Topic 11.4
More about stress and strain
Scaling up: the bigger they are, the
harder they fall
Aims
In this activity you will analyse what happens when the human body is scaled up in size. You
will consider the effect on stress and the breaking of bones in a ‘giant’. You will practise
using factors to increase a variable to see its effects on other quantities. Finally you will
estimate the energy stored in the leg bones. Making estimates is a useful scientific exercise
that shows your understanding.

To analyse what happens when the human body is scaled up in size.

To consider the effect on stress and the breaking of bones in a ‘giant’.

To practise using factors to increase a variable to see its effects on other quantities.

To estimate the energy stored in the leg bones, which requires an estimate of the
length of the bones in the leg for use in calculations.
Is there a limit to the size of the human body?
Imagine a person scaled up to be eight times taller. To keep the same shape then all linear
dimensions must be eight times bigger.
What happens to the person’s mass, weight, volume and the cross-sectional area of their bones?
1 To find out, consider first a small cube of
mass 2.7 g. The sides of the larger cube are
eight times larger than those of the small
cube. Both cubes are made from the same
material.
(a) State the density of the material used
in each cube.
(b) Calculate the ratio of the volumes of
the two cubes.
(c) Calculate the ratio of the masses of the
two cubes.
(d) Calculate the ratio of the surface areas of the shaded area of the two cubes.
(e) If a cube increases in size by a factor of x, by what factor do the volume and the area
of one face increase in size? Give your answers in terms of x.
AQA Physics A AS Level Extension Activity © Nelson Thornes Ltd 2008
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Topic 11.4
More about stress and strain
2 Now consider the effect when the human body is scaled up eight times.
A man has a mass of 70 kg and the minimum cross-sectional area of the bones in one leg
is 4.5 × 10−4 m2. In compression, the ultimate tensile stress of bone is approximately
1.0 × 107 N m−2.
(a) The man is standing on both legs, sharing his weight equally.
(i) Calculate the maximum stress in his leg bones. (Take g as 9.8 N kg−1.)
(ii) Calculate the ratio of the maximum stress in his leg bone to the breaking stress.
(b) Suppose that all linear dimensions of the man’s body are increased by a factor of
eight.
(i) Calculate the new maximum stress in his leg bones. (Hint: both weight and area
change.)
(ii) Calculate the ratio of the maximum stress in his leg bone to the breaking stress.
(c) Explain what happens in each leg if the ‘giant’ man runs.
(d) Some dinosaurs were eight times taller than a person. Describe how this was
possible.
3 Bone can be a brittle material.
(a) What is meant by a brittle material?
(b) Estimate the distance that the bones in the leg compress due to a person’s weight.
In compression, the Young modulus of bone is approximately 1.0 × 1010 N m−2.
Use data from question 2 above.
State clearly the estimate of the one other quantity that you need to know for your
calculation.
(c) Estimates are usually considered accurate if they are within a factor of 3 of the actual
answer. Explain why the estimate is not completely accurate.
(d) Using you answer to (b) estimate the energy stored in the bones in the legs when
standing.
AQA Physics A AS Level Extension Activity © Nelson Thornes Ltd 2008
2
Topic 11.4
More about stress and strain
Answers
Teaching notes
Students will need to have studied the material of Chapter 11. They may need help and
encouragement to deal with ratios and estimates.
Answers
1 (a) 2.7 g cm−3
(e) 512 or 512 : 1
(f) 512 or 512 : 1
(g) 64 or 64 : 1
(h) volume increases by x3; area increases by x2
2 (a) (i) stress =
(iii)
force
70  9.8
=
= 7.6  105 N m−2 (2 s.f.)
area
2  4.5  10 4
7.6  105
= 0.076
1.0  107
(b) (i) mass is 512 × 70 kg; area is 64  4.5  10−4 m2 for each leg
stress is eight times larger = 7.6  105  8 = 6.1  106 N m−2 (2 s.f.)
(ii) 0.076  8 = 0.61 (2 s.f.)
(c) As soon as the giant lifts one leg off the ground, the stress in the other leg exceeds the
breaking stress and the leg breaks.
(d) The bones in the dinosaur were larger in cross-sectional area than those of the ‘giant’.
3 (a) A brittle material snaps with little noticeable yield. A sudden impact causes it to
break; the fracture surface is sharp and the two broken parts fit together because there
has been no yielding at the point of contact.
stress
7.6  105
=
= 7.6  10−5
10
Young modulus
1.0  10
change in length of leg = strain  original length
estimate length of leg bones approximately 1.0 m
compression of leg = 7.6  10−5 m = 8  10−5 m (1 s.f. appropriate).
(c) The cross-sectional area or length of the bones was not accurate or varies from
person to person; different bones have different Young moduli, which was only given
approximately.
(b) strain =
1
1
force  l =
 35  9.8  8 10−5
2
2
= 1.37  10−2 J
(d) Energy stored in one leg =
Energy stored in two legs = 2.74  10−2 J = 2.7  10−2 J (2 s.f.)
AQA Physics A AS Level Extension Activity © Nelson Thornes Ltd 2008
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