Thread: Relationship of energy and momentum

What is the relationship between kinetic energy and momentum?

I'm thinking of things like a bullet hitting a stationary object. How much momentum is transfered and how much energy is transfered? How can you control these amounts? Are these things related? Does energy cause momentum and can momentum result in energy? What is the difference between pushing someone and punching someone? I imagine a push transfers more momentum while a punch transfers more energy. What is the constant variable, mass? Meaning, whether I'm pushing or punching, my mass stays the same.

The relationship can be seen in the formula for momentum (mass times velocity) and for kinetic energy (1/2 mass times the square of the velocity). Certainly they are related, but they are not the same.

In a collision between a bullet and a target, you have to consider whether the bullet stays in the target, passes through, or bounces off. If the bullet is absorbed by the target, then energy is not conserved. This is called an inelastic collision. Well, energy is always conserved but it changes from kinetic energy to heat, so it can't be used to find the final velocity after collision. If the "bullet" bounces off the target, it is called an elastic collision. If you know that the collision is elastic (no loss of KE) then you can use conservation of energy in your calculations. Momentum is always conserved.

A heavy, slow moving object has lots of momentum, as compared to a small, fast object of equal energy. This is because the energy increses as the square of the velocity, but momentum is just proportional to velocity.

If we are talking about bullets, there are different schools of thought among big game hunters as to whether momentum or energy is more important. Hunters of large animals like elephant and cape buffalo tend to prefer the heavy bullets. The momentum will carry the bullet deeper, whereas a faster lighter bullet may tend to expend its energy before reaching the vitals. If the game is smaller, you probably want a faster lighter bullet that will transfer its energy before passing through the animal.

Sorry about locking the thread. I don't know how I did that.

Originally Posted by DaBOB

What is the difference between pushing someone and punching someone? I imagine a push transfers more momentum while a punch transfers more energy. What is the constant variable, mass? Meaning, whether I'm pushing or punching, my mass stays the same.

Your mass, energy and momentum will all change. And they will all be conserved within the closed system you are operating withing.

In my experience, though I suppose my use of terms could be wrong, a strike tends to transfer either more momentum or more energy (as in one is generally more than the other). This is controllable.

Originally Posted by Harold14370

The relationship can be seen in the formula for momentum (mass times velocity) and for kinetic energy (1/2 mass times the square of the velocity). Certainly they are related, but they are not the same.

In a collision between a bullet and a target, you have to consider whether the bullet stays in the target, passes through, or bounces off. If the bullet is absorbed by the target, then energy is not conserved. This is called an inelastic collision. Well, energy is always conserved but it changes from kinetic energy to heat, so it can't be used to find the final velocity after collision. If the "bullet" bounces off the target, it is called an elastic collision. If you know that the collision is elastic (no loss of KE) then you can use conservation of energy in your calculations. Momentum is always conserved.

Can kinetic energy turn into something other than heat? Say you hit a target with your fist. Your fist stays at the point of impact and the target moves. Where does the kinetic energy go? Say the target has little breakable things inside (i.e. organs). Can those things absorb the kinetic energy? Is it as heat or motion? Momentum is what moves the target? Or do both momentum and kinetic energy move the target?

I realize the difference between these two concepts but they can both involve movement and I am assuming they can both transfer movement from one object to another.

Originally Posted by Harold14370

A heavy, slow moving object has lots of momentum, as compared to a small, fast object of equal energy. This is because the energy increses as the square of the velocity, but momentum is just proportional to velocity.

So these two objects an have the same energy but unequal momentum. Can they have the same momentum with unequal energy. I can't think of such an example.

Originally Posted by Harold14370

If we are talking about bullets, there are different schools of thought among big game hunters as to whether momentum or energy is more important. Hunters of large animals like elephant and cape buffalo tend to prefer the heavy bullets. The momentum will carry the bullet deeper, whereas a faster lighter bullet may tend to expend its energy before reaching the vitals. If the game is smaller, you probably want a faster lighter bullet that will transfer its energy before passing through the animal.

