How to Calculate the Shortest Chain Sling Length for Lifting a Bin?

[crashdirty86]

Okay so I am stuck on this problem.

A moveable bin and its contents have a combined weight of 2.8 kN. Determine the shortest chain sling ACB that can be used to lift the loaded bin if the tension in the chain is not to exceed 5 kN.

So the picture given is a crate with h = 0.7m and base 1.2m with the corners labeled A and B.

Point C is above, centered of the crate between A and B with the connected chain to another. Point C is the location of interest being as this is where all the forces are acting.

My problem lies within finding this shortest length for the chain sling. I have drawn my FBD by trying to resolve my forces into components, I just lack the values for the angles. I'm sure with some basic geometry I will get this values. Also since I am dealing with a max force, am I to assume that the vertical force acting along the y-axis of point C is to be the 5 kN?

If anyone can give some advice, I would be greatly appreciative. I do not need an answer drawn out, just a little motivation that I am on the right track. Thanks!

 

[Simon Bridge]

I ... lack the values for the angles.

These will be related to the dimensions of the chain-sling. Let the length of the chain, from A to C to B, be L. Can you find an equation relating the angles to this length?

am I to assume that the vertical force acting along the y-axis of point C is to be the 5 kN?

The 5kN is the maximum tension allowed in the chain.

In order to lift the bin, the is a minimum total vertical force. What is it?
What other forces contribute to the tension?

 

[crashdirty86]

Can you find an equation relating the angles to this length?The 5kN is the maximum tension allowed in the chain.

In order to lift the bin, the is a minimum total vertical force. What is it?
What other forces contribute to the tension?

By letting ABC be L, I guess I can then say that L/2 and the height give me the value for two legs of a triangle. Using the inverse tangent function would then give me the angle that I would need.

As for the forces acting at point C, there would be the two tensions, AC & BC and the upward force acting at this point. I feel like I am neglecting the gravitational force of the bin though?

 

[crashdirty86]

Okay I have figured it out now. I found that point C the weight of the bin is evenly distributed as vertical force components to AC and BC. Then the angle formed by the chain from the horizontal, or the hypotenuse, then takes on the max value of 5 kN. Hereafter, the angle that the chain forms can be used with the dimensions of the bin to find out what the shortest chain length, ABC, can be.

I have to say this one was a bit tricky. Thanks for your help Simon Bridge.

 

[Simon Bridge]

Well done. They can get trickier than that ;)

 

[jtbell]

Welcome to Physics Forums, and just so you know for the future, we have separate forums for getting help with exercises like this one, regardless of whether they're school assignments or just for your own benefit. Look at the subforums of "Homework and Coursework Questions":

https://www.physicsforums.com/forumdisplay.php?f=152

Please post future questions like this, in one of those forums.