Hey there! Sign in to join this conversationNew here? Join for free
x Turn on thread page Beta
    • Thread Starter
    Offline

    0
    ReputationRep:
    Hey, i am studying for my engineering materials exam, first year undergrad.

    What is the minimal diameter of a copper wire that can support the mass of 100 kg without breaking?
    The Young’ modulus of copper is 120 GPa, yield strength 190 MPa
    and tensile strength 250 MPa.


    I know to find the maximum diameter i have to use the tensile strength although using stress=force/area and i need to find diameter i'm not actually given force and need to find area which cant be found from the yield stress because i imagine the diameter for yield stress will be different than for tensile stress. Any help would be great, thanks !!
    Offline

    19
    ReputationRep:
    (Original post by Engclasshelp)
    Hey, i am studying for my engineering materials exam, first year undergrad.

    What is the minimal diameter of a copper wire that can support the mass of 100 kg without breaking?
    The Young’ modulus of copper is 120 GPa, yield strength 190 MPa
    and tensile strength 250 MPa.


    I know to find the maximum diameter i have to use the tensile strength although using stress=force/area and i need to find diameter i'm not actually given force and need to find area which cant be found from the yield stress because i imagine the diameter for yield stress will be different than for tensile stress. Any help would be great, thanks !!
    engineering forum if there is such place must be better
    Offline

    2
    ReputationRep:
    first find the weight on the copper wire using f=ma.
    f = 100kg \cdot 9.8ms^{-2} = 980N

    you know that stress = force / area, i.e.
    \tau = \tfrac{f}{a}

    rearrange to find the area:
     a = \tfrac{\tau}{f}

    substitute in what you know:
    a = \frac{980}{190*10^6} = 5 \cdot 10^{-6}m^2

    area of a circle is:
    a = \frac{\pi \cdot d^2}{4}

    rearrange to find the diameter:
    d = \sqrt{4 \cdot a \cdot \pi}

    and so
    d = \sqrt{4 \cdot 5 \cdot 10^{-6} \cdot \pi} = 0.0081m = 8.1mm

    i'm just guessing so i might be wrong.
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by samsama)
    first find the weight on the copper wire using f=ma.
    f = 100kg \cdot 9.8ms^{-2} = 980N

    you know that stress = force / area, i.e.
    \tau = \tfrac{f}{a}

    rearrange to find the area:
     a = \tfrac{\tau}{f}

    substitute in what you know:
    a = \frac{980}{190*10^6} = 5 \cdot 10^{-6}m^2

    area of a circle is:
    a = \frac{\pi \cdot d^2}{4}

    rearrange to find the diameter:
    d = \sqrt{4 \cdot a \cdot \pi}

    and so
    d = \sqrt{4 \cdot 5 \cdot 10^{-6} \cdot \pi} = 0.0081m = 8.1mm

    i'm just guessing so i might be wrong.
    Thanks so much!!
    • Study Helper
    Offline

    3
    ReputationRep:
    Study Helper
    (Original post by Engclasshelp)
    Hey, i am studying for my engineering materials exam, first year undergrad.

    What is the minimal diameter of a copper wire that can support the mass of 100 kg without breaking?
    The Young’ modulus of copper is 120 GPa, yield strength 190 MPa
    and tensile strength 250 MPa.


    I know to find the maximum diameter i have to use the tensile strength although using stress=force/area and i need to find diameter i'm not actually given force and need to find area which cant be found from the yield stress because i imagine the diameter for yield stress will be different than for tensile stress. Any help would be great, thanks !!
    Moved to Engineering forum
    Offline

    0
    ReputationRep:
    thx but your second to the last step, your rearranging is wrong
 
 
 
Turn on thread page Beta
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

Updated: June 29, 2016
Poll
Do you agree with the proposed ban on plastic straws and cotton buds?

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.