H6P8: Elongation
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?
Noted.
1.75
To find the resultant elongation of the steel cable, we can use the formula for linear elastic deformation:
Elongation = (Stress * Length) / (Young's Modulus)
Given:
Stress = 350 MPa
Length = 10 m
Young's Modulus = 200 GPa = 200,000 MPa
Let's plug in the values and calculate the elongation:
Elongation = (350 MPa * 10 m) / (200,000 MPa)
First, let's convert Young's Modulus to the same unit as stress (MPa):
200 GPa = 200,000 MPa
Now we can substitute the values:
Elongation = (350 MPa * 10 m) / (200,000 MPa)
Simplifying the equation:
Elongation = (3,500) / (200,000) m
= 0.0175 m
Since the unit of elongation is in meters, let's convert it to centimeters:
Elongation = 0.0175 m * 100 cm/m
= 1.75 cm
Therefore, the resultant elongation in the steel cable, under the given conditions, is 1.75 cm.