Question

A string or rope will break apart if it is placed under too much tensile stress. Thicker ropes can withstand more tension without breaking because the thicker the rope, the greater the cross-sectional area and the smaller the stress. One type of steel has density 7730 and will break if the tensile stress exceeds . You want to make a guitar string from a mass of 3.7 of this type of steel. In use, the guitar string must be able to withstand a tension of 900 without breaking. (a) Determine the maximum length the string can have.

Answer 1

Answer: The answer is 13.02 meter

Explanation: your question is incomplete, the complete question is this if A string or rope will break apart if it is placed under too much tensile stress. Thicker ropes can withstand more tension without breaking because the thicker the rope, the greater the cross-sectional area and the smaller the stress. One type of steel has a density of

7750kg/m3 and will break if the tensile stress exceeds 7.0×108N/m2.

You want to make a guitar string from a mass of 4.5 g of this type of steel. In use, the guitar string must be able to withstand a tension of 900 N without breaking. Your job is the following.

(a) Determine the maximum length the string can have

Answer:

As we know that density(p)= mass(m)/volume(V)

Solve for volume(V)= mass/density

If the given mass value is in gram then we have to divide it by 1000 to get the value in kilogram so our mass in kg will be 3.7/1000= 0.0037 kg

And if density is in kg/m^3

Then volume will be V= 0.0037/7730 =>

4.79^10-7m^3

Now we know that stress = Force/Area

For Area = force/stress => 900/7*10^8=> 2795.95m^2

For length= volume/Area => 4.79^10-7/2795.95

Length= 13.02 m