Tricky track problem (continued)

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In summary, the conversation discusses a difficult track problem involving Newton's second law and friction. The problem cannot be solved analytically and requires a numerical solution using a program such as Mathematica or through methods like Newton's method or the Runge-Kutta method. The conversation also mentions the importance of the normal force and its dependence on the speed of the collar in solving the problem. The speaker also expresses frustration with the problem and asks for help.
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Ravnus9
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Ok here is the track problem again except this time drawn out with some of my work... this is using Newtons second law... i used microsoft word to draw the track and spring so its a little ruff but you get the idea... still could use some help no matter which way i do it i end up getting one more unknown than i have equations... which is getting extremely old, please help, THANK YOU.
Nathan
 

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Nathan,

This problem is not easy at all, and I wonder how your teacher would solve it. Let us know what he said about the solution.

Energy is not conserved because of friction. The work of friction diminishes the mechanical energy. Friction is proportional to the normal force N, but the normal force depends on the speed of the collar, as the sum of the normal component of gravity and that of the spring force plus the normal force N from the track must be equal to the centripetal force, mv^2/R. The tangential acceleration of the collar is determined by the tangential components of gravity and spring force minus friction, which is proportional to N. You can plug in the expression for N from the previous equation and you get a second order nonlinear differential equation for the angle theta. This equation can be solved only numerically by a program. You find such program in Mathematica but there are others, or you can write yours, applying Newton's method, or the more sophisticated Runge-Kutta method.

ehild
 
  • #3


Hi Nathan,

Thank you for providing more information about the track problem. I can see that you have put in a lot of effort and have used Newton's second law to try and solve it. It can definitely be frustrating when we end up with more unknowns than equations, but don't give up just yet. There are a few things we can try to help us solve this problem.

Firstly, make sure you have clearly identified all the forces acting on the object on the track. This includes the force of gravity, the normal force, and the force of the spring. Also, don't forget about the friction force, which may also be present depending on the surface of the track.

Secondly, try breaking down the problem into smaller parts. Instead of trying to solve the entire track at once, focus on one section at a time. This may help you to better understand the forces and equations involved.

Lastly, don't be afraid to ask for help from a teacher or classmate. Sometimes a fresh pair of eyes can help us see things that we may have missed. Keep practicing and don't give up, you'll get there eventually. Good luck!
 

1. What is the "tricky track problem"?

The tricky track problem is a mathematical puzzle that involves a circular track with two trains traveling in opposite directions at different speeds. The goal is to determine the location of a point on the track where the two trains will collide.

2. How do you solve the tricky track problem?

There are several approaches to solving the tricky track problem, but the most common method involves setting up and solving a system of equations based on the given information about the trains' speeds and starting positions. Other methods, such as using graphical representations or programming algorithms, can also be used.

3. What are the key factors that affect the solution to the tricky track problem?

The key factors that affect the solution to the tricky track problem include the speeds of the two trains, the direction they are traveling, and their starting positions on the track. The track's length and shape can also play a role in the difficulty of the problem.

4. Is there a general formula for solving the tricky track problem?

No, there is not a general formula that can be used to solve the tricky track problem. Each scenario will have unique variables and conditions that require a specific approach to find the solution. However, there are common strategies and techniques that can be applied to different versions of the problem.

5. What are some real-world applications of the tricky track problem?

The tricky track problem has applications in various fields, such as transportation, logistics, and scheduling. For example, it can be used to optimize train schedules or determine the best starting positions for runners in a race. It also has connections to physics, as it involves concepts such as relative velocity and collision detection.

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