- #1

Hamiltonian

- 296

- 193

- Homework Statement
- A ##300## kg rock puts on an one-meter long aluminium column (##E = 7 * 10^{10} N/m^2##) with radius ##20## cm. (show in figure)

(a) Calculate the compressive strain of the column if a displacement of ##10##mm

occurred.

(b) What is the compressive force, ##G_{rock}## applied to the column

- Relevant Equations
- ##\sigma = E\epsilon## and ##\epsilon = \frac{\Delta L}{L}##

a) I can find the compressive strain on the aluminium column using the formula ##\sigma = E\epsilon## as we know ##\sigma = F/A##. The area of the column is ##A = \pi r^2 = 0.126m^2## and the force on the column is ##F = 300*(9.8)N = 2940N##. The stress therefore is ##\sigma = \frac{2940N}{0.126m^2} = 23333.333N/m^2##

hence plugging the stress(##\sigma##) and the Modulus of Elacticity(E) into our original equation we find the strain, ##\epsilon = \frac{\sigma}{E} = \frac{23333.33}{7*10^{10}} = 3333.332857*10^{-10}##.

But if we use the definition of strain ##\epsilon = \frac{\Delta L}{L}## we get ##\epsilon = \frac{0.01m}{1m} = 0.01##. The compressive strain obviously can't have two different values, so where have I gone wrong in my reasoning?

b) Also Just to be safe the compressive force ##G_{rock}## applied to the column would be the weight of the rock i.e., ##300g N = 2940N##?