Question

Given a 250Ω strain gage with a gage factor of 1 which is mounted to a metal bar 0.6m long. The bar is stretched under a tension force and the resistance changes to 251.4 Ω. How much was the bar stretched? _ _mm (Answer in mm to 2 decimal places) What is the length of the bar after it is stretched?

Answer 1

the bar was stretched by
`\mathbf{\Delta L = 3.36 \ mm}`

the length of the after it was stretched is
`\mathbf{L_(new) = 603.36 \ mm}`

Step-by-step explanation:

From the information given:

The strain gauge resistance R = 250 Ω

The gauge factor = 1

The original length L = 0.6 m = 600 mm

After the bar is being stretched under tension force;

the new resistance
`R_(new) = 251.42`

The gauge factor
`G = (\Delta R/R)/(\Delta L /L )`

where;

`\Delta R = R_(new) - R` and
`\Delta L = L_(new) - L`

ΔR = 251.4 - 250

ΔR = 1.4 Ω

`\Delta L = L_(new) - L`

`L_(new) = L + L ((\Delta R/R)/(G))`

`L_(new) = 0.6 + 0.6 ((\Delta 1.4/250)/(1))`

`L_(new) = 0.60336 \ m`

`\mathbf{L_(new) = 603.36 \ mm}`

Thus, the length of the after it was stretched is
`\mathbf{L_(new) = 603.36 \ mm}`

Thus, the bar was stretched by
`\Delta L = L_(new) - L`

`\Delta L = (603.36 - 600) \ mm`

`\mathbf{\Delta L = 3.36 \ mm}`