change rectangle height when mass changes

[bcoch]

I have a rectangle L=13.6"
W=3.7" L*W= 50.32"
I subtract a cutout with an area of 6.45 "

Total area is now 43.8697"

V= [(L*W)-slot area]*H...(height is 2.175")

Mass is 25lbs
Density is 0.262

I know that Vol* Density=Mass

I don't know how to arrange this information so there is a single formula that will automatically correct the height if the mass is change...

 

[mmm4444bot]

an area of 6.45 "

Total area is now 43.8697"

there is a single formula that will automatically correct the height

I cannot determine what you have been asked to do. Please type the entire exercise, as it was given to you.

Please note that neither 6.45" nor 43.8697" are measures of area. Area always involves some squared-unit of measure (i.e., 6.45 square inches).

Did they ask for a formula to "correct the height" or did they ask for a formula "for the height"? Did they tell you that the volume needs to remain constant?

:???:

 

[bcoch]

find the height as it changes with the mass

I have a rectangle (its actually an arbor weight used to raise or lower curtains in a theater) minus a cutout. I need to find a formula that calculates the new height that corresponds to a change in mass...so as I increase or decrease the mass/poundage, the formula should show the new corresponding height/thickness...the length and width are to remain the same

length is always 13.6 inches
width is always 3.7 inches
cutout/slot area is 6.45 inches

density is 0.262


if the height is 2.175 then the mass is 25 pounds...what is the height if I increase the mass to 30 pounds?
L times W minus slot...times height = Volume

[(L*W)-Slot}=43.8697 inches
43.8697*(height)2.175= (volume) 95.417inches cubed?? i think cubed???

Mass= Vol times Density
25lb= 95.417*0.262

write a formula that show the new height if I change the mass?

I feel like I'm almost there but just can't make it all the way

 

[mmm4444bot]

I have a rectangle ... minus a cutout

cutout ... area is 6.45 inches

NO rectangle has height. Rectangles have only two dimensions (i.e., zero height). What you're trying to describe is a rectangular solid with some sort of volume removed.

Also, NO area can be described as "6.45 inches". Your measurement describes the length of a straight-line segment only.

If there were no cutout, the exercise would be straightforward using the volume formula for a rectangular solid (Length x Width x Height). Until I understand what the shape of the volume cutout is, I am unable to help you.

Are you able to upload a diagram?

 

[bcoch]

change mass = change in height

hope you can zoom in on this... the dimensions are slightly different but close...in this diagram the length is 14", width is 4", Height is 1.75" ..a single slot is a radius of .5" and the rectangular part of the slot is 2.5 in long and 1 in wide density is still .262 ..these are the dimensions at 23 lbs.


area of both slots is Pi r^2 plus 2*( 2.5*1 inches)= 5.785 inches (cubed??)
then vol= [(L*W)- 5.785]* 1.75(H)
vol =87.876 (something units???)

Mass = Vol * Density
23 lbs= 87.976*0.262

again, if I change the mass how do I write a formula that correspondingly changes the height only all other dimensions stay the same.

I have to input the formula into the height column so when I change the mass column the height/thickness automatically changes

 

[bcoch]

block height thickness updates when mass is changed

OH! I just got it....h=(mass/density)/((L*W)-area of slots)

H=(23lbs*0.262)/((14"*4")-5.758" TRIUMPH!!!