Calculate the percentage increase in length of a wire of diameter 2.2 mm stretched by a load of 100 kg.Young's modulus of wire is 12.5 × 10^10 N/m^2
To calculate the percentage increase in length of the wire, we need to use Hooke's law, which states that the stress (strain) on a material is directly proportional to the applied force (load). In this case, the stress can be determined using the Young's modulus and the strain (change in length).
First, we need to find the cross-sectional area of the wire. The formula for the area of a circle is A = πr^2, where r is the radius of the wire. Since the diameter is given as 2.2 mm, the radius would be half of that, so r = 1.1 mm = 0.0011 m.
Area = π(0.0011)^2 = 3.80132711 × 10^-6 m^2 (rounded to 8 decimal places)
The stress (force per unit area) on the wire can be calculated using the formula Stress = Force/Area. The force is given as 100 kg, but we need to convert it to Newtons by multiplying it with the acceleration due to gravity: 9.8 m/s^2. So, Force = 100 kg * 9.8 m/s^2 = 980 N.
Stress = Force/Area = 980 N / 3.80132711 × 10^-6 m^2 = 2.575841 × 10^8 N/m^2 (rounded to 6 decimal places)
Next, we can calculate the strain (change in length) using the formula Strain = Stress / Young's modulus. The Young's modulus is given as 12.5 × 10^10 N/m^2.
Strain = 2.575841 × 10^8 N/m^2 / 12.5 × 10^10 N/m^2 = 2.0606728 × 10^-3 (rounded to 7 decimal places)
Finally, we can calculate the percentage increase in length using the formula Percentage Increase in Length = Strain * 100.
Percentage Increase in Length = 2.0606728 × 10^-3 * 100 = 0.20606728%
Therefore, the percentage increase in length of the wire when stretched by a load of 100 kg is approximately 0.2061%.
To calculate the percentage increase in length of a wire stretched by a load, we can use the formula for longitudinal strain.
The formula for longitudinal strain (ε) is given by:
ε = (F * L) / (A * E)
Where:
F = applied force or load (in Newtons)
L = original length of the wire (in meters)
A = cross-sectional area of the wire (in square meters)
E = Young's modulus of the wire (in Pascals)
First, let's calculate the original length of the wire:
No information is provided about the original length of the wire in the question, so we assume it to be 1 meter for simplicity.
L = 1 meter
Next, let's calculate the cross-sectional area of the wire:
The diameter of the wire is given as 2.2 mm. We need to convert it to meters.
1 mm = 0.001 meters
So, the diameter of the wire in meters (d) is:
d = 2.2 mm * 0.001 = 0.0022 meters
Now, we can use the formula to calculate the cross-sectional area (A) of the wire:
A = π * (d/2)^2
A = π * (0.0022/2)^2
Finally, we can substitute the known values into the strain formula and calculate the strain (ε):
ε = (F * L) / (A * E)
ε = (100 kg * 9.8 m/s^2 * 1 meter) / (π * (0.0022 meters/2)^2 * 12.5 × 10^10 N/m^2)
Solving this equation will give us the value of ε, the strain.
Once we have the strain value, we can calculate the percentage increase in length using the formula:
Percentage increase in length = ε * 100
Following the above steps, you can calculate the percentage increase in length of the wire.
Please give me my question answer
https://www.ajdesigner.com/phpstress/stress_strain_equation_stress.php
r =1.1*10^-3 meter
A = pi r^2 = 3.8 * 10^-6 m^2
F = m g =100*9.81 = 981 Newtons
stress = sigma= F /A = 981/3.8*10^-6 = 258 * 10^6 N/m^2
change in length/length = stress/Young's = 258*10^6 / 12.5*10^10 = 20.6*10^-4
multiply by 100 for percent
20.6*10^-2 = 0.206 percent
check my arithmetic