Solve Stress and Strain Qs | Equations, Diagrams, Steps

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Homework Help Overview

The discussion revolves around problems related to stress and strain in materials, specifically focusing on copper wires and rubber strands in a catapult scenario. Participants are exploring the relationships between force, area, and elongation, as well as the application of Young's modulus and Hooke's Law.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants are questioning the assumptions behind the strain calculations for wires of different diameters and discussing how to approach problems involving forces acting on a rod supported by multiple wires. There are inquiries about the relevance of torque in these scenarios and the need for clarity on units and definitions.

Discussion Status

Some participants have provided guidance on how to think about the problems, suggesting the need to consider ratios of forces and the relationships between stress and strain. There is an ongoing exploration of the first question before moving on to the second, indicating a productive direction in the discussion.

Contextual Notes

Participants have noted the importance of including units in problem statements and answers. There is also a mention of the need to clarify the definitions of strain and stress, as well as the assumptions made regarding the materials involved.

terainfizik
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Q: A copper wire of diameter d is stretched by a load hanging vertically from its lower end . The strain of the wire is 8.0x10^-4 . What's the strain in another copper wire of the same length but of diamteter 2d ?
A: 2x10^-4

Q: A light rod of length L hangs from the lower ends of two vertical wires M and N which are of the same natural length and diameter but ve differrent Young's moduli E1 and E2 respectively . A load is placed on the rod at a distance x from the wire M, so that the rod remains horizontal . What's the value of x in terms of L, E1 and E2 ?
A: (E2L)/ (E1+E2 )


Q - questions
A - answer

I would be glad anyone solve this as soon as possible . It would be great explain diagram , equations , steps by steps . Tnx . There ll be more questions.
 
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terainfizik said:
Q: A copper wire of diameter d is stretched by a load hanging vertically from its lower end . The strain of the wire is 8.0x10^-4 . What's the strain in another copper wire of the same length but of diamteter 2d ?
A: 2x10^-4
Are you saying that the 'A:' is your answer or the solution a book gives you? Because if it is your answer, then I believe it is correct. If not then where do you think you can start?

As for the second question, I have not done it because I am finding it surprisingly difficult to get my head around. :-p

The Bob (2004 ©)
 
It would be a good idea to include the units in your problem statement and answers. For you second problem you need to figure out the ratio of the forces acting the two wires that will stretch them by the same amount. It is then a statics problem to find the forces acting on the rod.
 
The Bob said:
Are you saying that the 'A:' is your answer or the solution a book gives you? Because if it is your answer, then I believe it is correct. If not then where do you think you can start?

As for the second question, I have not done it because I am finding it surprisingly difficult to get my head around. :-p

The Bob (2004 ©)


How to do for first questions ?
 
terainfizik said:
How to do for first questions ?

I'm almost 100% positive I've seen this same question a few days ago. Use 'search', it should help.
 
terainfizik said:
How to do for first questions ?
Strain is the force (tension in this case) divided by the area over which that force is distributed. If you double the diameter of the wire, what happens to the cross-sectional area?
 
Q: A light rod of length L hangs from the lower ends of two vertical wires M and N which are of the same natural length and diameter but ve differrent Young's moduli E1 and E2 respectively . A load is placed on the rod at a distance x from the wire M, so that the rod remains horizontal . What's the value of x in terms of L, E1 and E2 ?
A: (E2L)/ (E1+E2 )


Q - questions
A - answer


How about this questions ? I'm still don't get it .
 
You should concentrate on trying to solve question 1 before you even think about working on question 2.
 
terainfizik said:
How to do for first questions ?
Look at the relationship between the two different wires. Rather than expressing the Youngs Modulus with only two variables, express it with four (i.e. Force, Area, Original Length and Extension) and then consider which are constant and which are not. Once you have done this, and rearranged the formula, you will be left with a question of two main variables (i.e. Area and Extension) and, after rearranging again, will be left with the solution that you stated and I confirmed.

The Bob (2004 ©)
 
  • #10
terainfizik said:
Q: A light rod of length L hangs from the lower ends of two vertical wires M and N which are of the same natural length and diameter but ve differrent Young's moduli E1 and E2 respectively . A load is placed on the rod at a distance x from the wire M, so that the rod remains horizontal . What's the value of x in terms of L, E1 and E2 ?
A: (E2L)/ (E1+E2 )


Q - questions
A - answer


How about this questions ? I'm still don't get it .


