Taylor mechanics chap3,problem 4

In summary, Taylor mechanics chapter 3, problem 4 focuses on the application of conservation laws to a system of two particles interacting through a central force. The problem involves finding the equations of motion and using energy conservation to solve for the motion of the particles. The solution includes calculating the effective potential and analyzing the motion in terms of the total energy and angular momentum of the system. This problem serves as a useful exercise in applying the principles of conservation laws to understand the dynamics of physical systems.
  • #1
kylinsky
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Homework Statement


two man,each of equal mass m,are standing at one end of a stationary railroad flatcar with frictionless wheel and mass mcar.Find the car's speed if the two men run to the other end of the car and jump off simultaneously with the same speed u(relative to the car)

Homework Equations

The Attempt at a Solution


let vh be the men's speed relative to the ground at the instant they jump off the car.Thus
u= vh+vcar.Since the momentum of the system is conservative,2mvh=mcarvcar

After solving the equations,i got (2mu)/(2m+mcar) ,but i found a different answer from mine on the website http://chriskranenberg.wix.com/taylor-mechanics-solutions.I want to make sure which one is right[/B]
 
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  • #2
kylinsky said:

Homework Statement


two man,each of mass [m][/h],are standing at one end of a stationary railroad flatcar with frictionless wheel and mass [m][/fc].Find the car's speed if the two men run to the other end of the car and jump off simultaneously with the same speed u(relative to the car)

Homework Equations

The Attempt at a Solution


i got (2[m][/h]u)/(2[m][/h]+[m][/fc]) ,but i found a different answer from mine on the website http://chriskranenberg.wix.com/taylor-mechanics-solutions.I want to make sure which one is right[/B]
Your notation is strange. What is, for example, [m][/h] meant to convey?

You'll need to show the details of your own solution, how you arrived at your result. Helpers won't just confirm or deny a given solution for you.
 

What is the problem statement for Taylor mechanics chapter 3, problem 4?

The problem statement for chapter 3, problem 4 in Taylor mechanics is to find the equations of motion for a particle moving in a three-dimensional space under the influence of a central force.

What are the key concepts needed to solve Taylor mechanics chapter 3, problem 4?

To solve this problem, you will need to understand the concepts of central forces, Newton's laws of motion, and vector calculus.

What are the steps to solve Taylor mechanics chapter 3, problem 4?

The steps to solve this problem are: 1. Identify the central force acting on the particle. 2. Use Newton's second law of motion to write the equations of motion in terms of position and velocity vectors. 3. Apply vector calculus to solve for the equations of motion. 4. Solve the equations of motion for position and velocity as a function of time. 5. Check for any special cases or limiting conditions.

What are some real-world applications of the principles used in Taylor mechanics chapter 3, problem 4?

The principles used in this problem have applications in many areas of physics and engineering, such as celestial mechanics, orbital dynamics, and spacecraft trajectory planning.

What are some helpful tips for solving Taylor mechanics chapter 3, problem 4?

Some helpful tips for solving this problem include: - Draw a diagram to visualize the problem and identify key variables. - Make sure to use consistent units throughout the problem. - Understand the properties of central forces, such as their conservative nature and dependence on the distance between the objects. - Practice using vector calculus to solve for equations of motion. - Check your solution for any special cases or limiting conditions to ensure its validity.

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