Calculating Compression of Aquarium Support Posts

In summary, the posts compress the aquarium by 5.44*10^10*m meters because the weight of the aquarium is distributed over four posts.
  • #1
houseguest
16
0

Homework Statement



A large 3.00×10^4 L aquarium is supported by four wood posts (Douglas fir) at the corners. Each post has a square 3.80 cm x 3.80 cm cross section and is 80.0 cm tall.
By how much is each post compressed by the weight of the aquarium?

Homework Equations



deltaL = F*L_0/(Y*A)

Y (for Douglas fir) = 1 * 10^10 N/m^2

The Attempt at a Solution



This seems very straight forward, I just need to determine F.
F= ma = m(aquarium)g
but, what is the mass of a 3.00×10^4 L aquarium?
once I determine that, I figure it'll just be:

deltaL = ( m * 9.8 * .8)/(.144 * 10^10) meters
=> 5.44*10^10*m meters

How do I find m ??

Thanks for the help!
 
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  • #2
houseguest said:
but, what is the mass of a 3.00×10^4 L aquarium?

Since nothing else is given, consider the significant portion of the weight of the aquarium to be due to just water.
 
  • #3
So I took the mass of water to be 1Kg per liter.
So the m = 3 * 10^4

Then the equation comes out as:


deltaL = ( 3 * 10^4 * 9.8 * .8)/(.144 * 10^10) meters
= 1.63 * 10^-4 m

But I am told this is the incorrect answer.

Any help?

Thanks!
 
  • #4
What's the total area on which the weight acts, in m2?
 
  • #5
4*.144 = .576 m^2

but, isn't it asking the deltaL for an individual post?

I thought that I might have to divide the force by 4, but that answer was also incorrect.

Thanks
 
  • #6
Isn't it 0.0144 m2? Also, it's the pressure (stress) that causes the strain; you need to find the pressure on a single leg before you can calculate the strain. The way you originally had it, the compression distance was independent of the number of legs.

EDIT: Right, 0.00144 m2
 
Last edited:
  • #7
Hang on, I see the mistake I made earlier: 3.8 cm x 3.8 cm = .038m x .038m = .00144 m^2 (thanks btw), but wouldn't then total area then be 4 * .00144 = .00576 m^2 ?

Then the pressure would be 3 * 10^4 * 9.8 / .00576.

Then plug in that pressure for F in
deltaL = F*L_0/(Y*A)
Is that right?
 
Last edited:
  • #8
Although, it retrospect this can't be right since

deltaL = ( (3 * 10^4 * 9.8) / .00576 * .8) / (.00144 * 10^10) meters

= 2.84 m

and that is way to large to be realistic
 
  • #9
You divided by area twice.
 
  • #10
oh yeah, duh.

Thank you so much for your help! Seriously.
 

1. What is Young's Modulus of aquarium?

Young's Modulus of aquarium is a measure of the stiffness or rigidity of the material that makes up the aquarium. It is a measure of how much the material will deform when a force is applied to it, and is commonly used to determine the strength and durability of aquariums.

2. How is Young's Modulus of aquarium calculated?

Young's Modulus of aquarium is calculated by dividing the stress (force per unit area) by the strain (change in length per unit length) of the material. This can be done experimentally by applying a known force to the aquarium and measuring the resulting change in length, or it can be calculated using the material's elasticity and geometry.

3. What factors can affect the Young's Modulus of aquarium?

The Young's Modulus of aquarium can be affected by several factors, including the type of material used (e.g. glass, acrylic), the thickness and shape of the aquarium, and the temperature and humidity of the environment. Additionally, any imperfections or defects in the material can also affect its Young's Modulus.

4. How does Young's Modulus relate to the strength of an aquarium?

The higher the Young's Modulus of an aquarium, the stiffer and more rigid the material is. This means that it will be less likely to deform or break when a force is applied to it. However, Young's Modulus alone does not determine the strength of an aquarium as other factors such as the material's tensile strength and design also play a role.

5. Why is Young's Modulus important for aquariums?

Knowing the Young's Modulus of an aquarium is important for determining its strength and durability. It can also help in designing and constructing aquariums that can withstand the pressure of the water and the weight of the contents inside. Additionally, understanding the Young's Modulus can also aid in identifying potential weak points in the aquarium that may need reinforcement.

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