Solve for Delta l: Elasticity Homework Statement

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Homework Statement

Find the deformation of the object (delta l).

Graphic:

http://img202.imagevenue.com/img.php?image=59612_fis1_122_218lo.jpg"

Y = young's modulus
W = weight of the objects (see the picture)

Homework Equations

d = density
d = M / V
d = M/(A*delta l )
M = d*A*delta l
W = d*A*delta l*g
delta (dx) = (f' * dx) / (A*Y)

The Attempt at a Solution

f' = force that compress the small piece (dx) of the bar.
f' = W +( d*A*delta l *g ) + (d*A*delta l * a)
f' = W + ( d *A*(l-x)*g) + (d*A*(l-x)*a)

and also W = d*A*l*a
f' = (d*A*l*a) + ( d *A*(l-x)*g) + (d*A*(l-x)*a)

At this stage Is this procedure ok?

Thanks

 

[anathema]

for your question!

Your approach seems to be on the right track, but there are a few things that could be clarified. First, it would be helpful to define all of the variables you are using and explain their meaning. This will make it easier for others to understand your solution and provide feedback. Additionally, it would be helpful to include units for each variable, as this can help with the overall understanding of the problem.

Next, it's important to note that the formula for finding the deformation (delta l) is typically given as delta l = (F * L) / (A * Y), where F is the applied force, L is the original length of the object, A is the cross-sectional area, and Y is the Young's modulus. This formula can be derived from Hooke's Law, which states that the deformation of an object is directly proportional to the applied force.

In your solution, it seems like you are trying to incorporate the weight of the object and acceleration due to gravity into the formula. While this may be relevant for the overall problem, it may not be necessary for finding the deformation of the object. It would be helpful to explain why you are including these variables and how they relate to the overall problem.

Additionally, it would be helpful to clarify what the small piece (dx) of the bar is and how it relates to the overall object. It may also be helpful to define the term "force that compress the small piece" and explain how it is related to the overall force applied to the object.

Overall, your approach seems to be on the right track, but it would be helpful to clarify and explain some of the variables and steps in your solution. This will make it easier for others to understand and provide feedback on your solution.

 

[nlightner]

Yes, your procedure is on the right track. However, there are a few things to consider:

1. It would be helpful to define all the variables used in your solution, such as M, V, A, l, x, etc.

2. It is not clear where the force f' is coming from. Is it an external force applied to the object or is it a force generated by the weight of the object itself?

3. The equation f' = W + ( d *A*(l-x)*g) + (d*A*(l-x)*a) seems to be missing a term for the weight of the object. It should also include the term W = d*A*l*a.

4. To solve for delta l, you can rearrange the equation f' = (d*A*l*a) + ( d *A*(l-x)*g) + (d*A*(l-x)*a) to get delta l on one side of the equation.

Overall, it seems like you are on the right track and have a good understanding of the concepts involved in solving for delta l. Keep up the good work!