But, both momentum and energy are causing damage correct? Maybe I need more sleep, because this is totally screwing with my head.

So, it seems that more mass will add to momentum more than energy, while velocity will add more to energy than momentum?

Easiest way to think about it.
Momentum of the whole system is always conserved, ie product of the initial velocities and masses is equal to final product of velocities and masses.
Kinetic energy, on the other hand, can easily transform to potential energy. Say a bouncing rubber ball hits the ground, at impact, its kinetic energy is transformed to potential by the elasticity of the ball ( and heat ), and the potential energy in turn, becomes kinetic again in the bounce. It followes the law of least action where action is the sum over the path of the difference between kinetic and potential energies ( see Lagrange ).

Originally Posted by DaBOB

In my experience, though I suppose my use of terms could be wrong, a strike tends to transfer either more momentum or more energy (as in one is generally more than the other). This is controllable.

I don't quite know what you are asking.

Can kinetic energy turn into something other than heat? Say you hit a target with your fist. Your fist stays at the point of impact and the target moves. Where does the kinetic energy go? Say the target has little breakable things inside (i.e. organs). Can those things absorb the kinetic energy? Is it as heat or motion? Momentum is what moves the target? Or do both momentum and kinetic energy move the target?
I realize the difference between these two concepts but they can both involve movement and I am assuming they can both transfer movement from one object to another.

The kinetic energy can be transferred to the target. In an inelastic collision between a moving and a stationary objects, the two objects are both moving after the collision. If you calculate the KE of the system after the collision, you will find that it is less than that of the moving object before the collision. We interpret this as the energy being converted from KE to some other form of energy. In an elastic collision, the initial and final KE are equal.

So these two objects an have the same energy but unequal momentum. Can they have the same momentum with unequal energy. I can't think of such an example.

Yes, they can have the same energy and unequal momentum. Just choose m1, m2. v1 and v2 such that (1/2)m1*v1^2=(1/2)m2*v2^2 . If m1 is not equal to m2, then you will find that the momentum m1v1 is different than momentum m2v2.

But, both momentum and energy are causing damage correct? Maybe I need more sleep, because this is totally screwing with my head.

So, it seems that more mass will add to momentum more than energy, while velocity will add more to energy than momentum?

The bullet hitting the target causes the damage. Momentum and energy are just numbers we calculate that can help us predict what will happen, and compare what happens when there are different masses and velocities. The best way to see how that is done is to work through some examples, such as in this tutorial.
Momentum

Originally Posted by DaBOB

So these two objects can have the same energy but unequal momentum. Can they have the same momentum with unequal energy. I can't think of such an example.

Dont forget sound. You consider the objekts here in the collision but they also make a sound that goes out of the system of things. A sound has never been meassured with a thermometer to my knowledge so for regarding between objekts in a collision you can,t count it as a raise of temperature. Or an increased kinetic energy for a set of billardballs could also be regarded as a raise of potential thermic energy for the game (as a raise in temperature).

Sound and heath can,t be kept in the system of the collision but go out of the system. The objekt for which the kinetic change is least mostly will make the most sound and will deform or get damaged the most also.

If the materials behave perfectly elastic I don,t even think there is any heath. Heath means damage or other permanent deformation as hitting a block of clay. This deforms the clay but hardly damages it. It only damages the shape without anything breaking or tearing because it is sand in water.

Originally Posted by Harold14370

Originally Posted by DaBOB

In my experience, though I suppose my use of terms could be wrong, a strike tends to transfer either more momentum or more energy (as in one is generally more than the other). This is controllable.

I don't quite know what you are asking.

I think I started writing something and forgot to finish. I was just thinking about martial arts. Sometimes we strike in a way that makes the opponent move, and sometimes in a way that doesn't make them move but just really hurts. If I had a question it would be what "forces" are causing these two situations? Force vs K-energy?