Yeah first question, I done it , thank you . For second question ?
 
  • #11
terainfizik said:
Yeah first question, I done it , thank you . For second question ?
Dan already gave you a great start to solving this question.

You can re-read it here, or by scrolling up to #3.
 
  • #12
New Questions !

Q: A catapult consists of two strands of rubbe , each of unstretched length 0.20m and each of which stretches of which stretches by 0.1m under tension of 50N. A stone of mass of 0.060 kg is projected vertically upwards from the catapult after each strand has been extended to a total length of 0.35m. What's the energy stored in stretched catapult ? Find the maximum height attained by the stone . ( Assume that the rubber obeys Hooke's Law and that air resistance is negligible.)
( Acceleration of free fall , g=10ms^-2 )

A: 11.25J , 15.5m



Q: The maximum upward acceleration of a lift of total mass 2500kg is 0.5ms^-2. The lift is supported by a steel cable which has a maximum safe working stresss of 1.0x10^4 Pa . What minimum area of cross-section of cable should be used ? [ g = 10ms^-2)

A: 2.6x10^-4 m^2




How to do these questions ?
 
  • #13
OlderDan said:
It would be a good idea to include the units in your problem statement and answers. For you second problem you need to figure out the ratio of the forces acting the two wires that will stretch them by the same amount. It is then a statics problem to find the forces acting on the rod.


About the ratio forces acting on two wires , does the ''torque'' principle needed to applied ?
 
  • #14
Strain is the force (tension in this case) divided by the area over which that force is distributed.

i think you mean stress. strain is the elongation divided by the original length.
 
  • #15
terainfizik said:
About the ratio forces acting on two wires , does the ''torque'' principle needed to applied ?
Yes it does. I cannot think of a problem that has forces applied at different points of an object (like the rod) where it would not apply.
 
  • #16
terainfizik said:
Q: A catapult consists of two strands of rubbe , each of unstretched length 0.20m and each of which stretches of which stretches by 0.1m under tension of 50N. A stone of mass of 0.060 kg is projected vertically upwards from the catapult after each strand has been extended to a total length of 0.35m. What's the energy stored in stretched catapult ? Find the maximum height attained by the stone . ( Assume that the rubber obeys Hooke's Law and that air resistance is negligible.)
( Acceleration of free fall , g=10ms^-2 )

A: 11.25J , 15.5m



Q: The maximum upward acceleration of a lift of total mass 2500kg is 0.5ms^-2. The lift is supported by a steel cable which has a maximum safe working stresss of 1.0x10^4 Pa . What minimum area of cross-section of cable should be used ? [ g = 10ms^-2)

A: 2.6x10^-4 m^2




How to do these questions ?


How about those two question ?
 
  • #17
Need help !

terainfizik said:
Q: A catapult consists of two strands of rubbe , each of unstretched length 0.20m and each of which stretches of which stretches by 0.1m under tension of 50N. A stone of mass of 0.060 kg is projected vertically upwards from the catapult after each strand has been extended to a total length of 0.35m. What's the energy stored in stretched catapult ? Find the maximum height attained by the stone . ( Assume that the rubber obeys Hooke's Law and that air resistance is negligible.)
( Acceleration of free fall , g=10ms^-2 )

A: 11.25J , 15.5m



Q: The maximum upward acceleration of a lift of total mass 2500kg is 0.5ms^-2. The lift is supported by a steel cable which has a maximum safe working stresss of 1.0x10^4 Pa . What minimum area of cross-section of cable should be used ? [ g = 10ms^-2)

A: 2.6x10^-4 m^2




How to do these questions ?


How to do those two question ?
It's very important. Everyone on this thread .
 
  • #18
terainfizik said:
How to do those two question ?
It's very important. Everyone on this thread .
Tell us what you think needs to be done to solve these problems. We will help you, but not do them for you.
 
  • #19
OlderDan said:
Tell us what you think needs to be done to solve these problems. We will help you, but not do them for you.


Ok,why you don't do them ?
 
  • #20
terainfizik said:
Ok,why you don't do them ?
https://www.physicsforums.com/showthread.php?t=94379
 
  • #21
mickdriscoll said:
i think you mean stress. strain is the elongation divided by the original length.
Quite right. I did use the wrong word.
 

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