MECHANICS - DIFFICULT PULLEY PROBLEM - Please help

[romanalgo]

[FONT=arial, sans-serif]I have this pulley question (see attachment) for which I need to find the coordinate of the mass m1 as a function of time - x(t). Important things to note:

[/FONT][FONT=&quot]1) this is rigidly connected to the wall at height H.
2) there is string of length L - so there is tension
3) there is kinematic constraint .
4) x is the coordinate of the mass measured from that point
5 Pulley is massless and fixed


[/FONT]

 

[Steven G]

I have this pulley question (see attachment) for which I need to find the coordinate of the mass m1 as a function of time - x(t). Important things to note:

1) this is rigidly connected to the wall at height H.
2) there is string of length L - so there is tension
3) there is kinematic constraint .
4) x is the coordinate of the mass measured from that point
5 Pulley is massless and fixed

Where are you stuck? What have you tried? Please show us your work so we know where you need help. Thank you.

 

[romanalgo]

Where are you stuck? What have you tried? Please show us your work so we know where you need help. Thank you.

I have drawn the free body diagrams. But dont know how to go from there, please help.

 

[Deleted member 4993]

I have drawn the free body diagrams. But dont know how to go from there, please help.

Are you supposed to calculate y(t) and x(t) as the connected blocks move under the force of gravity?

Is there friction involved?

Please share your free-body diagram and kinemetic equations?

 

[HallsofIvy]

The downward force on mass 2 is \(\displaystyle m_2g\). The fact that the pulley is at height h means that there will be both vertical and horizontal force on mass 1. The horizontal force is \(\displaystyle \frac{m_2gx}{\sqrt{x^2+ h^2}}\) and the vertical force is \(\displaystyle \frac{m_2gh}{\sqrt{x^2+ h^2}}- m_1g\). The vertical force will be important if there is friction because then there will be a retarding horizontal force equal to the coefficient of friction times that vertical force.