Elastic Deformation

Chapter 6 MCQs

For Full Scale Course: Written and Compiled By Sir Hunain Zia (AYLOTI), World Record Holder With 154 Total Personal A Grades, 11 World Records and 7 Distinctions, Educate A Change.

1

A spring has an unstretched length of 18.0 cm. A load is added and the new length becomes 23.5 cm.

What is the extension of the spring in SI units?

A 0.055 m
B 0.235 m
C 5.5 m
D 41.5 m

2

A spring has an original length of 12.0 cm. When a 3.0 N load is attached, its length becomes 18.0 cm.

What is the spring constant?

A 0.50 N/m
B 18 N/m
C 50 N/m
D 500 N/m

3

A spring has spring constant 250 N/m. A load of 15 N is attached.

What is the extension?

A 0.060 m
B 0.60 m
C 16.7 m
D 3750 m

4

A spring has spring constant 4.0 N/cm. It is extended by 12 mm.

What force is needed?

A 0.48 N
B 3.0 N
C 4.8 N
D 48 N

5

A spring has a load–extension graph. The graph is a straight line through the origin. When the extension is 4.0 cm, the load is 2.8 N.

What is the spring constant?

A 0.70 N/m
B 7.0 N/m
C 70 N/m
D 700 N/m

6

A graph of extension against load is a straight line through the origin. The gradient of the graph is 0.25 cm/N.

What is the spring constant?

A 0.0025 N/m
B 4.0 N/m
C 40 N/m
D 400 N/m

7

A spring is stretched by different loads.

load / N	0	2	4	6	8	10	12
extension / cm	0	1.0	2.0	3.0	4.0	6.5	10.0

Between which two loads is the limit of proportionality?

A 0 N and 2 N
B 6 N and 8 N
C 8 N and 10 N
D 10 N and 12 N

8

The load–extension graph for a spring is a straight line from the origin to point X. After point X, the graph curves.

What does point X represent?

A the elastic limit
B the limit of proportionality
C the maximum load
D the spring constant

9

A spring is stretched by a force that is below the limit of proportionality. The force is then removed.

What happens to the spring?

A It returns to its original length.
B It remains permanently extended.
C Its mass decreases.
D Its spring constant becomes zero.

10

Two springs P and Q are stretched by the same load. Spring P has a greater spring constant than spring Q.

Which statement is correct?

A P has greater extension than Q.
B P has smaller extension than Q.
C P and Q must have the same extension.
D P must be longer than Q before loading.

For Full Scale Course: Written and Compiled By Sir Hunain Zia (AYLOTI), World Record Holder With 154 Total Personal A Grades, 11 World Records and 7 Distinctions, Educate A Change.

11

A spring has length 8.0 cm with no load. It has length 10.5 cm with a 5.0 N load.

What is its spring constant?

A 2.0 N/m
B 50 N/m
C 200 N/m
D 500 N/m

12

A force of 6.0 N causes a spring to extend by 15 mm.

What force is needed to produce an extension of 35 mm, assuming the limit of proportionality is not exceeded?

A 2.6 N
B 14 N
C 21 N
D 90 N

13

A spring extends by 2.0 cm when a load of 4.0 N is attached.

What extension is produced by an 11 N load, assuming proportionality?

A 2.75 cm
B 5.5 cm
C 8.0 cm
D 22 cm

14

A spring has a spring constant of 150 N/m. Its original length is 20.0 cm.

What is its length when a load of 4.5 N is attached?

A 3.0 cm
B 17.0 cm
C 23.0 cm
D 50.0 cm

15

A spring is stretched from 9.0 cm to 13.5 cm by a force of 1.8 N.

What is its spring constant?

A 0.40 N/m
B 4.0 N/m
C 40 N/m
D 400 N/m

16

A spring has spring constant 80 N/m. A force causes an extension of 2.5 cm.

What is the force?

A 0.20 N
B 2.0 N
C 32 N
D 200 N

17

A student plots load on the y-axis and extension on the x-axis.

Which statement about the gradient is correct for the straight-line region?

A gradient = extension / load
B gradient = load / extension
C gradient = load × extension
D gradient = extension − load

18

A student plots extension on the y-axis and load on the x-axis.

Which statement about the gradient is correct for the straight-line region?

A gradient = spring constant
B gradient = 1 / spring constant
C gradient = load × extension
D gradient = load / extension

19

A spring has a load–extension graph that is a straight line through the origin up to 6.0 N.

