1. Stress, Strain and Elastic Deformations
Physics 6B
Stress, Strain and
Elastic Deformations
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2. We already know about springs - remember Hooke’s Law : Fspring = -k•Δx
When a force is applied to an object, it will deform. If it snaps back to its original shape when the force is removed, then the deformation was ELASTIC.
We already know about springs - remember Hooke’s Law : Fspring = -k•Δx
Hooke’s Law is a special case of a more general rule involving stress and strain.
The constant will depend on the material that the object is made from, and it is called an ELASTIC MODULUS. In the case of tension (stretching) or compression we will call it Young’s Modulus*. So our basic formula will be:
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*Bonus Question – who is this formula named for? Click here for the answer

3. STRESS is the same idea as PRESSURE. In fact it is the same formula:
To use our formula we need to define what we mean by Stress and Strain.
STRESS is the same idea as PRESSURE. In fact it is the same formula:
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB

4. STRESS is the same idea as PRESSURE. In fact it is the same formula:
To use our formula we need to define what we mean by Stress and Strain.
STRESS is the same idea as PRESSURE. In fact it is the same formula:
STRAIN is a measure of how much the object deforms. We divide the change in the length by the original length to get strain:
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB

5. STRESS is the same idea as PRESSURE. In fact it is the same formula:
To use our formula we need to define what we mean by Stress and Strain.
STRESS is the same idea as PRESSURE. In fact it is the same formula:
STRAIN is a measure of how much the object deforms. We divide the change in the length by the original length to get strain:
Now we can put these together to get our formula for the Young’s Modulus:
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB

6. EXAMPLE: A nylon rope used by mountaineers elongates 1
EXAMPLE: A nylon rope used by mountaineers elongates 1.10m under the weight of a 65.0kg climber. If the rope is initially 45.0m in length and 7.0mm in diameter, what is Young’s modulus for this nylon?
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB

7. EXAMPLE: A nylon rope used by mountaineers elongates 1
EXAMPLE: A nylon rope used by mountaineers elongates 1.10m under the weight of a 65.0kg climber. If the rope is initially 45.0m in length and 7.0mm in diameter, what is Young’s modulus for this nylon?
ΔL=1.1m
L0=45m
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB

8. EXAMPLE: A nylon rope used by mountaineers elongates 1
EXAMPLE: A nylon rope used by mountaineers elongates 1.10m under the weight of a 65.0kg climber. If the rope is initially 45.0m in length and 7.0mm in diameter, what is Young’s modulus for this nylon?
A couple of quick calculations and we can just plug in to our formula:
ΔL=1.1m
L0=45m
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB

9. EXAMPLE: A nylon rope used by mountaineers elongates 1
EXAMPLE: A nylon rope used by mountaineers elongates 1.10m under the weight of a 65.0kg climber. If the rope is initially 45.0m in length and 7.0mm in diameter, what is Young’s modulus for this nylon?
A couple of quick calculations and we can just plug in to our formula:
ΔL=1.1m
L0=45m
7mm
Don’t forget to cut the diameter in half.
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB

10. EXAMPLE: A nylon rope used by mountaineers elongates 1
EXAMPLE: A nylon rope used by mountaineers elongates 1.10m under the weight of a 65.0kg climber. If the rope is initially 45.0m in length and 7.0mm in diameter, what is Young’s modulus for this nylon?
A couple of quick calculations and we can just plug in to our formula:
ΔL=1.1m
L0=45m
7mm
Don’t forget to cut the diameter in half.
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB

11. EXAMPLE: A steel wire 2.00 m long with circular cross-section must stretch no more than 0.25cm when a 400.0N weight is hung from one of its ends. What minimum diameter must this wire have?
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For Campus Learning Assistance Services at UCSB

12. EXAMPLE: A steel wire 2.00 m long with circular cross-section must stretch no more than 0.25cm when a 400.0N weight is hung from one of its ends. What minimum diameter must this wire have?
diam=?
L0=2m
ΔL=0.25cm
400N
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB

13. EXAMPLE: A steel wire 2.00 m long with circular cross-section must stretch no more than 0.25cm when a 400.0N weight is hung from one of its ends. What minimum diameter must this wire have?
We have most of the information for our formula. We can look up Young’s modulus for steel in a table:
diam=?
L0=2m
ΔL=0.25cm
400N
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB

