Answer:
A) ν = 0.292
B) ν = 0.381
Explanation:
Poisson's ratio = - (Strain in the direction of the load)/(strain in the direction at right angle to the load)
In axial tension, the direction of the load is in the length's direction and the direction at right angle to the load is the side length
Strain = change in length/original length = (Δy)/y or (Δx)/x or (ΔL/L)
A) Strain in the direction of the load = (2.49946 - 2.5)/2.5 = - 0.000216
Strain in the direction at right angle to the load = (7.20532 - 7.2)/7.2 = 0.0007389
Poisson's ratio = - (-0.000216)/(0.0007389) = 0.292
B) Strain in the direction of the load = (2.09929 - 2.1)/2.1 = - 0.0003381
Strain in the direction at right angle to the load = (5.30470 - 5.3)/5.3 = 0.0008868
Poisson's ratio = - (-0.0003381)/(0.0008868) = 0.381
Suppose a tank is made of glass and has the shape of a right-circular cylinder of radius 1 ft. Assume that h(0) = 2 ft corresponds to water filled to the top of the tank, a hole in the bottom is circular with radius in., g = 32 ft/s2, and c = 0.6. Use the differential equation in Problem 12 to find the height h(t) of the water.
Answer:
Height of the water = √(128)/147456 ft
Explanation:
Given
Radius, r = 1 ft
Height, h = 2 ft
Radius of hole = 1/32in
Acceleration of gravity, g = 32ft/s²
c = 0.6
Area of the hold = πr²
A = π(1/32)² ---- Convert to feet
A = π(1/32 * 1/12)²
A = π/147456 ft²
Area of water = πr²
A = π 1²
A = π
The differential equation is;
dh/dt = -A1/A2 √2gh where A1 = Area of the hole and A2 = Area of water
A1 = π/147456, A2 = π
dh/dt = (π/147456)/π √(2*32*2)
dh/dt = 1/147456 * √128
dh/dt = √128/147456 ft
Height of the water = √(128)/147456 ft
Answer:
CLIMATE CHANGE HAS inexorably stacked the deck in favor of bigger and more intense fires across the American West over the past few decades, science has incontrovertibly shown. Increasing heat, changing rain and snow patterns, shifts in plant communities, and other climate-related changes have vastly increased the likelihood that fires will start more often and burn more intensely and widely than they have in the past.
Explanation:
