Sliding object
Sliding object
(OP)
Hi All,
I have a question which we used to solve at university but to be fare I become a bit wee rusty on this now, so would appreciate if someone gives me a hand. Basically, there is an item which travels down the incline under 30 deg and flies out after some point. Need to find out max reaction force in rope.
I have a question which we used to solve at university but to be fare I become a bit wee rusty on this now, so would appreciate if someone gives me a hand. Basically, there is an item which travels down the incline under 30 deg and flies out after some point. Need to find out max reaction force in rope.






RE: Sliding object
Does the object decelerate or stops at all?
What is it you're trying to accomplish?
RE: Sliding object
Any more questions?
RE: Sliding object
I suppose you don't know the amount of stretch the rope will see, nor the time it takes to come to an abrupt stop?
RE: Sliding object
We are looking for stretch in the rope which is generally called reaction force.
Personally I think vertical acceleration have to be calculated first then the result should be added onto gravity factor.
RE: Sliding object
In Europe, not any kind of stretch is ever called a reaction force, but I have no idea what's going on in other parts of the world.
That's a good way to start, your object does have a certain amount of kinetic energy. How far have you gotten using this approach?
Considering your questions,
I wonder where that uni would be. Just so I could stay far enough away from there.
RE: Sliding object
1) Figure your unbalanced force parallel to the ramp. F = m x g x sin(30 deg) - u x m x g x cos(30 deg)
2) Use F = m x a to get the acceleration along the ramp. a = F / m.
3) Use standard equation of motion to get velocity at bottom of ramp, parallel to ramp. v = sqrt(2 x a x L_diag).
4) Split velocity from (3) into vertical and horizontal components. vx, vy1.
5) Add vertical speed gained from free fall at end. vy2 = vy1 + sqrt(2 x g x y_drop).
6) Vector sum final velocity. v = SQRT(vx^2 + vy2^2).
7) Calculate kinetic energy. KE = 1/2 x m x v^2.
8) Equate KE to strain energy in rope at full stop. 1/2 x m x v^2 = 1/2 x P x (P x L_rope) / (A_rope x E).
9) Solve for force in rope, P.
I worry that I've missed something of the dynamic character of the problem here, particularly in step 8.
The greatest trick that bond stress ever pulled was convincing the world it didn't exist.
RE: Sliding object
Potential energy of the mass, mgh, equals elastic strain energy in the rope from which you find the rope tension (reaction). I forgot the strain energy equation, though, something squared over 2 I think.
Bob
RE: Sliding object
With these physics things, there always seems to be a two line solution if you know the right approach. I considered the approach that you outlined but was unsure how to include the energy lost through friction between the sliding object and the ramp (assuming that there is some) in less steps that the solution that I proposed.
If this is real work, I'd recommend using two different methods and verifying agreement between the two.
KootK
The greatest trick that bond stress ever pulled was convincing the world it didn't exist.
RE: Sliding object
The string will have to have some elasticity or the forces will be infinite.
RE: Sliding object
RE: Sliding object
Of course, if you did go to such a magical university that could teach this, then you could read the answer from bowl of water.
Items to be obtained magically: C of F, length of slope, length of string, weight of object, string material characteristics and cross section.
Michael.
"Science adjusts its views based on what's observed. Faith is the denial of observation so that belief can be preserved." ~ Tim Minchin