14. EXAMPLE: A steel wire 2.00 m long with circular cross-section must stretch no more than 0.25cm when a 400.0N weight is hung from one of its ends. What minimum diameter must this wire have?
We have most of the information for our formula. We can look up Young’s modulus for steel in a table:
diam=?
L0=2m
ΔL=0.25cm
400N
The only piece missing is the area – we can rearrange the formula
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB

15. EXAMPLE: A steel wire 2.00 m long with circular cross-section must stretch no more than 0.25cm when a 400.0N weight is hung from one of its ends. What minimum diameter must this wire have?
We have most of the information for our formula. We can look up Young’s modulus for steel in a table:
diam=?
L0=2m
ΔL=0.25cm
400N
The only piece missing is the area – we can rearrange the formula
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB

16. EXAMPLE: A steel wire 2.00 m long with circular cross-section must stretch no more than 0.25cm when a 400.0N weight is hung from one of its ends. What minimum diameter must this wire have?
We have most of the information for our formula. We can look up Young’s modulus for steel in a table:
diam=?
L0=2m
ΔL=0.25cm
400N
The only piece missing is the area – we can rearrange the formula
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB

17. EXAMPLE: A steel wire 2.00 m long with circular cross-section must stretch no more than 0.25cm when a 400.0N weight is hung from one of its ends. What minimum diameter must this wire have?
We have most of the information for our formula. We can look up Young’s modulus for steel in a table:
diam=?
L0=2m
ΔL=0.25cm
400N
The only piece missing is the area – we can rearrange the formula
One last step – we need the diameter, and we have the area:
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB

18. EXAMPLE: A steel wire 2.00 m long with circular cross-section must stretch no more than 0.25cm when a 400.0N weight is hung from one of its ends. What minimum diameter must this wire have?
We have most of the information for our formula. We can look up Young’s modulus for steel in a table:
diam=?
L0=2m
ΔL=0.25cm
400N
The only piece missing is the area – we can rearrange the formula
One last step – we need the diameter, and we have the area:
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB

19. EXAMPLE: A steel wire 2.00 m long with circular cross-section must stretch no more than 0.25cm when a 400.0N weight is hung from one of its ends. What minimum diameter must this wire have?
We have most of the information for our formula. We can look up Young’s modulus for steel in a table:
diam=?
L0=2m
ΔL=0.25cm
400N
The only piece missing is the area – we can rearrange the formula
One last step – we need the diameter, and we have the area:
double the radius to get the diameter:
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB

20. EXAMPLE: When a weight is hung from a cylindrical wire of diameter D, it produces a tensile stress X in the wire. If the same weight is hung from a wire having twice the diameter as the first one, the tensile stress in this wire will be
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB

21. We can do this one just by staring at the formula for stress:
EXAMPLE: When a weight is hung from a cylindrical wire of diameter D, it produces a tensile stress X in the wire. If the same weight is hung from a wire having twice the diameter as the first one, the tensile stress in this wire will be
We can do this one just by staring at the formula for stress:
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB

22. We can do this one just by staring at the formula for stress:
EXAMPLE: When a weight is hung from a cylindrical wire of diameter D, it produces a tensile stress X in the wire. If the same weight is hung from a wire having twice the diameter as the first one, the tensile stress in this wire will be
We can do this one just by staring at the formula for stress:
The force is the same in both cases because it says they use the same weight.
The area is related to the square of the radius (or diameter), so when the diameter doubles the area goes up by a factor of 4.
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB

23. We can do this one just by staring at the formula for stress:
EXAMPLE: When a weight is hung from a cylindrical wire of diameter D, it produces a tensile stress X in the wire. If the same weight is hung from a wire having twice the diameter as the first one, the tensile stress in this wire will be
We can do this one just by staring at the formula for stress:
The force is the same in both cases because it says they use the same weight.
The area is related to the square of the radius (or diameter), so when the diameter doubles the area goes up by a factor of 4.
Thus the stress should go down by a factor of 4 (area is in the denominator)
Answer c)
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB