Answer:
165 mm
Explanation:
The mass on the piston will apply a pressure on the oil. This is:
p = f / A
The force is the weight of the mass
f = m * a
Where a in the acceleration of gravity
A is the area of the piston
A = π/4 * D1^2
Then:
p = m * a / (π/4 * D1^2)
The height the oil will raise is the heignt of a colum that would create that same pressure at its base:
p = f / A
The weight of the column is:
f = m * a
The mass of the column is its volume multiplied by its specific gravity
m = V * S
The volume is the base are by the height
V = A * h
Then:
p = A * h * S * a / A
We cancel the areas:
p = h * S * a
Now we equate the pressures form the piston and the pil column:
m * a / (π/4 * D1^2) = h * S * a
We simplify the acceleration of gravity
m / (π/4 * D1^2) = h * S
Rearranging:
h = m / (π/4 * D1^2 * S)
Now, h is the heigth above the interface between the piston and the oil, this is at h1 = 42 mm. The total height is
h2 = h + h1
h2 = h1 + m / (π/4 * D1^2 * S)
h2 = 0.042 + 10 / (π/4 * 0.14^2 * 0.8) = 0.165 m = 165 mm
Answer: 33.35 minutes
Explanation:
A(t) = A(o) *(.5)^[t/(t1/2)]....equ1
Where
A(t) = geiger count after time t = 100
A(o) = initial geiger count = 400
(t1/2) = the half life of decay
t = time between geiger count = 66.7 minutes
Sub into equ 1
100=400(.5)^[66.7/(t1/2)
Equ becomes
.25= (.5)^[66.7/(t1/2)]
Take log of both sides
Log 0.25 = [66.7/(t1/2)] * log 0.5
66.7/(t1/2) = 2
(t1/2) = (66.7/2 ) = 33.35 minutes
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Answer:
the maximum length of specimen before deformation is found to be 235.6 mm
Explanation:
First, we need to find the stress on the cylinder.
Stress = σ = P/A
where,
P = Load = 2000 N
A = Cross-sectional area = πd²/4 = π(0.0037 m)²/4
A = 1.0752 x 10^-5 m²
σ = 2000 N/1.0752 x 10^-5 m²
σ = 186 MPa
Now, we find the strain (∈):
Elastic Modulus = Stress / Strain
E = σ / ∈
∈ = σ / E
∈ = 186 x 10^6 Pa/107 x 10^9 Pa
∈ = 1.74 x 10^-3 mm/mm
Now, we find the original length.
∈ = Elongation/Original Length
Original Length = Elongation/∈
Original Length = 0.41 mm/1.74 x 10^-3
<u>Original Length = 235.6 mm</u>