Originally Posted by Harold

Can kinetic energy turn into something other than heat? Say you hit a target with your fist. Your fist stays at the point of impact and the target moves. Where does the kinetic energy go? Say the target has little breakable things inside (i.e. organs). Can those things absorb the kinetic energy? Is it as heat or motion? Momentum is what moves the target? Or do both momentum and kinetic energy move the target?
I realize the difference between these two concepts but they can both involve movement and I am assuming they can both transfer movement from one object to another.

The kinetic energy can be transferred to the target. In an inelastic collision between a moving and a stationary objects, the two objects are both moving after the collision. If you calculate the KE of the system after the collision, you will find that it is less than that of the moving object before the collision. We interpret this as the energy being converted from KE to some other form of energy. In an elastic collision, the initial and final KE are equal.

Mulling....

Originally Posted by Harold

So these two objects an have the same energy but unequal momentum. Can they have the same momentum with unequal energy. I can't think of such an example.

Yes, they can have the same energy and unequal momentum. Just choose m1, m2. v1 and v2 such that (1/2)m1*v1^2=(1/2)m2*v2^2 . If m1 is not equal to m2, then you will find that the momentum m1v1 is different than momentum m2v2.

duh...

Originally Posted by Harold

But, both momentum and energy are causing damage correct? Maybe I need more sleep, because this is totally screwing with my head.

So, it seems that more mass will add to momentum more than energy, while velocity will add more to energy than momentum?

The bullet hitting the target causes the damage. Momentum and energy are just numbers we calculate that can help us predict what will happen, and compare what happens when there are different masses and velocities. The best way to see how that is done is to work through some examples, such as in this tutorial.
Momentum

So, through a well coordinated, full body movement you could add more mass to the equation right? Rather than just using the mass of a fist for example. I wonder if you can add more mass than of your body alone? If one object is a stationary object on the earth, that creates velocity through a coordinated movement of it's own structure (as in a human body) could it use some mass of the earth to increase it's momentum?

So the amount of damage a system takes is more about the size and composition of that system. Which would be why certain strikes are meant for certain areas. Does Force come into this somehow. I guess I'm trying to figure out what terms are best used to describe the exchange of blows in a hand to hand fight. I imagine all of them would but some I'm having a harder time with. Mostly energy now. When I think of momentum I think of something that can start and stop. If I'm running I can lower my momentum by slowing down, and I can even stop it by stopping. Energy on the other hand is this abstract thing that turns into something else when I start or stop. I can see how an object with force or momentum could damage something in a collision but I don't understand where the energy goes or how it can damage something. Maybe it's because I read someone else's attempt to describe this and they said what causes damage is energy "because it travels further into the body." I don't get that at all. Energy is not a thing that can travel through the body, is it?

Still thinking...

So, through a well coordinated, full body movement you could add more mass to the equation right? Rather than just using the mass of a fist for example. I wonder if you can add more mass than of your body alone? If one object is a stationary object on the earth, that creates velocity through a coordinated movement of it's own structure (as in a human body) could it use some mass of the earth to increase it's momentum?

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Momentum is used from where and when a system runs as "by itself". For instance for billard it can start with the liear momentum of a stick where the billardplayer "throws" the stick to the ball. Between transferring energy to the stick and touching the ball there is a pause where the stick moves linear. From there the billardplayer doesn,t add more energy. Not to push and not to acellerate or decelerate the stick. From there you can use P=MV for stick and then see how it continues further in the balls and to the sides. Another option is a combined action ; based on using the momentum of the stick and accelerate through during contact. Acccelerate through can also be decreasing the normal deceleration from contacting a ball.

Accelerate or not is not the real critical point for the distinction. The distinction is whether or not the player still transfers energy when the ball is allready contacted (and he contacting the stick). For this part the stick can be considered as a medium between the billiard player and the ball to transfer energy to the ball.