Answer:
a) Y = 4.16 10¹⁰ N / m²
, b) B= 37.4 10¹⁰ Pa
Explanation:
a) For this exercise we must use the Young's modulus formula
Y = P / DL / L
We look for the magnitude salt system SI
d₁ = 10.7000 mm = 10.7000 10⁻³ m
l₁ = 95,000 mm = 95,000 10⁻³ m
l₂ = 95.040 mm = 95.040 10⁻³ m
d₂ = 10.698 mm = 10.698 10⁻³ m
The pressure is
P = F / A
A = π r²
P = F / pi r²
P = 6300 / π (10.7 10⁻³)²
P = 17,5155 10⁶ Pa.
Change in length
ΔL = l₂-l₁
ΔL = (95.04000 -95.000) 10⁻³
ΔL = 0.040 10⁻³ m
Let's calculate
Y = 17,515 10⁶ 95,000 10⁻³ / 0.040 10⁻³
Y = 4.16 10¹⁰ N / m²
This Young or elasticity module is very close to the medium density fiberboard or solid poly styrene module
b) If in addition to the length the diameter also changes, the whole body volume changes, so we can use the ratio of the volume module
B = -P / DV / V
Let's look for the initial volume of the cylinder
V₁ = π r₁² l₁
r₁ = d₁ / 2 = 10.7000 10⁻³ / 2
r₁ = 5.3500 10⁻³ m
r₂ = 10.698 / 2 10⁻³
r₂ = 5.349 10⁻³ m
V₁ = π (5.35 10⁻³)² 95.00 10⁻³
V₁ = 8.5424 10⁻⁶ m³
Let's calculate the final volume
V₂ = π r₂² L₂
V₂ = π 5.349² 10⁻⁶ 95.040 10⁻³
V₂ = 8.54282 10⁻⁶ m³
Let's look for the volume change
ΔV = V₂ - V₁
ΔV = (8.54280 - 8.5424) 10⁻⁶
ΔV = 0.0004 10⁻⁶ m³
Let's calculate the Bulk module
B = 17,515 10⁶ 8.5424 10⁻⁶ /(0,0004 10⁻⁶)
B = 3.74 10¹¹ Pa
B= 37.4 10¹⁰ Pa
This volume module corresponds to some type of glass made with poly styrene
