Max height of a concrete column

[Quantum Singularity]

Homework Statement

For a concrete column of constant cross sectional area, what is the maximum possible height if the compressible strength is 2.0 x 10⁷ N/m²? The density of concrete is 2.3 x 10³ kg/m³.

Homework Equations

$$\frac{F}{A}$$

The Attempt at a Solution

I am not really sure what I am doing wrong, or what I have to do differently, but so far I have tried a few different things.
First I tried setting the force equal to 2*10², and trying to solve for height:
$$\frac{2*10^7}{2.3*10^3*9.8}\approx890$$
This was incorrect however. From there, I tried adding a π to the denominator, but that didn't work. I then tried taking the square root because I realized the r term was squared. After that I realized the r term doesn't even really have a place in the equation because I am looking for height, not radius. How do I correctly approach the problem? I honestly have no clue what I am doing here.

 

[Chestermiller]

Your answer looks correct to me.

 

[SteamKing]

Homework Statement

For a concrete column of constant cross sectional area, what is the maximum possible height if the compressible strength is 2.0 x 10⁷ N/m²? The density of concrete is 2.3 x 10³ kg/m³.

Homework Equations

$$\frac{F}{A}$$

The Attempt at a Solution

I am not really sure what I am doing wrong, or what I have to do differently, but so far I have tried a few different things.
First I tried setting the force equal to 2*10², and trying to solve for height:
$$\frac{2*10^7}{2.3*10^3*9.8}\approx890$$
This was incorrect however. From there, I tried adding a π to the denominator, but that didn't work. I then tried taking the square root because I realized the r term was squared. After that I realized the r term doesn't even really have a place in the equation because I am looking for height, not radius. How do I correctly approach the problem? I honestly have no clue what I am doing here.

The first thing is to understand what the numbers mean that you are given. In your attempted calculation above, you should always do a check of the units in the result to see if these agree with the answer you are supposed to obtain.

The maximum compressive stress of the concrete is 2.0 × 10⁷ N/m², which you would presumably obtain from the equation σ = F / A.

It is given that the column is uniform, so this suggests that A is a constant.

What other quantity is needed to give the stress in the column?

Given the density of the concrete (2.3 × 10³ kg/m³), how would you determine the maximum stress in the column? Where would this stress be located?

 

[Nidum]

edit : removed redundant post

 

[Chestermiller]

edit : removed redundant post

The cross sectional areas cancel out. The compressive stress on the bottom is just the hydrostatic relation $\rho g h$.

 

[Quantum Singularity]

The first thing is to understand what the numbers mean that you are given. In your attempted calculation above, you should always do a check of the units in the result to see if these agree with the answer you are supposed to obtain.

The maximum compressive stress of the concrete is 2.0 × 10⁷ N/m², which you would presumably obtain from the equation σ = F / A.

It is given that the column is uniform, so this suggests that A is a constant.

What other quantity is needed to give the stress in the column?

Given the density of the concrete (2.3 × 10³ kg/m³), how would you determine the maximum stress in the column? Where would this stress be located?

I would think that the stress would be located in the center of the column. From the equations in my book, I only see where force and area are the quantities shown. The equation it gives me for force near the beginning of the chapter that this is reviewing equates it to length, a delta l, and a young's modulus number, which I don't think helps me either.

Your answer looks correct to me.

This is a review for my final, so I am able to see the answers, and it shows the answer as being 89m, instead of the 890m that I got, unless I am just missing something on units somewhere. It is really annoying seeing the error like that with it being a factor of 10 off.

 

[SteamKing]

I would think that the stress would be located in the center of the column.

This column is presumably standing vertically, as most columns are won't to do.

Why would you think that the stress in a vertical column would occur in the middle? Draw a free body diagram of a vertical column to check.

From the equations in my book, I only see where force and area are the quantities shown. The equation it gives me for force near the beginning of the chapter that this is reviewing equates it to length, a delta l, and a young's modulus number, which I don't think helps me either.

You don't need to know Young's modulus to solve this problem.

This is a review for my final, so I am able to see the answers, and it shows the answer as being 89m, instead of the 890m that I got, unless I am just missing something on units somewhere. It is really annoying seeing the error like that with it being a factor of 10 off.

You can always check the book answer to see if it matches the information given in the problem statement. Answers in the book have been known to be wrong.

 

[Quantum Singularity]

This column is presumably standing vertically, as most columns are won't to do.

Why would you think that the stress in a vertical column would occur in the middle? Draw a free body diagram of a vertical column to check.You don't need to know Young's modulus to solve this problem.You can always check the book answer to see if it matches the information given in the problem statement. Answers in the book have been known to be wrong.

That is what I am thinking might be the case, but that would mean my professor is wrong because it is his final exam review. As for the free body diagram, I have decided to abandon the problem and the rest of the review for now because the exam is tomorrow and this professor hasn't cared enough to actually teach me anything of value. I have some other homework I need to do before the final anyways, and because the final curves and everyone else in the class has the same problems as me, the stuff I am having problems with shouldn't hurt me too bad. Thanks for the help though, hopefully next semester I can get someone who actually wants to teach physics.