A uniform bar 1.900m in length and having a cross sectional area of 10.500cm^2 is subject to a loading of 5550.000N. This load causes an extension of the bar length of 1.100mm. Calculate the stress and strain produced.
Stress = Load/ Area
Strain = Change in length/ length
cross section = 10.500cm = 105mm
bar length = 1.100mm
Would I first need to solve for the Area? How do I find the Area? Help.
ANS 1 = kPa (round to 3 decimal places)
ANS 2 = (round to 6 decimal places)
To find the stress and strain produced by the loading on the bar, you need to calculate the area of the bar's cross-section. Given that the bar's cross-sectional area is 10.500 cm^2, you want to convert it to square millimeters (mm^2) since the other measurements are given in millimeters.
Since 1 cm is equal to 10 mm, you can convert the area from cm^2 to mm^2 by multiplying it by (10 mm)^2, which is 100 mm^2. So the area of the bar's cross-section is:
Area = 10.500 cm^2 * (100 mm^2 / 1 cm^2)
Area = 1050 mm^2
Now that you have the area, you can proceed to calculate the stress and strain.
1. Stress:
Stress is defined as the force applied per unit area. In this case, the force is given as 5550.000 N, and you found the area to be 1050 mm^2.
Stress = Load / Area
Stress = 5550.000 N / 1050 mm^2
Stress = 5.286 N/mm^2
Stress = 5.286 kPa (since 1 N/mm^2 is equal to 1 kPa)
So the stress produced by the loading is approximately 5.286 kPa.
2. Strain:
Strain is the ratio of the change in length of the bar to its original length. In this case, the bar experiences an extension of 1.100 mm, and its original length is 1.900 m, or 1900 mm.
Strain = Change in length / Length
Strain = 1.100 mm / 1900 mm
Now you can divide these two values to find the strain:
Strain = 1.100 mm / 1900 mm
Strain ≈ 0.000578
So the strain produced by the loading is approximately 0.000578.
Therefore, the answers are as follows:
ANS 1 = 5.286 kPa (rounded to 3 decimal places)
ANS 2 = 0.000578 (rounded to 6 decimal places)
Area 10.5cm²=10.5*10^(-4) m²
Load = 5550 N
Stress
=load/area
=5550/(10.5*10^-4) Pa
=5285.714 kPa
Strain:
1.1mm/1.9 m
=1.1*10-3 m / 1.9m
=0.000 579 (no units)