Which conclusion is valid up to 6.0 N?

A extension is directly proportional to load
B extension is inversely proportional to load
C spring constant increases with load
D load is independent of extension

20

A spring has spring constant 300 N/m. Which load gives an extension of 8.0 mm?

A 0.024 N
B 2.4 N
C 24 N
D 37.5 N

21

A spring extends by 4.0 cm under a load of 12 N. A second spring extends by 6.0 cm under the same load.

Which spring is stiffer?

A first spring
B second spring
C both equally stiff
D cannot be determined because original lengths are not given

22

A spring has a length of 14.0 cm with a 2.0 N load and 22.0 cm with a 6.0 N load.

Assuming proportionality, what is the spring’s original length?

A 4.0 cm
B 10.0 cm
C 12.0 cm
D 18.0 cm

23

A spring has a length of 16.0 cm with a 3.0 N load and 28.0 cm with a 9.0 N load.

Assuming proportionality, what is the spring constant?

A 0.50 N/cm
B 2.0 N/cm
C 20 N/cm
D 50 N/cm

24

A spring obeys proportionality up to 8.0 N. Its extension at 8.0 N is 5.0 cm.

What is the extension at 12.0 N?

A exactly 7.5 cm
B less than 7.5 cm
C greater than 7.5 cm
D cannot be predicted from proportionality

25

A spring is stretched beyond its limit of proportionality.

Which statement must be correct?

A The spring has broken.
B Extension is no longer directly proportional to load.
C The spring cannot return to its original length.
D The spring constant is definitely zero.

For Full Scale Course: Written and Compiled By Sir Hunain Zia (AYLOTI), World Record Holder With 154 Total Personal A Grades, 11 World Records and 7 Distinctions, Educate A Change.

26

A spring has a load–extension graph. The graph is straight from 0 N to 5 N, then curves upwards so that extension increases more rapidly per extra newton.

Which statement is correct after 5 N?

A The spring constant remains constant.
B The spring constant effectively decreases.
C The spring constant effectively increases.
D The extension becomes zero.

27

A spring has a load–extension graph. Load is on the y-axis and extension is on the x-axis. Spring X has a steeper straight-line graph than spring Y.

Which statement is correct?

A X has a greater spring constant than Y.
B X has a smaller spring constant than Y.
C X extends more than Y for the same load.
D X and Y have equal spring constants.

28

A graph of extension against load is plotted. Spring X has a steeper straight-line graph than spring Y.

Which statement is correct?

A X has a greater spring constant than Y.
B X has a smaller spring constant than Y.
C X needs greater load for the same extension.
D X is stiffer than Y.

29

A spring extends by 3.0 cm under a 9.0 N load. Another spring extends by 5.0 cm under a 10 N load.

What is the ratio of spring constant of the first spring to the second spring?

A 2 : 3
B 3 : 2
C 5 : 3
D 9 : 10

30

A spring has a spring constant of 25 N/m. Another spring has a spring constant of 0.50 N/cm.

Which statement is correct?

A The first spring is stiffer.
B The second spring is stiffer.
C Both have the same stiffness.
D They cannot be compared because the units are different.

31

A spring extends by 1.5 cm when a load of 3.0 N is attached. A second load is added so that the total load is 7.0 N.

Assuming proportionality, what is the total extension?

A 2.0 cm
B 3.5 cm
C 4.0 cm
D 10.5 cm

32

A spring has a natural length of 25.0 cm. A load of 2.0 N makes its length 29.0 cm. Another load is added and the total load becomes 5.0 N.

Assuming proportionality, what is the final length?

A 10.0 cm
B 31.0 cm
C 35.0 cm
D 72.5 cm

33

A spring is stretched by a force of 5.0 N and extends by 20 mm.

Which pair of values would be expected if the spring obeys proportionality?

A 10 N gives 30 mm extension
B 2.5 N gives 10 mm extension
C 1.0 N gives 5.0 mm extension
D 15 N gives 90 mm extension

34

A student calculates spring constant using k = F / x but uses the final length instead of the extension.

What is the likely effect?

A The calculated spring constant is too large.
B The calculated spring constant is too small.
C The calculated spring constant is unchanged.
D The calculated spring constant becomes negative.

35

A spring has original length 10.0 cm. A 4.0 N load makes its length 18.0 cm.

A student wrongly uses 18.0 cm as the extension.

What value of spring constant does the student calculate?

