a wire 100 cm long and 0.2 cm in diameter is suspended from a support. a 10 kg mass is hung from the lower end of the wire.
a find the stress
b find the strain
c young's modulus of elasticity
It seems to me much more info is required.
Thanks, so that's why I cant solve it. :(
I want to learn
To find the stress, strain, and Young's modulus of elasticity in this scenario, we need to understand the definitions of these terms and use the appropriate formulas.
a) Stress (σ) is defined as the internal resistance experienced by a material to deformation. It is calculated by dividing the applied force (F) by the cross-sectional area (A) of the material.
To find the stress in this wire, we first need to calculate the cross-sectional area. The cross-sectional area of a wire can be approximated using the formula for the area of a circle: A = πr², where r is the radius of the wire. In this case, the diameter (d) of the wire is given, so the radius (r) can be found by dividing the diameter by 2.
Given:
Length of the wire (L) = 100 cm
Diameter of the wire (d) = 0.2 cm
Applied force (F) = 10 kg * 9.8 m/s² (since weight = mass * acceleration due to gravity)
First, convert the length and diameter to meters:
Length of the wire (L) = 100 cm = 1 m
Diameter of the wire (d) = 0.2 cm = 0.002 m
Next, calculate the radius (r) using the formula:
r = d/2 = 0.002 m / 2 = 0.001 m
Now, calculate the cross-sectional area (A) of the wire:
A = πr² = π(0.001 m)² ≈ 0.00000314 m²
Finally, find the stress (σ) using the formula:
σ = F/A
Substitute the force (F) and cross-sectional area (A) values into the equation to get the stress in Pascal (Pa) or N/m².
b) Strain (ε) is a measure of the deformation of a material relative to its original length. It is calculated by dividing the change in length (ΔL) by the original length (L₀).
In this case, the change in length is equal to the length (L) of the wire due to the force applied. Therefore, the strain (ε) can be calculated as:
ε = ΔL/L₀ = L/L₀
Substitute the values for length (L) and original length (L₀) into the equation to find the strain.
c) Young's modulus of elasticity (E) is a measure of the stiffness of a material and describes how much it elongates or compresses under applied stress. It can be determined using the formula:
E = σ/ε
Substitute the values for stress (σ) and strain (ε) into the equation to find Young's modulus of elasticity.
Remember to use consistent units throughout the calculations.