Sliding object

[ul92]

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.

 

[kingnero]

When? while sliding down, when freefalling, when accelerating/decelerating, while swinging, in steady state?
Does the object decelerate or stops at all?
What is it you're trying to accomplish?

 

[ul92]

Well, first object slides down, then fly and lastly, because it has been tied, the rope stops it abruptly and it swings down. The max reaction force comes up between freefalling and swinging - at the minor moment when rope is restricting item to fall further.

Any more questions?

 

[kingnero]

The rate of deceleration will predict the force.
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?

 

[ul92]

Mate, While going slope down the object will accelerate rather than decelerate.
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.

 

[kingnero]

Mate, While going slope down the object will accelerate rather than decelerate.

True, but you don't want to know the reaction force at the time your object is sliding down the slope, do you mate?

We are looking for stretch in the rope which is generally called reaction force.

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.

Personally I think vertical acceleration have to be calculated first then the result should be added onto gravity factor.

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 have a question which we used to solve at university but to be fare I become a bit wee rusty on this now

I wonder where that uni would be. Just so I could stay far enough away from there.

 

[KootK]

Fun. If this is for a real thing, you GOTTA share the application. Also, put absolutely no stock in what follows.

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.

 

[BUGGAR]

Why not just use energy equations.
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

 

[KootK]

@Buggar

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.

 

[BUGGAR]

How about just subtracting the friction force from the driving force in the energy equation. Your driving force is, of course, mg, and the friction force is Mu(N), with involvement of all the appropriate sine theta's. I think you will have to add the static and dynamic frictions.
The string will have to have some elasticity or the forces will be infinite.

 

[precast78]

I would just calculate it like if the object was free falling the same distance as that setup and figure out the force. The friction force will be an additional factor of safety.

 

[paddingtongreen]

If you learned how to do this in uni, it must have been Hogwarts because it certainly isn't one for Muggles like me. You could assume the C of F as 1.0 or 0. If it is 1.0, nothing happens if it is zero, the thing slides down under the force component parallel to the slope until it jumps off, then it falls freely and you have to magically obtain a beginning length for the string.

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