Dynamics Coursework; Velocity/Acceleration/Kinetic Friction

AI Thread Summary
The discussion centers on solving a dynamics problem involving a concrete block and a log on a ramp. In Case 1, the user has derived two equations related to the forces acting on the block and log but is struggling with three unknowns. They seek guidance on how to solve these equations to determine the velocity and acceleration of the block as it hits the ground. The user also plans to tackle Cases 2 and 3 later but is currently focused on finding a solution for Case 1. Assistance with the equations and problem-solving approach is requested to move forward.
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Homework Statement


The 125kg concrete block A is released from rest in the position shown and pulls the 200kg log up the theta=30degrees ramp.

Case 1: if the coefficient of kinetic friction between the log and the ramp is Uk=0.5
(a) Find the magnitudes of velocity and acceleration of the block A as it hits the ground at B

Case 2: If it is changed to a log with 400kg, consider kinetic friction between the log and ramp Uk=0.5. Determine the value of the critical slope (theta), that if theta is larger than this value, the log will slip down when the concrete block A is released.

Case 3: If theta=30degrees and it is changed to a log of 400kg, determine the value of the friction coefficient (the critical friction coefficient) that would result in a zero acceleration of the block.


The Attempt at a Solution


Attachments:
'pic' shows a diagram of the problem
'001' shows my cable and FBD for how i have set up my equations
'002' shows my working so far for the first question

Attempts:
Case 1: I have achieved 2 equations as shown in 002
0.5(173.205)-2T+200sin30=(200/9.8)Ac
or 186.6025-2T=(200/9.8)Ac
and 125-T=(125/9.8)Aa

I currently have 2 equations with 3 unknowns, and don't quite know how to approach that.
For Case 1, I simply have to work out those 3 variables and then find velocity of Block A using Aa and fall distance, but really need a little assistance working out those set of equations.

Am currently working on other problems until I can get Case 1 done, then I will post attempts at Case 2 and 3, but if anyone can allude as to how I should approach them when I get there, that would be fantastic too.

Thankyou!
 
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Replying because it doesn't seem that the attachments worked.
 

Attachments

  • pic.jpg
    pic.jpg
    7.2 KB · Views: 1,145
  • 001.jpg
    001.jpg
    4.4 KB · Views: 1,340
  • 002.jpg
    002.jpg
    6.3 KB · Views: 1,281
I also found the third equation to use as 0=2Aa+2Ac.

Using this I found T, and substituted it into find Aa and Ac.
However, by this method Aa and Ac and equal with opposite signs (as I should have predicted from the above formula). This is incorrect, so I'm stumped again.
 
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