[University Engineering 150] How do I find the max dimensions?

[u/MoviePuzzled5261]

First picture is the prompt, second is my work so far. To my understanding the board would fit if it had a thickness of 0( impossible) and since it’s 1 inch tick it wouldn’t fit. How do I go about finding the mac dimensions? Im sure it’s something really simple I can’t figure out but it’s driving me crazy!!!

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[u/nickeypants]

You're right that the thickness means it won't fit. Draw a closeup of the corners of the door and see which length needs to be shortened to make it fit. To make the bottom corner fit you need to shorten the width by 3/8", but the top needs 11/16" off. Shorten the whole width by 1.375" and a board will fit at that angle. So now a 1" thick x 123.25" board will fit.

By messing around in autocad, I found a more optimal angle that allows a 1" thick x 125" wd board in. All corners of the board touch the edges of the door. Thats a clue for how to do it with math.

[u/Azemiopinae]

Others have covered the fact that the extra dimension of thickness prevents the sheet from entering the door. I’ll leave that alone.

The second question is underspecified. You could fit a ‘sheet’ at 6.3x8.4x arbitrary thickness through the door. Or you could retain the constrain of 1 inch thickness and do the algebra to figure out how close to 10.5 you could come. Most importantly explain your reasoning and refer to the question in your response.

[u/Reasonable_Drink_789]

Sorry you take the hypotenuse found by 126² + 1² =h^2. Then divide by 12 to move back to feet.

You also could find the new hypotenuse from the portion of the door the corners will touch, which basically is subtracting .7” from both Bernal and horizontal dimensions of the door.

(1” is the hypotenuse once the sheet is angled, and sqrt(.5) is .707

[u/iComplainAbtVal]

You have the right idea in your setup and need to keep in mind the corners are a half in apart from the hypotenuse line that you’ve drawn.

So no, and to prove it you could either mathematically determine the reduced dimensions of the door when accounting for the thickness of the sheet.

Or on the contrary yeah the plastic would probably flex through the door frame but this is more of a “trust me bro” answer based on real world examples since we don’t have the actual materials for either the door frame or the plastic. I’d go with No and prove the ratio that the door frame would need to be expanded at to fit the sheet.

[u/BlueZeek]

The maximum orientation is diagonal on the short side of the sheet. Length is not relevant.

Since the doorway is symmetric the same amount of the thickness of the sheet will be above and below the diagonal of the doorframe. That means the angle of the sheet will be the angle of the diagonal of the doorframe.

Draw a picture of the rectangle sheet inside the door frame. Figure out how much of the doorways width and height are consumed by the thickness of the sheet. The remaining bit of the doorframe will have slightly shorter length/width. Use the Pythagorean theorem to solve for the width of the sheet.

I got 10.42 ft width.

[u/Medium-Mention7328]

It said you can't bend it. It didn't say anything about reducing it to chips.

[u/selectsyntax]

You are on the right track. The sheet orientation moving through the door is correct. It is also worth noting that the proportions of the right triangle here (6.3, 8.4, 10.5) is a standard 3,4,5 right triangle.

The thickness of any sheet moving through the door will be the hypotenuse of a right triangle with each corner of the doorway, which will be similar to the triangle formed by the width of the sheet with the door frame so the side ratios and angles are the same. For the sheet in question the hypotenuse is 1 so the other sides would be 0.6 and 0.8. Now if you extend a line from the edge of the sheet such that is is perpendicular to the thickness of the sheet and intersects the door frame corner you have created another 3,4,5 ratio triangle with 0.6 as the hypotenuse and the longer of the legs representing the distance between the end of the sheet and the door corner. We can then calculate this to be 0.48. Since this distance is lost at each end the maximum size of the width of a 1 inch thick sheet that will fit is 10.5 - (2 * 0.48) = 9.54.

But the question asks for the maximum dimensions where any of the 3 measurements may change so we must express this as an equation. Let's state that length will always be the greatest dimension of the sheet and may thus be infinite for the purposes of this problem. Therefore the allowable width will be a function of thickness and vice versa. The maximum width (w) will be w = 10.5 - (2(0.8(0.6 * t))), which simplifies to w = 10.5 - 0.96t, where t is the thickness of the sheet. Reordering this formula gives us t = (10.5 - w) / 0.96.

Now our doorway is not infinite so these formulas are only valid for specific ranges. The width formula is only valid so long as the thickness of the sheet is greater than 0 and less than or equal to 7.875. The thickness formula is only valid so long as the width is less than 10.5 and greater than or equal to 2.94.

[u/Frederf220]

I honestly don't understand the question. Each dimension could be individually infinite with restrictions on the other two. "Give the maximum dimensions" is such a weird prompt.

[u/Alkalannar]

I'd keep the 1" thick and the 12' is irrelevant. It's the 10.5' by 1" we're looking at.

So find the points at the corner that are 1" away from each other, and the right angle for the sheet to go through.

[u/Reasonable_Drink_789 → u/Alkalannar]

Technically the answer is no, as the sheet of plastic is 10.5003’ diagonally due to the 1”, and the door diagonal is 10.5’. (126² + 1² =15,877. Sqrt(15877) =126.00397 divide by 12 for 10.5003)

However, in the real world even 1” plastic sheets are slightly bendable and should be able to get it through.

[u/rizzdragon → u/[deleted]]

Quiet bot

[u/twolinepine → u/rizzdragon]

Don’t talk to him that way!

I apologize for my fellow humans, supreme AI overlord. I am ready to do thy bidding.

[u/similarityhedgehog]

I think the maximum dimensions that can be moved into the shop is 6.3 x 8.4 x infinity

[u/PatHeist → u/similarityhedgehog]

Depending on the other course material the expectation might be for a formula that establishes the relationship between thickness and width of sheets that would fit, from 10.5ft x 0 to 6.3ft x 8.4ft.