of velocity to maintain that height for some set distance so that you can move over an object that you're trying to jump over.

Maybe so, but I suspect there's a slowing of the horizontal motion when high jumpers go to jump. It's true they don't sprint up to the bar, so perhaps the slowing is not so much. I agree the pole vaulter does sprint to the bar, it's very clear they are doing that to store potential energy in their pole, so that may be a better example. I feel some of the same principles apply to the high jumper, but perhaps not as clearly.