Compute the distance x and tension of each cable

• MrMechanic
In summary: Basically what you need to do is work out what the distance x is, and then work out what the tension in each of the cables is.
MrMechanic

Homework Statement

The thin steel plate, weighing 82lb/ft^2, is being lifted slowly by the cables AC and BC. Compute the distance x and find the corresponding tension in each of the cables.
[See attachments for Figure]

Homework Equations

Summation of X = 0
Summation of Y = 0
Moment=Rd

The Attempt at a Solution

So i tried to get the weight of the steel plate. here's the solution..
2(21) + 4(12) + 1/2(9)(4) = 108ft^2
now i multiply the given 82lb/ft^2 to cancel out the ft^2
i get 8856lb.. After that i don't know where to start next. Can you guys help me out?
I really think the problem is easy but i got lost on where to start...

Attachments

• Untitled.png
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I've not done many of these but I imagine it will swing so that the centre of gravity is below the hook. So where is the centre of gravity?

MrMechanic said:

Homework Statement

The thin steel plate, weighing 82lb/ft^2, is being lifted slowly by the cables AC and BC. Compute the distance x and find the corresponding tension in each of the cables.
[See attachments for Figure]

Homework Equations

Summation of X = 0
Summation of Y = 0
Moment=Rd

What do you mean by
"Summation of X = 0
Summation of Y = 0
Moment=Rd"

The plate is moving with a small constant speed upward. What is the acceleration then? It is kept horizontal, it does not turn. What do these mean on the forces and torques (moments) acting on it?

MrMechanic said:

The Attempt at a Solution

So i tried to get the weight of the steel plate. here's the solution..
2(21) + 4(12) + 1/2(9)(4) = 108ft^2
now i multiply the given 82lb/ft^2 to cancel out the ft^2
i get 8856lb.. After that i don't know where to start next. Can you guys help me out?
I really think the problem is easy but i got lost on where to start...

ehild

so you mean forces along x-axis is = to 0 and also the torque.
And how would i find the two angles there.
Should I Sum all the torque along A?

The sum of the x components of the forces is 0, and also the sum of the y components of the forces.

Also the sum of all torques about any point is zero. You can choose A.

You need to write up three equations in terms of x and the the unknown angles.

AS CWatters wrote, x is related to the position of the CM.

ehild

The information doesn't seem to be complete. It looks like the top of the plate is horizontal, and it looks like AC and BC have the same length. But these cannot both be true, and neither is clearly given as true. At a guess, AB is horizontal. At the least, that's the easier version of the problem.

I've looked at it again and I think haruspex has a point. I think they are asking you to work out what value of x is needed for the top edge of the plate to stay horizontal (and not as I suggested above that it will rotate). This implies AC and BC are different lengths but the lengths aren't specified so that's ok.

1. What is the formula for calculating the distance x between two points?

The formula for calculating the distance x between two points is d = √((x2 - x1)^2 + (y2 - y1)^2), where (x1, y1) and (x2, y2) are the coordinates of the two points.

2. How do I determine the tension in a cable?

The tension in a cable can be determined by using the formula T = F * sin(θ), where T is the tension, F is the force applied to the cable, and θ is the angle of the cable with respect to the horizontal.

3. What units are used for distance and tension?

The units for distance are typically in meters (m) or feet (ft), while the units for tension are in Newtons (N) or pounds (lbs).

4. Can I use the same formula for calculating the distance and tension for all types of cables?

No, the formula for calculating the distance and tension may vary depending on the type of cable and the conditions in which it is being used. For example, the formula for calculating the tension in a horizontal cable will be different from that of a diagonal cable.

5. How accurate are the distance and tension calculations?

The accuracy of the distance and tension calculations depends on the accuracy of the measurements and the assumptions made in the calculations. It is important to have precise measurements and to consider all relevant factors in order to get an accurate result.

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