8/11/2019 Henament Physics Exercise Young Modulis

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Use g = 9.80 N kg – 1 when answering these

questions. The following information applies toquestions 1 – 4. Steel wire is used to support

some extremely heavy pictures during an

exhibition at the National Gallery. The following

graph shows the stress – strain relationship for the

 particular steel alloy used. At point W the wire

loses its elastic properties, and it snaps at point

X.

1 a  What is the maximum stress that this

wire can tolerate before it undergoes plastic

deformation?

b  What is the largest strain that this wire will

tolerate while still obeying Hooke’s law? 

c  Calculate the gradient of this graph in the

interval up to and including the elastic limit.

d  What physical constant does the gradient

represent?

e  What is the tensile strength of this material?

2  A 1.0 m piece of this steel wire has a radius of

1.0 mm.

a What is the maximum extension that this wire

can tolerate without breaking?

b  What is the maximum extension that this wire

can tolerate before it undergoes plastic

deformation?

3  A tensile force of 1.0 kN is applied to

the wire described in Question 2. Use the graph

above to find the subsequent extension of the

wire:

a  while the force is still acting

b some time after the force has been removed.

4  This wire is now placed under a tensile

stress of 5.0 × 10 8  Pa.

a  Choose the correct response. Up to this point,

the wire has exhibited brittle/ductile behaviour.

b What is the extension of the wire while it

is supporting this load?

c  If the crate is removed, will the wire return to

its original length? Explain your answer.

5  A metal rod 2.00 m long and 1.00 cm 2  in

cross-section is subjected to a tensile force of

5.00 kN. As a result its length increases by 0.800

mm. Calculate Young’s modulus for the

material from which the rod is made.

6  a  In general, how does the value of Young’s

modulus for a particular material relate to its

stiffness?

b  The value of Young’s modulus for three

different metals is as follows:steel 2.0 × 10 11 N m – 2 

aluminium 7.0 × 10 10 N m – 2 

tungsten 3.5 × 10 11 N m – 2 

Rank these metals in order of increasing

flexibility.

7 The value of Young’s modulus for

aluminium is 7.0 × 10 10 N m  – 2 . An

aluminium rod of radius 5.00 mm used in a

crankshaft in an engine is subjected to a

compressive force during which its length is

decreased by 1.0%. Calculate the value of the

force acting on the crank.The following data for

human bone applies to questions 8 and 9.

Tensile strength = 1.2 × 108  N m  – 2 

Compressive strength = 1.7 × 108 N m  – 2 

Young’s modulus = 1.6 × 1010

  N m – 2

 

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Elastic limit = 1.0 × 10 8  N m  – 2 

8  The human femur has an average cross-

sectional area of 3.0 cm 2 and an unloaded

length of 0.40 m.

a  What is the maximum compression that this bone can tolerate while behaving elastically?

b Are bones more likely to break while

under tension or compression? Discuss.

c The bones of elderly people are said to be

more brittle than those of younger people.

Suggest some reasons why this might be so in

the light of your knowledge of materials.

9 It is estimated that in sporting activities, the

largest compression that a femur of length 40

cm will encounter will be about 0.30 mm.

Calculate the compressive stress on the bone for

this compression of the femur.

10  Use the stress – strain graph to answer the

following questions.

a  Which one or more of the materials is brittle?

b  Which material is the stiffest?

c  Which material is the least stiff?

d  Which material is the strongest?

e Which material is the most ductile?f Which line would correspond to a material

suit-able for building car bodies?

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