# Classical mechanics confusions

• Faiq
In summary: There is no "missing energy" in this problem. The kinetic energy of the rocket is always greater than the kinetic energy of the exhaust stream.

## 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?

Faiq said:
Kinetic energies and momentum would still be conserved.

Faiq said:
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?

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.

cnh1995
Faiq said:
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.

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

Delta² said:
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

Stephen Tashi said:
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

Faiq said:
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?

Energy losses to such as friction?

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?

Faiq said:
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?

Faiq said:
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.

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?

Faiq said:
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.

Oh okay thanks

## 1. What is classical mechanics?

Classical mechanics is the branch of physics that studies the motion of macroscopic objects and the forces that act upon them. It is based on the laws of motion and gravitation formulated by Sir Isaac Newton in the 17th century.

## 2. What are the main principles of classical mechanics?

The main principles of classical mechanics are the laws of motion, which state that an object will remain at rest or in motion at a constant velocity unless acted upon by an external force. The other principle is the law of gravitation, which describes the attractive force between two objects with mass.

## 3. How is classical mechanics different from quantum mechanics?

Classical mechanics deals with the motion of macroscopic objects, while quantum mechanics deals with the behavior of subatomic particles. Classical mechanics is deterministic, meaning that the future behavior of a system can be predicted with certainty, while quantum mechanics is probabilistic, meaning that the behavior of particles can only be described in terms of probabilities.

## 4. What are some common misconceptions about classical mechanics?

One common misconception is that classical mechanics only applies to objects on Earth, when in fact it also applies to objects in space. Another misconception is that classical mechanics is entirely replaced by quantum mechanics, when in reality classical mechanics is still used to describe many macroscopic phenomena.

## 5. How is classical mechanics relevant in modern science and technology?

Classical mechanics is still widely used in many fields of science and engineering, including mechanics, thermodynamics, and electromagnetism. It is also the basis for many modern technologies, such as airplanes, cars, and bridges. Without a solid understanding of classical mechanics, many of these advancements would not be possible.