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?
L=10 cm,
E= 200 GPa=200•10⁹ Pa
σ=F/A =350 MPa =350•10⁶ Pa
ε= ΔL/L
Hook's law E=
σ=E•ε=E•ΔL/L,
ΔL= σ•L/ E =350•10⁶•10/200•10⁹ =0.0175 cm
1.75 cm that is the correct one
To calculate the resultant elongation of the steel cable, we can use Hooke's Law, which relates stress and strain.
Hooke's Law states that stress (σ) is proportional to strain (ε), where the constant of proportionality is called the Young's modulus (E).
The formula for stress is:
σ = F / A
where σ is the stress, F is the applied force, and A is the cross-sectional area of the cable.
The formula for strain is:
ε = ΔL / L
where ε is the strain, ΔL is the change in length, and L is the original length of the cable.
The Young's modulus can be written as:
E = σ / ε
Rearranging the formula for strain, we have:
ΔL = ε * L
Substituting the formula for Young's modulus, we can rewrite strain as:
ε = σ / E
Therefore, the formula for the change in length is:
ΔL = (σ / E) * L
Given that the stress (σ) is 350 MPa, the Young's modulus (E) is 200 GPa, and the original length (L) is 10 m, we can substitute these values into the formula:
ΔL = (350 MPa / 200 GPa) * 10 m
To simplify the calculation, we need to convert the units so that they are consistent.
Converting MPa to Pa, we have:
350 MPa = 350 * 10^6 Pa
Converting GPa to Pa, we have:
200 GPa = 200 * 10^9 Pa
Substituting these values:
ΔL = (350 * 10^6 Pa / 200 * 10^9 Pa) * 10 m
Simplifying further:
ΔL = (350 / 200) * 10 m
ΔL = 1.75 m
Finally, we need to convert the elongation from meters to centimeters:
ΔL = 1.75 m * 100 cm/m
ΔL = 175 cm
Therefore, the resultant elongation of the steel cable is 175 cm.