> #materials-science , #mechanics , #physics > Determine the average normal stress and strain in rod AB. if the load has a mass of 75kg. The diameter and length of the rod AB is 8mm and 2.5m, respectively Take E=210Gpa?
Oct 29, 2023

# Determine the average normal stress and strain in rod AB. if the load has a mass of 75kg. The diameter and length of the rod AB is 8mm and 2.5m, respectively Take E=210Gpa?

Determine the average normal stress and strain in rod AB. if the load has a mass of 75kg.
The diameter and length of rod AB is 8mm and 2.5m, respectively. Take E=210Gpa
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Oct 29, 2023
To determine the average normal stress in rod AB, we need to calculate the force applied to the rod.

First, we need to calculate the weight of the load. The weight can be calculated using the formula:

Weight = mass * acceleration due to gravity

Given that the mass of the load is 75 kg and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the weight:

Weight = 75 kg * 9.8 m/s^2 = 735 N

Next, we need to calculate the cross-sectional area of the rod. The diameter of the rod is given as 8 mm, which can be converted to meters by dividing by 1000:

Diameter = 8 mm = 8/1000 m = 0.008 m

The cross-sectional area of the rod can be calculated using the formula:

Area = π * (diameter/2)^2

Area = π * (0.008/2)^2 = π * (0.004)^2 = 0.00005027 m^2

Now, we can calculate the average normal stress using the formula:

Stress = Force / Area

Stress = 735 N / 0.00005027 m^2 = 14,610,000 Pa

Finally, we can convert the stress to GPa by dividing by 1,000,000,000:

Stress = 14,610,000 Pa / 1,000,000,000 = 0.01461 GPa

Therefore, the average normal stress in rod AB is approximately 0.01461 GPa.

To determine the average normal strain in rod AB, we need to use Hooke's Law, which states that stress is proportional to strain. The formula for strain is:

Strain = Stress / Young's Modulus

Given that the Young's Modulus (E) is 210 GPa, we can calculate the average normal strain:

Strain = 0.01461 GPa / 210 GPa = 0.00006957

Therefore, the average normal strain in rod AB is approximately 0.00006957.
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