A steel cable 10 m long is pulled in tension with a stress of 350 MPa. Assume that the Young's modulus of the steel cable is about 200 GPa. If only elastic deformation occurs, what is the resultant elongation in cm?

1.75 To find the resultant elongation of the steel cable, we can use the formula for strain and the definition of Young's modulus.

Young's modulus is defined as the ratio of stress to strain, and strain is defined as the change in length divided by the original length.

So, we start by rearranging the Young's modulus equation to solve for strain:

Young's modulus (E) = stress (σ) / strain (ε)

strain (ε) = stress (σ) / Young's modulus (E)

Plugging in the given values:

stress (σ) = 350 MPa = 350 * 10^6 Pa
Young's modulus (E) = 200 GPa = 200 * 10^9 Pa

Now, we can calculate the strain:

strain (ε) = (350 * 10^6) / (200 * 10^9)

Next, we can use the definition of strain to calculate the change in length (ΔL) of the steel cable:

strain (ε) = ΔL / original length (L0)

Rearranging the equation:

ΔL = strain (ε) * original length (L0)

Plugging in the original length:

L0 = 10 m = 1000 cm

ΔL = (strain (ε)) * (original length (L0))

Finally, we can calculate the resultant elongation (ΔL) in centimeters:

ΔL = (strain (ε)) * (original length (L0))
= ((350 * 10^6) / (200 * 10^9)) * 1000
= 1.75 cm

Therefore, the resultant elongation of the steel cable is 1.75 cm.