Classical mechanics confusions

[Faiq]

Homework Statement

Q1. What's the reason behind two identical objects interchanging their velocities upon head-on collision?
Why can't just each individual particles just reverse its direction and keep traveling at its original speed? Kinetic energies and momentum would still be conserved.

Q2. Why can't we use the formula of Kinetic energy where kinetic energy is half mass times velocity squared to find kinetic energies of objects whose mass is changing? Is there a way to modify the formula to get the desired output?

 

[DrClaude]

Kinetic energies and momentum would still be conserved.

Are you sure about that?

Q2. Why can't we use the formula of Kinetic energy where kinetic energy is half mass times velocity squared to find kinetic energies of objects whose mass is changing? Is there a way to modify the formula to get the desired output?

How is the mass changing?

 

[Delta2]

Q1: No, momentum is not conserved in your scenario. Momentum is a vector, it has magnitude and direction, and though in your scenario the magnitude of the momentum of each particle remains the same, the direction reverses for each particle, so the direction of the total momentum also reverse, so momentum is not conserved.

Q2: Not sure here, I think you can use the formula for kinetic energy but you can't use the work-energy theorem.

 

[Stephen Tashi]

Q1. What's the reason behind two identical objects interchanging their velocities upon head-on collision?
Why can't just each individual particles just reverse its direction and keep traveling at its original speed? Kinetic energies and momentum would still be conserved.

I don't understand the distinction you are making between "interchanging their velocities" and "each individual ... just reverse direction...". If particle A is assigned the velocity of particle B after the collision, does particle A "just reverse direction" ?

Q2. Why can't we use the formula of Kinetic energy where kinetic energy is half mass times velocity squared to find kinetic energies of objects whose mass is changing?

What is your definition of "object"? The state of an object in classical mechanics includes a description of its mass. If the "object" represents a stick and you break it in half, which of the halves is the original "object"? It would help if you gave an specific example of a problem in classical mechanics where an "object" has a changing mass.

 

[hilbert2]

^ I think he means something like an accelerating rocket that is losing mass by combusting its fuel...

 

[Faiq]

Q1: No, momentum is not conserved in your scenario. Momentum is a vector, it has magnitude and direction, and though in your scenario the magnitude of the momentum of each particle remains the same, the direction reverses for each particle, so the direction of the total momentum also reverse, so momentum is not conserved.

Q2: Not sure here, I think you can use the formula for kinetic energy but you can't use the work-energy theorem.

thank you for question 1

 

[Faiq]

I don't understand the distinction you are making between "interchanging their velocities" and "each individual ... just reverse direction...". If particle A is assigned the velocity of particle B after the collision, does particle A "just reverse direction" ?
What is your definition of "object"? The state of an object in classical mechanics includes a description of its mass. If the "object" represents a stick and you break it in half, which of the halves is the original "object"? It would help if you gave an specific example of a problem in classical mechanics where an "object" has a changing mass.

An object which is constantly gaining or losing mass, like spaceship losing mass by combusting its fuel

 

[jbriggs444]

An object which is constantly gaining or losing mass, like spaceship losing mass by combusting its fuel

So you are asking why we cannot use $E=\frac{1}{2}mv^2$ to determine the current kinetic energy of a rocket ship that is losing mass as it fires its thrusters?

We can use $E=\frac{1}{2}mv^2$ to determine the kinetic energy of such a rocket. That formula will give a perfectly correct answer.

But if you add the starting kinetic energy of the rocket to the chemical energy in the fuel being burned you get a result that is (almost always) larger than the resulting kinetic energy of the rocket. There is some missing energy. Can you imagine where that "missing" energy might have gone?

 

[Faiq]

Energy losses to such as friction?

 

[Faiq]

Like if I have a problem like
A rocket has a mass of 16000kg. It loses mass at a rate of 15kg/s. It maintains a steady velocity of 200m/s. What is the Kinetic energy of the rocket?
What will be the value of m here?

 

[jbriggs444]

Energy losses to such as friction?

That is not it. The rocket can be in space and the only force can be that of its own thrust. What about the kinetic energy of the exhaust stream?

Like if I have a problem like
A rocket has a mass of 16000kg. It loses mass at a rate of 15kg/s. It maintains a steady velocity of 200m/s. What is the Kinetic energy of the rocket?
What will be the value of m here?

What will be the value of m when? The mass of the rocket is changing over time. The kinetic energy of the rocket at a particular time depends on its mass at that time.

 

[Faiq]

Yes that's what I was talking about. So is there a specific kind of energy for objects whose mass changes over time. Like kinetic energy is related with changes in motion, is there a type of energy related to changes in mass?

 

[jbriggs444]

Yes that's what I was talking about. So is there a specific kind of energy for objects whose mass changes over time. Like kinetic energy is related with changes in motion, is there a type of energy related to changes in mass?

Kinetic energy is not specifically related to changes in motion. It is defined by $KE=\frac{1}{2}mv^2$. The velocity there need not change. Nor must the mass be a constant.

 

[Faiq]

Oh okay thanks