# Taylor Mechanics Section 3.2

• Bashyboy
In summary, the section discusses the momentum of a moving rocket with a changing mass. It explains that at time t, the momentum of the rocket is P(t) = mv and at a short time later t+dt, the mass is (m + dm) and the momentum is (m+dm)(v+dv). The ejected fuel has a negative mass (-dm) and a velocity v - vex. The total momentum at t+dt is calculated by subtracting the momentum of the fuel from the rocket's momentum. However, the book does not account for the momentum of the fuel at time t, which can be represented as (m+dm)v - (dm)v. This is because before the fuel burns, it has

#### Bashyboy

Hello,

I am reading section 3.2, concerning the analyzation of a moving rocket with a changing mass. (I couldn't find a preview of the book in google books, so hopefully someone out there has this textbook.) Here is an except from the book, but be warned that I am adding notes in brackets:

"At time t, the momentum [of the rocket] is P(t) = mv [m and v are the mass and velocity of the rocket at time t]. A short time later at t + dt, the rockets mass is (m + dm), where dm is negative, and its momentum is (m+dm)(v+dv). The fuel ejected in the time dt has mass (-dm) and velocity v - vex [v is the velocity of the rocket as viewed by some stationary person on earth, and vex is rate at which the fuel flows out, relative to the rocket]. Thus, the total momentum (rocket plus the fuel just ejected) at t + dt is
P(t+dt) = (m + dm)(v+dv) - dm(v - vex)."

As one might notice, as I did, they accounted for the momentum of the fuel at time t+dt, which is - dm(v - vex) (there's a negative because the momentum is in the opposite direction); but at time t, they did not, for the expression is P(t) = mv. Where is the momentum term for the fuel at time t?

Bashyboy said:
Where is the momentum term for the fuel at time t?

Before it burns, the fuel has the same velocity as the rocket, so its momentum is part of the P(t) = mv.

You could write
(m+dm)v - (dm)v
if you really want to separate out "the momentum of the fuel of mass -dm that you are going to burn next" and "the momentum of everything else". But of course (m+dm)v - (dm)v = mv.

Isn't the velocity of the fuel at any instant v - vex?

The fuel has velocity v before it burns, and v - vex after it burns.

At time t, the bit of fuel with mass dm hasn't burned yet. At time t+dt, it has burned.

Hello,

Thank you for sharing your thoughts on section 3.2 of the book. It is important to note that the momentum of the fuel at time t is accounted for in the term (v - vex). This term represents the velocity of the fuel relative to the rocket, which is the momentum of the fuel at time t. Additionally, the term -dm represents the change in mass of the rocket due to the fuel being ejected, and is also accounted for in the total momentum at time t + dt. This is a common approach in physics when dealing with systems where the mass is changing, as it allows for a more accurate analysis of the overall momentum. I hope this helps to clarify any confusion.

## 1. What is the main concept of Taylor Mechanics Section 3.2?

The main concept of Taylor Mechanics Section 3.2 is the study of motion and forces in a system using the principles of Newton's laws of motion and conservation of energy.

## 2. How does Taylor Mechanics Section 3.2 differ from other sections?

Taylor Mechanics Section 3.2 specifically focuses on the application of Newton's laws and energy conservation to problems involving systems of particles, rather than single particles.

## 3. What are some common topics covered in Taylor Mechanics Section 3.2?

Some common topics covered in Taylor Mechanics Section 3.2 include equilibrium, friction, circular motion, and work and energy.

## 4. How can I apply the concepts learned in Taylor Mechanics Section 3.2 to real-world situations?

The concepts learned in Taylor Mechanics Section 3.2 can be applied to real-world situations such as analyzing the forces and motion of objects in machines, understanding the physics behind sports and games, and predicting the behavior of celestial bodies.

## 5. What are some recommended resources for further studying Taylor Mechanics Section 3.2?

Some recommended resources for further studying Taylor Mechanics Section 3.2 include textbooks, online lecture videos, practice problems and solutions, and interactive simulations or demonstrations.

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