Answer:
T_t = Ts (1-A √ (Rs/D)
Explanation:
The black body radiation power is given by Stefan's law
P = σ A e T⁴
This power is distributed over a spherical surface, so the intensity of the radiation is
I = P / A
Let's apply these formulas to our case. Let's start by calculating the power emitted by the Sun, which has an emissivity of one (e = 1) black body
P_s = σ A_s 1 T_s⁴
This power is distributed in a given area, the intensity that reaches the earth is
I = P_s / A
A = 4π R²
The distance from the Sun Earth is R = D
I₁ = Ps / 4π D²
I₁ = σ (π R_s²) T_s⁴ / 4π D²
I₁ = σ T_s⁴ R_s² / 4D²
Now let's calculate the power emitted by the earth
P_t = σ A_t (e) T_t⁴
I₂ = P_t / A_t
I₂ = P_t / 4π R_t²2
I₂ = σ (π R_t²) T_t⁴ / 4π R_t²2
I₂ = σ T_t⁴ / 4
The thermal equilibrium occurs when the emission of the earth is equal to the absorbed energy, the radiation affects less the reflected one is equal to the emitted radiation
I₁ - A I₁ = I₂
I₁ (1 - A) = I₂
Let's replace
σ T_s⁴ R_s²/4D² (1-A) = σ T_t⁴ / 4
T_s⁴ R_s² /D² (1-A) = T_t⁴
T_t⁴ = T_s⁴ (1-A) (Rs / D) 2
T_t = Ts (1-A √ (Rs/D)
Answer:
The question is incomplete, the complete question is "A car drives on a circular road of radius R. The distance driven by the car is given by d(t)= at^3+bt [where a and b are constants, and t in seconds will give d in meters]. In terms of a, b, and R, and when t = 3 seconds, find an expression for the magnitudes of (i) the tangential acceleration aTAN, and (ii) the radial acceleration aRAD3"
answers:
a.
b.
Explanation:
First let state the mathematical expression for the tangential acceleration and the radial acceleration.
a. tangential acceleration is express as
since the distance is expressed as
the derivative is the velocity, hence
hence when we take the drivative of the velocity we arrive at
b. the expression for the radial acceleration is expressed as
First recall the equation that relates frequency to wavelength:
v = fw
Note that the v is the speed of light, a constant. Now plug in the information we know!
(3×10^8) = (6.67 × 10^14) w
Hit the numbers on the calculator and you'll get the wavelength, w. If you comment your answer I'll check it for you. :)
Answer:
4.2591 cm
Explanation:
We have given focal length of the lens f=6.91 cm
Object distance u =11.1 cm
We have to find the image distance that is v
For the lens we know that
So
It will accelerate at 6.2 m/s/s west.