A 22 N/m
B 50 N/m
C 222 N/m
D 400 N/m

36

Using the same spring in Q35, what is the correct spring constant?

A 22 N/m
B 50 N/m
C 222 N/m
D 400 N/m

37

A spring has a load of 6.0 N attached. Its extension is measured as 0.030 m.

The load is increased to 10.0 N. The extension becomes 0.052 m.

What can be concluded?

A The spring is definitely still obeying proportionality.
B The spring is no longer exactly proportional over this range.
C The spring constant is zero.
D The extension is independent of load.

38

A spring extends by 2.0 cm when a 5.0 N load is attached. The load is increased to 15 N, and the extension becomes 7.5 cm.

Which statement is correct?

A The spring obeys proportionality throughout.
B The spring extends less than expected at 15 N.
C The spring extends more than expected at 15 N.
D The load is inversely proportional to extension.

39

A student measures extension for increasing loads.

load / N	1	2	3	4	5
extension / mm	4	8	12	16	19

Which load is the first clear sign that the spring is no longer exactly proportional?

A 2 N
B 3 N
C 4 N
D 5 N

40

A force stretches a rubber band. The rubber band returns to its original length when the force is removed, but its load–extension graph is not a straight line.

Which statement is correct?

A It is elastic but not proportional.
B It is proportional but not elastic.
C It has no extension.
D It has no force acting on it while stretched.

For Full Scale Course: Written and Compiled By Sir Hunain Zia (AYLOTI), World Record Holder With 154 Total Personal A Grades, 11 World Records and 7 Distinctions, Educate A Change.

41

Two identical springs are hung side by side and support one load together. Each spring carries half the load.

Compared with using one spring alone with the same total load, what is the extension of each spring?

A one quarter as much
B half as much
C the same
D twice as much

42

Two identical springs are connected end to end. A load is attached to the lower spring.

Compared with using one spring alone with the same load, what is the total extension?

A one quarter as much
B half as much
C the same
D twice as much

43

A spring of spring constant k is cut into two equal halves.

A load is attached to one half of the spring.

Compared with the original whole spring under the same load, what is the extension of the half-spring?

A one quarter as much
B half as much
C the same
D twice as much

44

Two springs are connected in parallel. Spring P has spring constant 100 N/m and spring Q has spring constant 300 N/m. A load causes both springs to have the same extension of 0.020 m.

What is the total load supported?

A 2.0 N
B 4.0 N
C 6.0 N
D 8.0 N

45

Two springs are connected in series. Spring P has spring constant 100 N/m and spring Q has spring constant 300 N/m. A load of 6.0 N is attached.

What is the total extension?

A 0.020 m
B 0.060 m
C 0.080 m
D 0.240 m

46

A spring is used to measure force. Its spring constant is 40 N/m. The smallest scale division on the ruler beside it is 1.0 mm.

What is the smallest change in force that can be detected from one scale division?

A 0.004 N
B 0.040 N
C 0.40 N
D 40 N

47

A force meter contains a spring. A 2.0 N force produces an extension of 5.0 cm.

What force produces an extension of 12.5 cm, assuming proportionality?

A 0.80 N
B 5.0 N
C 20 N
D 31 N

48

A spring stretches by 6.0 cm under a 4.0 N load. A second spring stretches by 9.0 cm under a 3.0 N load.

Which comparison is correct?

A first spring has twice the spring constant of second spring
B first spring has the same spring constant as second spring
C first spring has half the spring constant of second spring
D second spring is stiffer than first spring

49

A load is added to a spring and then removed. The spring is found to be longer than it was originally.

Which statement is correct?

A The spring has undergone permanent deformation.
B The spring must have obeyed proportionality throughout.
C The spring constant must have increased.
D The extension was zero while the load was attached.

50

A student wants to identify the limit of proportionality from a load–extension graph.

Which feature should the student look for?

A the point where the graph first stops being a straight line
B the point where the graph reaches the largest load
C the point where the extension becomes zero
D the point where the spring first breaks

For Full Scale Course: Written and Compiled By Sir Hunain Zia (AYLOTI), World Record Holder With 154 Total Personal A Grades, 11 World Records and 7 Distinctions, Educate A Change.

