bar subjected to gravity load (two segments)
the bar in the fig has constant cross sectional area A .the top half of the bar is made of material with mass density and youngs module, the bottom half of the bar made of density and young module total length of bar is 2 when bar is hung with ceiling it stretches its own weight no other loads are applied neglect gravity load on the top half of the bar
You have not provided nor adquately described the Figure.
You have not capitalized the first words of sentences.
You have not provided values or symbols for Young's modulus and density.
I don't understand what you mean by "it stretches its own weight".
You need to take more care copying your problems in a format that makes sense. Showing ome of your own wirk would also be a good idea.
To determine the elongation of a bar subjected to a gravity load, we can use the concepts of stress and strain, as well as Hooke's Law.
Since the bar is only subjected to its own weight, we can neglect the gravity load on the top half of the bar, as mentioned in the problem statement.
Let's denote the length of the bottom half of the bar as L1 and the length of the top half as L2 (such that L1 + L2 = 2, the total length of the bar).
First, let's calculate the weight of the bottom half of the bar. The weight of an object can be calculated using the formula:
Weight = Mass x Gravity
Mass = Density x Volume
The density of the bottom half of the bar is given by p1, and the volume is given by A x L1 (cross-sectional area multiplied by length). Therefore, the weight of the bottom half of the bar can be calculated as:
Weight1 = p1 x A x L1 x g
where g is the acceleration due to gravity.
Next, let's calculate the weight of the top half of the bar. Since we need to exclude the weight of the top half, we can consider the density and length of the entire bar. The weight of the top half of the bar can be calculated as:
Weight2 = p x A x L2 x g
where p is the density of the entire bar.
Now, let's consider the elongation of the bar. According to Hooke's Law, the elongation (ΔL) of a material is directly proportional to the applied load (F) and inversely proportional to its Young's modulus (E), given by the equation:
ΔL = (F x L) / (A x E)
In this case, the applied load is the weight of the bottom half of the bar, and the total length of the bottom half is L1. Therefore, the elongation of the bottom half of the bar can be calculated as:
ΔL1 = (Weight1 x L1) / (A x E1)
where E1 is the Young's modulus of the material in the bottom half of the bar.
Since the top half of the bar is not subjected to the gravity load, its elongation will only depend on its own weight (Weight2) and the Young's modulus of the material in the top half (E2). Therefore, the elongation of the top half of the bar can be calculated as:
ΔL2 = (Weight2 x L2) / (A x E2)
Finally, the total elongation of the bar (ΔL) can be calculated by adding the elongation of the bottom half and the top half:
ΔL = ΔL1 + ΔL2
This equation should give you the elongation of the bar when it is hung from the ceiling with only its own weight applied.