# Solve Stress and Strain Qs | Equations, Diagrams, Steps

• terainfizik
In summary: Yes, you can use the torque principle to find the ratio of forces. Remember that torque is the product of force and distance, so you can use the known values (length, diameter, and strain) to solve for the unknown force. Then, you can compare the two forces to find the ratio.
terainfizik
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

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.

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.

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.

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

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.

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

Yeah first question, I done it , thank you . For second question ?

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.

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 ?

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 ?

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.

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.

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 ?

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 .

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.

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 ?

terainfizik said:
Ok,why you don't do them ?

mickdriscoll said:
i think you mean stress. strain is the elongation divided by the original length.
Quite right. I did use the wrong word.

## 1. What is stress and strain in relation to materials?

Stress is the amount of force applied to a material per unit area, while strain is the resulting deformation or change in shape of the material. They are used to measure the strength and elasticity of materials.

## 2. How are stress and strain related?

Stress and strain are directly proportional to each other, meaning that an increase in stress will result in a corresponding increase in strain. This relationship is known as Hooke's Law.

## 3. What is the difference between normal stress and shear stress?

Normal stress is the force applied perpendicular to the cross-sectional area of a material, while shear stress is the force applied parallel to the cross-sectional area. Normal stress is responsible for changes in the length or volume of a material, while shear stress is responsible for changes in shape or orientation.

## 4. How do I calculate stress and strain using equations and diagrams?

To calculate stress, divide the applied force by the cross-sectional area of the material. Strain can be calculated by dividing the change in length or volume by the original length or volume. Diagrams, such as stress-strain curves, can also be used to visualize the relationship between stress and strain for a specific material.

## 5. What steps should I follow to solve stress and strain problems?

1. Identify the type of stress and strain involved (normal or shear)
2. Calculate the stress and strain values using the appropriate equations
3. Plot the data on a stress-strain diagram (if applicable)
4. Determine the elastic limit and yield point of the material
5. Analyze the behavior of the material under different amounts of stress
6. Use the data to make predictions about the material's strength and elasticity

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