A copper wire 1mm in diameter and 2m long is used to support a mass of 5kg.by how much does the wire stretch under this load?
To determine how much the wire stretches under the given load, we need to use Hooke's Law. Hooke's Law states that the amount of stretching or compression of an object is proportional to the force applied to it, provided that the force is within the object's elastic limit.
The first step is to calculate the cross-sectional area of the copper wire. The diameter is given as 1mm, so we first need to convert it to meters:
Diameter = 1mm = 0.001m
The radius is half the diameter:
Radius = 0.001m / 2 = 0.0005m
Now, we can calculate the cross-sectional area using the formula:
Area = π * radius^2
Area = 3.1415 * (0.0005m)^2 = 0.0007854m^2
Next, we need to determine the Young's modulus of copper. Young's modulus is a material property that describes its stiffness or resistance to being deformed.
For copper, the typical value of Young's modulus is about 117 GPa (Gigapascals) or 117 x 10^9 Pa (Pascals).
Now, we can use Hooke's Law formula:
Stress = Young's modulus * Strain
Strain = Stress / Young's modulus
Since the wire is supporting a mass of 5kg, we can calculate the force applied to the wire using Newton's second law:
Force = mass * acceleration due to gravity
Force = 5kg * 9.8m/s^2 = 49N (Newtons)
Now, we can calculate the stress on the wire:
Stress = Force / Area
Stress = 49N / 0.0007854m^2
Now that we have the stress, we can find the strain:
Strain = Stress / Young's modulus
Strain = Stress / (117 x 10^9 Pa)
Finally, we can calculate the wire's elongation (stretch):
Elongation = Strain * Original Length
The original length of the wire is given as 2m:
Elongation = Strain * 2m
Now you can substitute the values and calculate the elongation.