Physics Young modulus question? Calculating force? Watch

maddie.gardiner
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Calculate the force which will produce an extension of 0.30 mm in a steel wire with a length of 4.0 m and a cross sectional area of 2.0 x 10^-6 m^2.

Young modulus of steel: 2.1 x 10^11 Pa.

HOW DO I DO THIS LIKE even just the equation would help... (sucks that I missed the first two weeks of Physics)
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Lee R.
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Do you know your equations for stress and strain and how they link to the Young's Modulus?

Edit: just saw what you put in brackets.
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Stress = Force (N) / Cross sectional area (m^2)
Strain = Extension / Original Length (be consistent with what the measurement is in, like both values must be in metres or millimetres to produce a ratio and produce no unit for strain)
Young's Modulus = Stress / Strain
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maddie.gardiner
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(Original post by Lee R.)
Do you know your equations for stress and strain and how they link to the Young's Modulus?

Edit: just saw what you put in brackets.
Spoiler:
Show
Stress = Force (N) / Cross sectional area (m^2)
Strain = Extension / Original Length (be consistent with what the measurement is in, like both values must be in metres or millimetres to produce a ratio and produce no unit for strain)
Young's Modulus = Stress / Strain
I do have those equations but I'm not sure how I'd use them to find the force?
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StrawbAri
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Basically this and then just substitute values to get the force
Sorry my handwriting is so messy. And also remember to make sure the values of the original length and the extension are both in the same units (ie both metres or both millimetres)
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maddie.gardiner
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(Original post by StrawbAri)
Basically this and then just substitute values to get the force
Sorry my handwriting is so messy. And also remember to make sure the values of the original length and the extension are both in the same units (ie both metres or both millimetres)
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THANK YOU!!!! and you're writing is fine
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0le
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Let me run through what those formulae mean, at least how I used to interpret them.



Young's modulus = stress/ strain.

In this context stress arises from an applied force of some sort. Strain is the deformation as a result of the strain. The Young's modulus therefore measures the stiffness of an object.An object with a high Young's modulus, will be very stiff, and consequently, for a given stress, have little strain (deformation).

Stress = Force / Cross sectional Area,

Stress here usually refers to some form of internal force reaction to an applied mechanical load. It actually corresponds to the internal forces inside a body which are reacting to that external load. Pressure on the other hand is related to the load that is actually applied, i.e. the external force. Stress is usually denoted by two symbols, sigma for the normal direction (tensile/ compressive stress) and Tau for the tangential direction (shear stress). The stress tensor consists of all components of the normal and tangential terms.

In Fluid Dynamics, pressure measures the energy contained within a given volume of fluid due to the molecular motion of the molecules. Stress on the other hand, in fluid dynamics, is typically referred to as "viscous stress" and corresponds to the stresses caused by bulk motion of the fluid, i.e. due to velocity gradients. Viscous stresses are denoted by sigma, but unlike structure analysis, this can act is an arbitrary direction. The stress tensor in this case, quite literally, is the viscous stress itself. Sometimes the pressure term is called "pressure stress" and is added to the "viscous stress" to give a "molecular stress".

Strain = Extension / original length

This is an approximation of the deformation in a body. Calculating strain in this way is called "engineer's strain". A better approximation is called "true strain". This measures the strain based on the cross sectional area at a instance of measurement, whereas engineering strain assumes a cross sectional area on the undeformed object. For simple calculations in low strains, the above quoted formula will usually suffice.
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maddie.gardiner
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(Original post by djpailo)
Let me run through what those formulae mean, at least how I used to interpret them.



Young's modulus = stress/ strain.

In this context stress arises from an applied force of some sort. Strain is the deformation as a result of the strain. The Young's modulus therefore measures the stiffness of an object.An object with a high Young's modulus, will be very stiff, and consequently, for a given stress, have little strain (deformation).

Stress = Force / Cross sectional Area,

Stress here usually refers to some form of internal force reaction to an applied mechanical load. It actually corresponds to the internal forces inside a body which are reacting to that external load. Pressure on the other hand is related to the load that is actually applied, i.e. the external force. Stress is usually denoted by two symbols, sigma for the normal direction (tensile/ compressive stress) and Tau for the tangential direction (shear stress). The stress tensor consists of all components of the normal and tangential terms.

In Fluid Dynamics, pressure measures the energy contained within a given volume of fluid due to the molecular motion of the molecules. Stress on the other hand, in fluid dynamics, is typically referred to as "viscous stress" and corresponds to the stresses caused by bulk motion of the fluid, i.e. due to velocity gradients. Viscous stresses are denoted by sigma, but unlike structure analysis, this can act is an arbitrary direction. The stress tensor in this case, quite literally, is the viscous stress itself. Sometimes the pressure term is called "pressure stress" and is added to the "viscous stress" to give a "molecular stress".

Strain = Extension / original length

This is an approximation of the deformation in a body. Calculating strain in this way is called "engineer's strain". A better approximation is called "true strain". This measures the strain based on the cross sectional area at a instance of measurement, whereas engineering strain assumes a cross sectional area on the undeformed object. For simple calculations in low strains, the above quoted formula will usually suffice.
Thank you, this made it so easy to understand. I wasn't originally doing Physics, so I missed the first few weeks and they covered most of this. Thank you
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NeronAzemi
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Youngs modulus =stress÷strainStress=force÷are aStrain=change in length / length
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