- #1
Carson Birth
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Homework Statement
A point mass, sliding over an even, horizontal plane is bounded on an inextensible, massless thread. During the motion, the thread is pulled by a force F with constant velocity ##v_{o} ## through a hole O. In the beginning (##t_{o} ## = 0) r(##t_{o} ##)=b holds (the length of the thread on the plane is b at the beginning then will get shorter due to the force F as it is pulled through). The initial velocity of the point mass perpendicular to the thread is ##v_{1} ## in ##\phi ## direction, and the angle ##\phi ##(##t_{o} ##) = ##\phi_{o} ## = 0Formulate the system's equation of motion and the equation of constraint forces in polar coordinates. Apply Newton's Law. Also the polar coordinate system is attached to the masspoint with r pointing away from the hole and ##\phi ## pointing toward the trajectory.
Homework Equations
##\overrightarrow{a} ## = (##\ddot{r} ## - r##\dot{\phi}^2 ##) in r direction + (r##\ddot{\phi} ##+2##\dot{r} ####\dot{\phi} ##) in ##\phi ## direction
The Attempt at a Solution
I separated the forces into there respected directions:
##\ddot{\phi} ## direction: mr##\ddot{\phi} ## + m2##\dot{r}####\dot{\phi} ## = 0
r direction: F + mr##\dot{\phi}^2 ## = 0
Now I am pretty sure there isn't any constraint forces, since there is no N force effecting the mass point.
So now I need to create an equation of motion, and from my understanding I need to create one equation. Is it as simple as just solving for ##\dot{\phi} ## and plugging it into the other equation? I had a similar equation where I solved the ##\phi ## direction equation as a differential but it didnt have the 2##\dot{r}####\dot{\phi} ## term with it, it was a gravity force making it very simple to solve. I know this isn't for people to solve my homework so I am just looking for advice on how to get it all set up for the further sub-questions. Any advice would be appreciated :D