Answer Key

Q	Ans	Q	Ans	Q	Ans	Q	Ans	Q	Ans
1	A	11	C	21	A	31	B	41	B
2	C	12	B	22	B	32	C	42	D
3	A	13	B	23	A	33	B	43	B
4	C	14	C	24	D	34	B	44	D
5	C	15	C	25	B	35	A	45	C
6	D	16	B	26	B	36	B	46	B
7	C	17	B	27	A	37	B	47	B
8	B	18	B	28	B	38	C	48	A
9	A	19	A	29	B	39	D	49	A
10	B	20	B	30	B	40	A	50	A

For Full Scale Course: Written and Compiled By Sir Hunain Zia (AYLOTI), World Record Holder With 154 Total Personal A Grades, 11 World Records and 7 Distinctions, Educate A Change.

Detailed Explanations

1. A

Extension = stretched length − original length
Extension = 23.5 cm − 18.0 cm
Extension = 5.5 cm
Convert to metres:
- 5.5 cm = 0.055 m
Answer = 0.055 m

2. C

Original length = 12.0 cm
New length = 18.0 cm
Extension = 6.0 cm = 0.060 m
k = F / x
k = 3.0 / 0.060
k = 50 N/m

3. A

k = F / x
So x = F / k
x = 15 / 250
x = 0.060 m
C is the classic “divide wrong way” trap.

4. C

k = 4.0 N/cm
Extension = 12 mm = 1.2 cm
F = kx
F = 4.0 × 1.2
F = 4.8 N

5. C

Extension = 4.0 cm = 0.040 m
Load = 2.8 N
k = F / x
k = 2.8 / 0.040
k = 70 N/m

6. D

Graph is extension against load.
Gradient = extension / load
Gradient = 0.25 cm/N
Convert:
- 0.25 cm = 0.0025 m
- gradient = 0.0025 m/N
Since k = F / x:
- gradient = x / F = 1 / k
k = 1 / 0.0025
k = 400 N/m
Brutal graph trap: if extension is on the y-axis, gradient is not k. It is 1/k.

7. C

Up to 8 N:
- 2 N → 1.0 cm
- 4 N → 2.0 cm
- 6 N → 3.0 cm
- 8 N → 4.0 cm
This is proportional.
At 10 N, expected extension would be 5.0 cm, but actual extension is 6.5 cm.
Therefore proportionality breaks between 8 N and 10 N.

8. B

The limit of proportionality is the point where the graph first stops being a straight line.
Before point X:
- load ∝ extension
After point X:
- load is no longer directly proportional to extension
Answer = limit of proportionality

9. A

Below the limit of proportionality, the spring behaves elastically.
When the load is removed, it returns to its original length.
Permanent extension usually happens after the elastic limit, not simply after proportionality.

10. B

k = F / x
For the same load F:
- larger k means smaller x
Spring P has the greater spring constant.
So P stretches less than Q.

For Full Scale Course: Written and Compiled By Sir Hunain Zia (AYLOTI), World Record Holder With 154 Total Personal A Grades, 11 World Records and 7 Distinctions, Educate A Change.

11. C

Original length = 8.0 cm
Loaded length = 10.5 cm
Extension = 2.5 cm = 0.025 m
k = F / x
k = 5.0 / 0.025
k = 200 N/m

12. B

6.0 N gives 15 mm.
Extension and force are proportional.
Force for 35 mm:
- F = 6.0 × 35 / 15
- F = 14 N
Answer = 14 N

13. B

4.0 N gives 2.0 cm.
Extension per newton = 2.0 / 4.0 = 0.50 cm/N
For 11 N:
- extension = 11 × 0.50
- extension = 5.5 cm

14. C

k = 150 N/m
F = 4.5 N
x = F / k
x = 4.5 / 150
x = 0.030 m = 3.0 cm
Original length = 20.0 cm
New length = 20.0 + 3.0
New length = 23.0 cm

15. C

Original length = 9.0 cm
New length = 13.5 cm
Extension = 4.5 cm = 0.045 m
k = F / x
k = 1.8 / 0.045
k = 40 N/m

16. B

k = 80 N/m
Extension = 2.5 cm = 0.025 m
F = kx
F = 80 × 0.025
F = 2.0 N

17. B

Load is on the y-axis.
Extension is on the x-axis.
Gradient = y / x
Gradient = load / extension
Since k = F / x, gradient = spring constant

18. B

Extension is on the y-axis.
Load is on the x-axis.
Gradient = extension / load
Since k = load / extension:
- gradient = 1 / k
Answer = 1 / spring constant

19. A

A straight line through the origin means direct proportionality.
Therefore extension is directly proportional to load.
This is true only up to 6.0 N.

