Copper has a breaking stress of about
3 × 10^8 N/m2.
What is the maximum load that can be
hung from a copper wire of diameter 0.5 mm?
Answer in units of N.
If 55% of this maximum load is hung from the copper wire, by what percentage of its length will it stretch?
Answer in units of %.
I got the first one which is 58.90486N. I have no idea how to do the second though.
To determine the maximum load that can be hung from a copper wire of diameter 0.5 mm, we can use the formula:
Stress = Force / Area
The breaking stress of copper given is 3 × 10^8 N/m^2. Since the diameter is given, we need to find the cross-sectional area of the wire first.
1. Calculate the radius of the wire:
Radius = Diameter / 2 = 0.5 mm / 2 = 0.25 mm = 0.25 × 10^(-3) m
2. Calculate the area of the wire:
Area = π * (Radius)^2 = π * (0.25 × 10^(-3))^2 = 0.19635 × 10^(-6) m^2
3. Use the stress formula to find the maximum load (force):
Stress = Force / Area
Force = Stress * Area
Force = (3 × 10^8 N/m^2) * (0.19635 × 10^(-6) m^2)
Force ≈ 58.91 N (rounded to two decimal places)
So, the maximum load that can be hung from a copper wire of diameter 0.5 mm is approximately 58.91 N.
Now, let's move on to the second part of the question. We need to calculate the percentage of elongation or stretch when 55% of the maximum load is hung from the wire.
To determine the percentage of elongation, we can use Hooke's law, which states that the elongation of a material is directly proportional to the force applied.
1. Find the force corresponding to 55% of the maximum load:
Force = 55% of the maximum load
Force = 55/100 * 58.91 N
Force ≈ 32.40 N (rounded to two decimal places)
2. Next, we need to know the Young's modulus of copper, which is approximately 1.1 × 10^11 N/m^2.
3. Calculate the elongation or stretch using Hooke's law:
Stress = Force / Area
Stress = Force / (π * (Radius)^2)
Stress ≈ 32.40 N / (π * (0.25 × 10^(-3))^2)
Elongation = (Stress / Young's modulus) * Original length
Elongation = [(32.40 N / (π * (0.25 × 10^(-3))^2)) / (1.1 × 10^11 N/m^2)] * Original length
Here, the original length of the wire is not given, so you will need to provide that value to calculate the elongation accurately.
4. Once you have the elongation value, you can calculate the percentage of elongation:
Percentage of elongation = (Elongation / Original length) * 100
By following these steps, you can calculate the percentage of elongation or stretch based on the specific values given in the problem.
To calculate the percentage by which the copper wire will stretch when 55% of the maximum load is hung from it, we need to use Hooke's Law. Hooke's Law states that the elongation or stretch of a material is directly proportional to the applied force.
First, let's find the force applied when 55% of the maximum load is hung from the copper wire.
Maximum load = 58.90486 N (as you calculated)
Force applied = 55% of maximum load
Force applied = 0.55 * 58.90486 N
Force applied = 32.39717 N (approx)
Next, we need to determine the Young's modulus for copper, which is a measure of its stiffness or resistance to deformation. For copper, the Young's modulus is approximately 1.1 × 10^11 N/m^2.
We can use Hooke's Law to find the percentage of elongation:
Elongation = (Force applied * Length) / (Young's modulus * Cross-sectional area)
We know the force applied is 32.39717 N. Now, let's find the cross-sectional area of the wire.
Cross-sectional area = π * (radius)^2
Cross-sectional area = π * (0.00025 m)^2 (since the diameter is given, we divide it by 2 to get the radius)
Cross-sectional area = 0.00019634954 m^2 (approx)
Now, we can calculate the elongation:
Elongation = (32.39717 N * Length) / (1.1 × 10^11 N/m^2 * 0.00019634954 m^2)
Since we want the answer in percentage, we need to multiply the elongation by 100.
Elongation (in %) = Elongation * 100
Note: The value of Length is missing from the given information. To calculate the percentage of elongation, we need to know the length of the wire.
Please provide the length of the wire so we can proceed with the calculation.