# What is the diameter of the cylindrical rod

• Perodamh
In summary, to find the diameter of a cylindrical rod of copper with a yield strength of 240MPa and a length of 380mm that can withstand a load of 6660N with an elongation of 0.5mm, we can use the formula E = stress/strain and plug in the given values to get a diameter of 7.65 mm.
Perodamh

## Homework Statement

A cylindrical rod of copper (E = 110GPa) having a yield strength of 240MPa is to be subjected to a load of 6660N. If the length of the rod is 380mm, what must be the diameter to allow an elongation of 0.5mm.

## Homework Equations

E = stress/ strain
stress = Force/Area ; Area = pi*(diameter)/4
strain = elongation/original length
E= young's modulus = 110GPa = 110 * 10^9Pa
yield strength = 240MPa = 240 * 10^6Pa
Force = 6660N
elongation = 0.5mm
original length = 380mm

## The Attempt at a Solution

I'm trying to understand relation between yield strength and young modulus.So far all i got from google is that it is the max stress a body goes through before plastic deformation occurs, but how do i plug that in anywhere? Thanks

You don't really need the yield strength to solve this problem. Young's modulus is all you need.

phyzguy said:
You don't really need the yield strength to solve this problem. Young's modulus is all you need.
Thanks, was wondering why it was there, I tried another go at the problem, by plugging in values and got (0.586 * 10^-4)m. Don't know how correct that is?

Perodamh said:
Thanks, was wondering why it was there, I tried another go at the problem, by plugging in values and got (0.586 * 10^-4)m. Don't know how correct that is?

Show us your work so we can see how you got there. then we can make meaningful comments.

phyzguy said:
Show us your work so we can see how you got there. then we can make meaningful comments.
E = stress / strain
stress = F / A
Area = pi*(diameter)^2/4
strain= elongation/original length
making d subject of formula = sqrt(4*F*L/(E*pi*elongation))
plugging in values after conversion to S.I units gave 58617.25 * 10^-9m which is same as 0.586 * 10^-4m

Well, I agree with this, "making d subject of formula = sqrt(4*F*L/(E*pi*elongation))", but that's not the answer I got, so one of us made a mistake. I suggest you check your numbers

Perodamh said:
E = stress / strain
stress = F / A
Area = pi*(diameter)^2/4
strain= elongation/original length
making d subject of formula = sqrt(4*F*L/(E*pi*elongation))
plugging in values after conversion to S.I units gave 58617.25 * 10^-9m which is same as 0.586 * 10^-4m
Seems too small. Did you forget to take the square root?

haruspex said:
Seems too small. Did you forget to take the square root?
phyzguy said:
Well, I agree with this, "making d subject of formula = sqrt(4*F*L/(E*pi*elongation))", but that's not the answer I got, so one of us made a mistake. I suggest you check your numbers
I skipped the square root part so uhm 0.765 * 10^-2

Perodamh said:
I skipped the square root part so uhm 0.765 * 10^-2

That's what I got. 7.65 mm.

phyzguy said:
That's what I got. 7.65 mm.
Neat, thanks so much

## What is the diameter of the cylindrical rod?

The diameter of a cylindrical rod is the distance across the circular cross-section of the rod, passing through the center point.

## How is the diameter of a cylindrical rod measured?

The diameter of a cylindrical rod can be measured using a caliper, which is a tool with two jaws that can be adjusted to fit around the rod and provide an accurate measurement.

## What is the unit of measurement used for the diameter of a cylindrical rod?

The diameter of a cylindrical rod is typically measured in either inches or millimeters, depending on the country or industry standards.

## How does the diameter of a cylindrical rod affect its strength?

The larger the diameter of a cylindrical rod, the stronger it is. This is because a larger diameter allows for more material to be distributed around the perimeter, increasing its ability to handle stress and weight.

## Can the diameter of a cylindrical rod vary along its length?

Yes, it is possible for the diameter of a cylindrical rod to vary along its length. This can be due to manufacturing processes or intentional design choices to create a tapered or variable diameter rod.

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