Question

The modulus of elasticity for a prosthetic material is 20 GPa. A 3 cm long sample of this material is circular in cross section with a radius of 1 cm. this sample is stretched 3.003 cm. what tensile force was applied to the material to create stretch?

Supposedly the answer is 6,283 N

Answer 1

please you have to apply this formula:
\[\frac{ F }{ S }=E \frac{ \Delta }{ L }\]
where E is the Young modulus, Delta is your strtching, L is length of your sample, S is the cross section and F is the force applied

Answer 2

\[e = \sigma/\epsilon \]
\[\sigma = F/A\]
\[A = pir ^{2}\] = .000314
then I don't know what e equals in Pa

Answer 3

\[\epsilon = (.03003-.03)/(,03) = .00\]

Answer 4

.001*

Answer 5

I think Young modulus is equals to 20GPa*cross section

Answer 6

so E=6.3*10^3

Answer 7

huh?
When i do this: \[20 GPa = F/ (.000314/.001) F= 6.28\]

Answer 8

sorry E = 6.3*10^6

Answer 9

I am lost

Answer 10

also me!

Answer 11

so i know A = .00314 & E= .001 then I have to plug it into the equation of \[\sigma=F/A\]

Answer 12

Please A=pi*10^(-4) m^2
do you agree?

Answer 13

Are you getting 6,283 as an answer?

Answer 14

no

Answer 15

that is suppose to be the answer to this problem, but I can't figure it out

Answer 16

Sorry, if i want the Young modulus I have to multiply this:
20*10^9*pi*10^(-4), do you agree?

Answer 17

NO, I don't understand where you are getting all that from

Answer 18

since your E have a dimension of a pressure

Answer 19

sorry E has a dimension...

Answer 20

can you just start from the beginning I am really confused. my prof said use the area of a circle... then solve for E , then plug those answers into the tensile force equation. I am getting tripped up on why 20 GPa changes... and how do we know

Answer 21

The formula for F, is:
\[F=E \frac{ \Delta }{ L }A\]
where E is the Young modulus, but E has the dimension of a force not of a pressure

Answer 22

okay, so how do you change GPa into the force of pressure then?

Answer 23

sorry E has the dimension of a pressure, sorry! I'm very sorry!

Answer 24

so I try to substitute your numerical data into the formula above

Answer 25

\[F=20*10^{9}\frac{ 3*10^{-2} }{ 3 }* \pi *10^{-4}=62.8*10^{3}N\]

Answer 26

uhhh, this makes no sense to me. Im so lost....

Answer 27

I know, nevertheless I have susbstitute your numerical data into formula above, and that formula is correct

Answer 28

1GPa=10^9 Pa, do you agree?

Answer 29

yes

Answer 30

stretching=3*10^(-3)cm, sorry not 3*10^(-2)cm, do you agree?

Answer 31

cross section A=3.14*10^(-4)m^2, do you agree?

Answer 32

since 1 cm=10^(-2) m

Answer 33

can you not do 10X 3 and put them in decimals. I'm getting confused

Answer 34

I know that A = pi (.01m) squared = .003
I know that E = (.03003 - .03)/(.03 = .001

Answer 35

so to find force= (20 GPa)/(.000314/.001) = 6.28

Answer 36

but i don't get how the answer is 6280

Answer 37

I got:

Answer 38

\[F=20*10^{9}\frac{ 3*10^{-5} }{ 3*10^{-2} }*\pi*10^{-4}=\]
\[=62.8*10^{2}Newton=6,280Newton\]

Answer 39

please keep in mind that youe stretching is 3.003-3=0.003 cm

Answer 40

yeah i know but i don't get your method. i don't get the 20 to the 9th and 3 times 10 to the -5th and why you are multiplying by pi and 10 to the -4

Answer 41

because cross section is:
\[\pi*1cm ^{2}=\pi*10^{-4}m ^{2}\]
since:
\[1m ^{2}=10^{4}cm ^{2}\]

Answer 42

i still don't understand. I'm just going to give up. i said use decimals and you keep using 10 to the 4th and stuff. just forget it

Answer 43

cross section A = pi*1cm^2 do you agree?

Answer 44

yes

Answer 45

please keep in mind you have exprees all your quantity in MKS unit

Answer 46

now 1cm=0.01m do you agree?

Answer 47

yea

Answer 48

and 1 cm^2=0.0001 m^2 =10^(-4) m^2 do you agree?

Answer 49

yeah, but i prefer decimals

Answer 50

ok! then please use this:
1 cm^2=0.0001 m^2
and stretching =0.00003 m
length=0.03 m

Answer 51

so yours is really saying:

F=20000000000 (.0003/.03) x pi .001 ?

Answer 52

i don't know why you multiply the answer by 10^2 newtons

Answer 53

no, please note that
A =pi*0.0001 m^2
stretching =0.00003 m

Answer 54

because I use the so called scientific notation, pratically the notation in which appear power of 10

Answer 55

oops sorry appear powers of 10...

Answer 56

did you get the right answer?

Answer 57

?
E= (.03003 - .03) / (.03) = .001
A= pi (.01)^2 = .000314

Answer 58

ok!

Answer 59

no

Answer 60

ok!

Answer 61

i don't get it

Answer 62

what if the problem had 20 pa instead of GPa what would the answer be then

Answer 63

using decimal I can write:
\[F=20000000000*\frac{ 0.00003 }{ 0.03 }*\pi*0.0001\]

Answer 64

how did you get .00003

Answer 65

because your stretching is equals to final length-initial length, namely
final length=3.003 cm and
initial length=3 cm,
so stretching=3.003-3=0.003 cm, finally
stretching = 0.00003 meters

Answer 66

@Summersnow8

Answer 67

ok

Answer 68

did yo get your answer, using decimal and not power of 10 instead?

Answer 69

no, i don't get why we don't just use 20....

Answer 70

im stuck on that

Answer 71

It is very simple, now I rewrite your answer using only decimals:

Answer 72

\[F=20000000000*\frac{ 0.00003 }{ 0.03 }*\pi*0.0001\]

Answer 73

where all quantities are measured with MKS units, namely
length in meters,
section in squared meters
Young modulus in Pascal
force in Newton

Answer 74

please complete the calculus above

Answer 75

yeah I know. but how do i get the answer to Pa

Answer 76

and what if 20 is already in Pa do I have to convert?

Answer 77

i got 3283.18

Answer 78

please the answer is a force not a pressure

Answer 79

6283

Answer 80

did you get 6283?

Answer 81

yeah

Answer 82

ok! perfect! well done!

Answer 83

that was too hard

Answer 84

so if 20 Pa was in place of 20GPa i would just use 20?

Answer 85

that's right! because Pa is an unit of measure that belongs to MKS system of measure units

Answer 86

so then the answer would be 6.28

Answer 87

@Michele_Laino

Answer 88

no, sorry you will get a force which is 0.000000001 times the force you got now!

Answer 89

huh? so......... it would be .000000002

Answer 90

.00000000628?

Answer 91

no, sorry 0.000000001*6280= 0.00000628 Newton

Answer 92

how do you know how many decimals?

Answer 93

because if the Young modulus is 20Pa then it is 10^-9 times the preceding Young modulus which was 10GPa, so our answer will be 10^-9 times preceding answer

Answer 94

sorry ...whic was 20 GPa, ...

Answer 95

I get when we use 20 GPa.... but lets say for this problem instead of 20 GPa it says 20 Pa.... what would the answer be then

Answer 96

as I said before, your answer will be:
F=0.00000628 Newton

Answer 97

whats the conversion then? instead of using 20000000000