while flying a plane parallel to the ground a pilot releases a fuel tank in order to reduce the planes mass. what is the tanks f
1 answer:
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Answer:
T₀ = 2π T =
T₀
Explanation:
When the block is oscillating it forms a simple harmonic motion, which in the case of a spring and a mass has an angular velocity
w =
To apply this formula to our case, let's look for the equivalent constant of the springs.
Let's start with the springs in parallels.
* the three springs in the upper part, when stretched, lengthen the same distance, therefore the total force is
F_total = F₁ + F₂ + F₃
the springs fulfill Hooke's law and indicate that the spring constant is the same for all three,
F_total = - k x - k x - kx = -3k x
therefore the equivalent constant for the combination of the springs at the top is
k₁ = 3 k
* the two springs at the bottom
following the same reasoning the force at the bottom is
F_total2 = - 2 k x
the equivalent constant at the bottom is
k₂ = 2 k
now let's work the two springs are equivalent that are in series
the top spring is stretched by an amount x₁ and the bottom spring is stretched x₂
x₂ = x -x₁
x₂ + x₁ = x
if we consider that the springs have no masses we can use Hooke's law
therefore the equivalent constant is the series combination is
we substitute the values
\frac{1}{k_{eq} } = \frac{1}{3k } + \frac{1}{2k }
\frac{1}{k_{eq} } = \frac{5}{6k} }
k_eq =
therefore the angular velocity is
w =
angular velocity, frequency, and period are related
w = 2π f = 2π / T
T = 2π / w
T = 2π
T₀ = 2π
T = T₀
Answer:
It takes <em>40 hours</em> to melt the block of ice.
Explanation:
According to the principles of radiation and heat transfer respectively:
<em>ΔQ = I(dt)eAcosθ </em>(I = Solar energy density; dt = time taken; e = emissivity; A = Area of block; θ = angle between the sun ray and the horizontal)
<em>ΔQ = mLf</em> (ΔQ = Heat change; m = mass of ice; Lf = Specific latent heat of fusion of ice)
but m = ρV = ρ.A.<em>d</em>x, therefore, the heat transfer equation can be re-written as:
<em>ΔQ = ρ.A.dx.Lf</em>
Lets equate the radiation equation and the modified heat transfer equation, we have:
<em>ρ.A.dx.Lf = I(dt)eAcosθ</em>
<em>ρ.dx.Lf = I(dt)ecosθ </em>(Striking out the area)
Let's make <em>dt</em> the subject of formula,
dt = ρ.dx.Lf /I.e.cosθ
ρ = Density of ice,
Lf =
e = 0.050
θ = 32 deg. C
Now, let's substitute the terms:
Therefore, the time taken for the ice to completely melt is <em>40 hours</em> (Two significant figures)