The flight of a kicked football follows the quadratic function f(x)=−0.02x2+2.2x+2, where f(x) is the vertical distance in feet
1 answer:
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Answer:
Explanation:
The mean free path of an atom can be calculated using the following equation:
(1)
Where:
is referred to as the Universal gas constant
represents the absolute standard temperature
denotes the diameter of helium atoms
symbolizes Avogadro's number
indicates absolute standard pressure
(2)
(3)
(4)
If the radius equals half of that diameter:
(5)
Eventually:
(6)
(7)
Nonetheless, we were tasked with finding this radius in nanometers. Knowing :
(8)
Ultimately:
Represents the radius of the helium atom in nanometers.
If the plate separation is modified after the battery is disconnected, the updated distance between plates is 9.21 mm
If changes are made while the battery remains connected, the new separation becomes 0.11 mm
The capacitance for an air-filled parallel plate capacitor can be expressed as:
In this equation, refers to the permittivity of free space, A stands for the plate area, and D represents the separation distance.
Thus,
.......(1)
Therefore, should the distance between the plates shift from d₁ to d₂, the capacitance ratio in both scenarios can be represented as:
......(2)
Scenario (i)
When the capacitor is fully charged and then disconnected from the battery before adjusting the plate distance, the charge will remain steady while the capacitance varies.
The initial energy E₁ stored in the capacitor can be expressed as:
......(3)
Once the separation changes to d₂, capacitance becomes C₂, but the charge Q remains unchanged.
Thus,
......(4)
By dividing equation (4) by (3),
According to equation (2),
This results in a 3.5 fold increase in energy.
Scenario (2)
If the capacitor is kept connected to the power source, the voltage V across the plates will remain unchanged.
The initial energy is described as
......(5)
The final energy when the plate separation transitions to d₂ can be written as:
.....(6)
Referencing equations (5) and (6)
From equation (2),
Thus, in this particular scenario,
Therefore,
Adjusting plate separation after battery disconnection yields 9.21 mm
If modified while connected, the new separation measures 0.11 mm
Answer:
a, 71.8° C, 51° C
b, 191.8° C
Explanation:
Given the data:
D(i) = 200 mm
D(o) = 400 mm
q' = 24000 W/m³
k(r) = 0.5 W/m.K
k(s) = 4 W/m.K
k(h) = 25 W/m².K
The heat generation formula can be articulated as follows:
q = πr²Lq'
q = π. 0.1². L. 24000
q = 754L W/m
Thermal conduction resistance, R(cond) = 0.0276/L
Thermal conduction resistance, R(conv) = 0.0318/L
Applying the energy balance equation,
Energy In = Energy Out
This equates to q, which is 754L
From the initial analysis, the temperature at the interface between the rod and sleeve is found to be 71.8° C
Additionally, the outer surface temperature records as 51° C
Furthermore, based on the second analysis, the calculated temperature at the center of the rod is determined to be 191.8° C