20. B

k = 300 N/m
x = 8.0 mm = 0.0080 m
F = kx
F = 300 × 0.0080
F = 2.4 N

21. A

Same load is used.
First spring extends 4.0 cm.
Second spring extends 6.0 cm.
The spring with less extension for the same force is stiffer.
So the first spring is stiffer.

22. B

From 2.0 N to 6.0 N, load increases by 4.0 N.
Length increases from 14.0 cm to 22.0 cm.
Length increase = 8.0 cm
Extension per newton = 8.0 / 4.0 = 2.0 cm/N
At 2.0 N, extension = 2.0 × 2.0 = 4.0 cm
Original length = 14.0 − 4.0
Original length = 10.0 cm

23. A

Load increases from 3.0 N to 9.0 N.
Increase in load = 6.0 N
Length increases from 16.0 cm to 28.0 cm.
Increase in extension = 12.0 cm
Extension per newton = 12.0 / 6.0 = 2.0 cm/N
k = load / extension
k = 1 / 2.0
k = 0.50 N/cm
This is also 50 N/m, but the option given is 0.50 N/cm.

24. D

The spring obeys proportionality only up to 8.0 N.
12.0 N is beyond this range.
So we cannot use proportionality to predict the extension.
The answer is cannot be predicted from proportionality.
This is a savage wording trap. “Would be 7.5 cm” only works if it still obeyed Hooke’s law.

25. B

Beyond the limit of proportionality:
- extension is no longer directly proportional to load.
The spring has not necessarily broken.
It may or may not return to original length depending on whether the elastic limit has been exceeded.
So the only statement that must be correct is B.

For Full Scale Course: Written and Compiled By Sir Hunain Zia (AYLOTI), World Record Holder With 154 Total Personal A Grades, 11 World Records and 7 Distinctions, Educate A Change.

26. B

After 5 N, extension increases more rapidly for each extra newton.
That means more extension is produced by the same extra force.
k = F / x
If x increases more for each F, the effective spring constant decreases.
Answer = spring constant effectively decreases

27. A

Load is on y-axis.
Extension is on x-axis.
Gradient = load / extension = k
Steeper graph means greater gradient.
So spring X has a greater spring constant.
Greater k = stiffer spring.

28. B

Extension is on y-axis.
Load is on x-axis.
Gradient = extension / load = 1/k
Steeper graph means larger extension for each newton.
So k is smaller.
Spring X has a smaller spring constant than Y.
This is the evil twin of Q27.

29. B

First spring:
- k₁ = 9.0 / 3.0 = 3.0 N/cm
Second spring:
- k₂ = 10 / 5.0 = 2.0 N/cm
Ratio k₁ : k₂ = 3.0 : 2.0
Answer = 3 : 2

30. B

First spring:
- k = 25 N/m
Second spring:
- 0.50 N/cm
Convert second to N/m:
- 1 cm = 0.01 m
- 0.50 N/cm = 50 N/m
Second spring has greater k.
So the second spring is stiffer.

31. B

3.0 N gives 1.5 cm.
Extension per newton = 1.5 / 3.0 = 0.5 cm/N
Total load = 7.0 N
Total extension = 7.0 × 0.5
Total extension = 3.5 cm

32. C

Natural length = 25.0 cm
With 2.0 N, length = 29.0 cm
Extension = 4.0 cm
Extension per newton = 4.0 / 2.0 = 2.0 cm/N
With 5.0 N:
- extension = 5.0 × 2.0 = 10.0 cm
Final length = 25.0 + 10.0
Final length = 35.0 cm

33. B

5.0 N gives 20 mm.
Extension per newton = 20 / 5.0 = 4.0 mm/N
For 2.5 N:
- extension = 2.5 × 4.0
- extension = 10 mm
Answer = 2.5 N gives 10 mm extension

34. B

k = F / extension.
Final length is larger than extension because:
- final length = original length + extension
If the student uses final length instead of extension, the denominator is too large.
So calculated k is too small.

35. A

Student wrongly uses 18.0 cm as extension.
Convert:
- 18.0 cm = 0.180 m
k = F / x
k = 4.0 / 0.180
k = 22.2 N/m
Closest option = 22 N/m

36. B

Correct extension = final length − original length
Extension = 18.0 − 10.0 = 8.0 cm
Extension = 0.080 m
k = 4.0 / 0.080
k = 50 N/m

37. B

At 6.0 N:
- k = 6.0 / 0.030 = 200 N/m
At 10.0 N:
- k = 10.0 / 0.052 = 192 N/m approximately
The value of k is not exactly constant.
Therefore the spring is no longer exactly proportional over this range.

