The formula for true strain after derivation from basic terms is; ε_t = In(1 + ε_e)
<h3>How to derive the expression for True Strain?</h3>
Formula for Engineering Stress is;
σ_e = Load/Area
Formula for true stress is;
σ_t = Force/Instantaneous Area
Formula for Engineering Strain is;
ε_e = ΔL/L₀
Formula for true strain is;
dε_t = dL/L
Total true strain is gotten from;
ε_t = ∫(dL/L) between boundaries of L_f and L_o
When we integrate between those boundaries, we have;
ε_t = In[(L₀ + ΔL)/L₀
⇒ ε_t = In[(1+ ΔL/L₀)
⇒ ε_t = In(1 + ε_e)
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Answer:
Change in length = 0.1257 mm
Change in diameter= -0.03771mm
Explanation:
Given
Diameter, d = 15 mm
Length of rod, L = 200mm
F = Force= 300N
d = 0.015m
Ep=2.70 GPa, np=0.4.
First, we have to calculate the normal stress using
σ = F/A where F = Force acting on the Cross-sectional area
A = Area
Area is calculated as πd²/4 where d = 0.015m
A = 22/7 * 0.015²/4
A = 0.000176785714285m²
A = 1.768E-4m²
So, stress. σ = 300N/1.768E-4m²
σ = 1696832.579185520Pa
σ = 1.697MPa
Calculating E(long)
E(long) = σ /Ep
E(long) = 1.697E-3/2.70
E(long) = 0.0006285
At this point, we fan now calculate the change in length of the element;
∆L = E(long) * L
∆L = 0.0006285 * 200mm
∆L = 0.1257mm
Calculating E(lat)
E(lat) = -np * E(long)
E(lat) = -4 * 0.0006285
E(lat) = -0.002514
At this point, we can now calculate the change in diameter of the element;
∆D = E(lat) * D
∆L = -0.002514 * 15mm
∆L = -0.03771mm
Answer:Non-uniform motion
Explanation:
This is an example of Non-uniform motion because unequal distance traveled by an object in equal interval of time is termed as Non-Uniform motion and here also the distance traveled by object is 1 ft ,4 ft and 8 ft which is different from each other.
In Uniform motion distance traveled is equal in equal interval of time .
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