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Problem 54 Hard Difficulty

The steel I-beam in the drawing has a weight of 8.00 kN and is being lifted at a constant velocity. What is the tension in each cable attached to its ends?

Answer

4.26 $\mathrm{kN}$

Discussion

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DG

David Base G.

October 23, 2020

Finally, the answer I needed, thanks Eric

SA

Sharieleen A.

October 26, 2020

This will help a lot with my midterm

Ha

Haru A.

October 30, 2020

JL

Januel L.

December 10, 2020

Video Transcript

and this problem. We have an I beam that's being lifted by a crane. The cables attached to the I B make a make a 70 degree angle with it. The IBM weighs eight killer Newton's, and it's being listed at a constant velocity. So I need to do is isolate the forces that act on the IBM sauce. Try being here and then we have a tension in the left cable and attention in the right cable. We'll call this T one and P two now. We also have the weight backing and assuming that the beam is uniform, the way sweat at the geometric center and we'll call that ducky. And so this angle between the beam and the load is data being on the tension. And so we have components of each of these tensions. You have a component in the why direction and we have a component in the extraction. So in the wind direction, because of the angle, this is T to sign data and the other one is t One sign ate up in the horizontal direction. You have t one co sign data and this one over here is T too ho sai data. So how so? Make the forces in each of the verdict on the horizontal direction. So let's do it in the horizontal direction. First of the summation of forces in the ex direction and others we've called X to the right positive. So that's equals t one ho sign data minus t, too. Ho sai data. And because the acceleration is zero that is all equal to zero francelino the coastline data you find the team one plus equal t to let's just call that tea. So in the vertical direction, get up is positive. So we have p one sign Tina plus t two sides Rena minus stop you and again since it's being lifted to the constant velocity of ex elevation is zero. Now we can get rid of the indices on our attention because you know that they are the same. So we saw this for tea and we find the t equals w divided by to sign. Hey, Noah plugging in the numbers eight Killer news over to sign of 70 degrees and that is equal to 4.26 We look at our answer that I've boxed here. It's symbolic form. You can see that as expected, the tension increases as the way increases, and I let you think about how the tension varies as the angle say that changes.