# find length of the rod?

A metal rod is 7.39 mm in diameter and 120 mm long before being loaded in tension. When subjected to a force of 1.5 kN, it will undergo 0.1% strain. What is the length of the rod (mm) in this loaded condition?

ps: I think this related to engineering stress and true stress?

### 2 Answers

- Steve4PhysicsLv 72 months agoFavorite Answer
Long method:

Strain = (change in length) / (original length)

In symbols this is:

ε = ΔL/L₀

0.1% is the same as 0.1* 1/100 which is 0.001

Put these together and we get

0.001 = ΔL/(120mm)

ΔL = 0.001*120mm = 0.12mm

So loaded length is L + ΔL = 120mm + 0.12mm = 120.12mm

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Short method

Loaded length = 1.001 *120mm = 120.12mm

Explanation

To increase something by 7% for example, you multiply it by 1.07

A strain of 0.1% just means length increases by 0.1%. This is the same as multiplying by 1.001

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Don’t confuse strain and stress. Stress is force/area.

- FiremanLv 72 months ago
By Strain (ɛ) = [ΔL/L]

=>0.1% = [ΔL/L] x 100%

=>0.1 x 10^-3 = ΔL/(120)

=>ΔL = 0.012 mm

=>L(loaded) = L + ΔL = 12 + 0.012 = 12.012 mm