Ask Your Question
0

physics problem solving with differential equations

asked 2013-02-16 07:17:39 -0600

sps gravatar image

Hi, I'm new in this community.

I want to solve a physic problem which requires differential equation system solutions.

I don't know if my equations are correctly set. Any suggestion is good. My problem is described by this image: http://img805.imageshack.us/img805/70...

I have two masses (1/3m the first, 2/3m the second) linked with a rope. The rope is free to slide around a nail (the big black point in the image). The image shows the starting condition: a man keeps the first mass stopped and so the rope is kept stretched by the second mass.

I search three functions describing the kinematics of two masses after the man will leave the fist mass: vertical movement of mass A y(t), vertical movement of mass B j(t), and horizontal movement of mass B x(t).

My Cartesian reference system is x-y system in the image.

I have to solve the following equations: 1) -2/3mg+T=2/3md2/dt2_y 2) -1/3mg+Sy=1/3md2/dt2_j 3) Sx=1/3m*d2/dt2_x 4) abs(T)=sqrt(Sx^2+Sy^2) 5) abs(y(t))=sqrt(x(t)^2+j(t)^2)

From the forth and the fifth equations I obtain two equations, so I have 5 equations in 5 unknowns. They are: 1) T force sustaining the second mass 2) Sx x-component of force sustaining the first mass 3) Sy y-component of force sustaining the first mass 4) y(t) position of the second mass 5) x(t) x-position of the first mass 6) j(t) y-position of the first mass

I hope my explanation is clear.

How can I obtain my solutions using Sage?

Thank you very much!!

edit retag flag offensive close merge delete

1 answer

Sort by ยป oldest newest most voted
1

answered 2013-02-16 07:22:26 -0600

sps gravatar image

I want to solve a physic problem which requires differential equation system solutions.

I don't know if my equations are correctly set. Any suggestion is good. My problem is described by this image: http://img805.imageshack.us/img805/70...

I have two masses (1/3m the first, 2/3m the second) linked with a rope. The rope is free to slide around a nail (the big black point in the image). The image shows the starting condition: a man keeps the first mass stopped and so the rope is kept stretched by the second mass.

I search three functions describing the kinematics of two masses after the man will leave the fist mass: vertical movement of mass A y(t), vertical movement of mass B j(t), and horizontal movement of mass B x(t).

My Cartesian reference system is x-y system in the image.

I have to solve the following equations: 1)

  1. List item -2/3mg+T=2/3md2/dt2_y
  2. List item -1/3mg+Sy=1/3md2/dt2_j
  3. List item Sx=1/3m*d2/dt2_x
  4. List item abs(T)=sqrt(Sx^2+Sy^2)
  5. List item abs(y(t))=sqrt(x(t)^2+j(t)^2)

From the forth and the fifth equations I obtain two equations, so I have 5 equations in 5 unknowns. They are: 1. List item T force sustaining the second mass 2. List item Sx x-component of force sustaining the first mass 3. List item Sy y-component of force sustaining the first mass 4. List item y(t) position of the second mass 5. List item x(t) x-position of the first mass 6. List item j(t) y-position of the first mass

I hope my explanation is clear.

How can I obtain my solutions using Sage?

Thank you very much!!

edit flag offensive delete link more

Comments

no one could help me? Is it to difficult this problem?

psp gravatar imagepsp ( 2013-10-24 06:30:59 -0600 )edit

No one could help me anyway? Just suggestions? Nothing?

psp gravatar imagepsp ( 2013-10-29 04:28:34 -0600 )edit

Your Answer

Please start posting anonymously - your entry will be published after you log in or create a new account.

Add Answer

Question Tools

Stats

Asked: 2013-02-16 07:17:39 -0600

Seen: 737 times

Last updated: Feb 16 '13