38. C

5.0 N gives 2.0 cm.
If proportional, 15 N should give:
- extension = 3 × 2.0 = 6.0 cm
Actual extension = 7.5 cm
Actual extension is greater than expected.
So the spring extends more than expected at 15 N.

39. D

Proportional pattern:
- 1 N → 4 mm
- 2 N → 8 mm
- 3 N → 12 mm
- 4 N → 16 mm
At 5 N, expected extension = 20 mm.
Actual extension = 19 mm.
First clear sign of non-proportionality = 5 N

40. A

The rubber band returns to original length, so it is elastic.
But the graph is not straight, so extension is not directly proportional to load.
Therefore it is elastic but not proportional.
Elastic does not always mean Hooke’s law. That’s the trap.

For Full Scale Course: Written and Compiled By Sir Hunain Zia (AYLOTI), World Record Holder With 154 Total Personal A Grades, 11 World Records and 7 Distinctions, Educate A Change.

41. B

Two identical springs side by side share the load.
Each spring carries half the load.
Since extension ∝ force, each spring extends half as much.
Answer = half as much

42. D

Two identical springs in series each carry the same load.
Each spring extends by the normal amount.
Total extension = extension of first spring + extension of second spring
Total extension is twice as much

43. B

Cutting a spring in half makes it stiffer.
Half the spring has double the spring constant.
For the same load:
- x = F / k
If k doubles, x halves.
Extension of half-spring = half as much

44. D

Springs are in parallel, so they have the same extension.
Force in P:
- Fₚ = kx = 100 × 0.020 = 2.0 N
Force in Q:
- Fq = 300 × 0.020 = 6.0 N
Total load = 2.0 + 6.0
Total load = 8.0 N

45. C

Springs are in series, so each spring carries the same load.
Extension of P:
- xₚ = F / k = 6.0 / 100 = 0.060 m
Extension of Q:
- xq = 6.0 / 300 = 0.020 m
Total extension = 0.060 + 0.020
Total extension = 0.080 m

46. B

k = 40 N/m
Smallest scale division = 1.0 mm = 0.0010 m
Smallest detectable force change:
- F = kx
- F = 40 × 0.0010
- F = 0.040 N

47. B

2.0 N gives 5.0 cm.
Extension increases from 5.0 cm to 12.5 cm.
Scale factor = 12.5 / 5.0 = 2.5
Force = 2.0 × 2.5
Force = 5.0 N

48. A

First spring:
- k₁ = 4.0 / 6.0 = 0.667 N/cm
Second spring:
- k₂ = 3.0 / 9.0 = 0.333 N/cm
First spring has twice the spring constant of second spring.
So first spring is twice as stiff.

49. A

If the spring is longer after the load is removed, it has not returned to original length.
This is permanent deformation.
It does not mean proportionality was obeyed.
It usually means the spring was overloaded.

50. A

The limit of proportionality is found where the graph first stops being a straight line.
It is not necessarily where the spring breaks.
It is not simply the highest load.
Answer = first stops being a straight line

For Full Scale Course: Written and Compiled By Sir Hunain Zia (AYLOTI), World Record Holder With 154 Total Personal A Grades, 11 World Records and 7 Distinctions, Educate A Change.

Common Traps From This Chapter

Trap	Correct Rule
Using final length as extension	extension = final length − original length
cm used directly in N/m formula	convert cm to m
mm used directly in N/m formula	convert mm to m
k formula	k = F / x
Extension formula	x = F / k
Load–extension graph, load on y-axis	gradient = k
Extension–load graph, extension on y-axis	gradient = 1/k
Steeper load–extension graph	larger k, stiffer spring
Steeper extension–load graph	smaller k, less stiff spring
Limit of proportionality	point where graph first stops being straight
Beyond limit of proportionality	not directly proportional
Beyond limit of proportionality	not necessarily broken
Elastic behaviour	returns to original length
Permanent deformation	does not return to original length
Same load, smaller extension	larger spring constant
Same load, larger extension	smaller spring constant
Springs in parallel	share load, smaller extension
Springs in series	extensions add
Half a spring	stiffer, smaller extension
Rubber band returning to length	elastic, even if graph is curved

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