The following was an opening question with the Engineer to see if he was capable of solving Incline Plain relationships. He passed.
There are equations concerning only the causeway, and they are informative. I will post them as well asap. I will not be answering, and squabbling about any questions, as I need to construct a CAD drawing for a barge stress analysis. There will be plenty of time for that.
Thanks a lot for your email.
I’ve seen the exercise example you sent me, which is very straight forward.
The double ramp equilibrium can be considered in two different configurations:
1.With Friction between the boxes and the ramp
Of course the second option is just theoretical, due to the fact that it’s impossible to reach a frictionless condition unless using very high density lubricants, air cushion effects, magnetic fields etc…
I’ve considered the first option only, due to the considerations I’ve done above with regards to the friction.
Please find attached a simple powerpoint document with the solution you requested.
It could look very weird that a mass of only 60lbs could balance a mass of 100.000lbs, but the explanation is related to the fact that the friction component of the force generated by the mass A is more than an order magnitude higher than the weight component, therefore it takes only a small mass B to reach stable equilibrium.
Please let me know if that makes sense to you.
The linear force along the ramp changes for BOTH weights proportionally as you change the angle. This means that the ratio of the linear forces generate by each weight remains the same.
A 1 ton weight generates about 160 lb of linear force on a 4.6 degree ramp.
A 0.25 ton weight generates about 40 lb of linear force on that 4.6 degree ramp.
The ratio is 160/40 = 4, just as it is for the ratio of the gross weights.
The same 1 ton weight generates about 347 lb on a 10 degree ramp.
The same 0.25 ton weight generates about 87 lb on that 10 degree ramp.
The ratio is 347/87 = 4, just as it was with the other angle.
So changing the angle lessens the linear forces generated by BOTH weights proportionally.
Edited 1 time(s). Last edit at 28-May-18 15:39 by Steve Clayton.