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 calculate the maximum load that can be hung from a copper wire of diameter 0.5 mm, we need to use the concept of breaking stress and the formula for the cross-sectional area of a wire.
Step 1: Calculate the cross-sectional area of the wire.
The formula for the cross-sectional area of a wire is A = πr², where A is the cross-sectional area and r is the radius of the wire.
Given that the diameter of the wire is 0.5 mm, we can find the radius by dividing the diameter by 2:
Radius (r) = 0.5 mm / 2 = 0.25 mm = 0.25 × 10^(-3) m
Substitute this value into the formula to find the cross-sectional area:
A = π(0.25 × 10^(-3))^2 = π (6.25 × 10^(-7)) m²
Step 2: Calculate the maximum load (force).
The formula to calculate the maximum load is F = stress × A, where F is the force or maximum load, stress is the breaking stress of the material, and A is the cross-sectional area of the wire.
Given that the breaking stress of copper is approximately 3 × 10^(8) N/m², and the calculated cross-sectional area is π (6.25 × 10^(-7)) m², we can substitute those values into the formula to find the maximum load:
F = (3 × 10^(8)) × π (6.25 × 10^(-7)) N
This calculation gives us the answer to the first question: the maximum load that can be hung from the copper wire is approximately 58.90486 N.
Now let's move on to the second question: what percentage of its length will the copper wire stretch if 55% of the maximum load is hung from it?
To calculate the percentage elongation or stretch, we need the Young's modulus of copper and apply the formula:
Percentage elongation = (load / (Young's modulus × original length)) × 100
Unfortunately, the Young's modulus of copper is not provided, so we cannot calculate the percentage of stretch in this case. To proceed further, we would need the Young's modulus value.
To find the maximum load that can be hung from a copper wire of diameter 0.5 mm, we first need to calculate the cross-sectional area of the wire.
The formula for the cross-sectional area (A) of a wire is given by:
A = πr^2
where r is the radius of the wire. In this case, the diameter is given as 0.5 mm, so the radius (r) is half of the diameter, which is 0.5/2 = 0.25 mm = 0.00025 m.
Now we can calculate the cross-sectional area:
A = π(0.00025)^2 = 1.9635 x 10^-7 m^2.
The maximum load that can be hung from the wire is given by the product of the breaking stress and the cross-sectional area:
Maximum load = Breaking stress x Cross-sectional area
Maximum load = (3 x 10^8 N/m^2) x (1.9635 x 10^-7 m^2)
Maximum load ≈ 58.90486 N
So, you correctly calculated the maximum load to be approximately 58.90486 N.
Now, let's move on to the second part of the question. We need to determine the percentage by which the wire will stretch when 55% of the maximum load is hung from it.
To do this, we can use Hooke's law, which states that the elongation or deformation of an elastic material is directly proportional to the force applied.
The formula for elongation (ΔL) is given by:
ΔL = (F / A) / Y
where F is the force applied, A is the cross-sectional area of the wire, and Y is Young's modulus for copper, which is approximately 1.1 x 10^11 N/m^2.
In this case, we only need to find the percentage of elongation, which can be calculated using the formula:
Percentage of elongation = (ΔL / original length) x 100
However, we don't know the original length of the wire. So, for the purpose of this calculation, let's assume the original length of the wire is 1 meter.
First, let's calculate the elongation ΔL when 55% of the maximum load is applied to the wire.
ΔL = (F / A) / Y
ΔL = [(0.55 x 58.90486 N) / (1.9635 x 10^-7 m^2)] / (1.1 x 10^11 N/m^2)
After calculating this, we can then find the percentage of elongation:
Percentage of elongation = (ΔL / original length) x 100
With the calculated ΔL and assumed original length of 1 meter, you can now determine the percentage of elongation.
Force=E*a*deltaL/L
solve for delta L/L
E is Youngs modullus for Copper, look that up