Respuesta :
Answer:
[tex]F=5.8\times 10^{8}\ N[/tex]
[tex]F=35.57\times 10^{21}\ N[/tex]
Explanation:
Given that
Intensity I
[tex]I= 1.39\ KW/m^2[/tex]
[tex]Speed\ of \ light = 2.99\times 10^8\ m/s[/tex]
Radius of earth,R = 6370 Km
We know that surface area of earth, A
[tex]A=\pi R^2[/tex]
[tex]A=\pi (6370\times 10^3)^2\ m^2[/tex]
[tex]A=1.27\times 10^{14}\ m^2[/tex]
As we know that pressure due to intensity given as
[tex]P=\dfrac{I}{V}[/tex]
V =Velocity of light
[tex]V=3\times 10^8\ m/s[/tex]
[tex]P=\dfrac{1.39\times 1000}{=3\times 10^8}[/tex]
[tex]P=4.6\times 10^{-6}\ Pa[/tex]
We know that force F
F = P .A
[tex]F=4.6\times 10^{-6}\times 1.27\times 10^{14}\ N[/tex]
[tex]F=5.8\times 10^{8}\ N[/tex]
b)Gravitational force F
[tex]F=G\dfrac{m.M}{r^2}[/tex]
[tex]M = mass\ of\ sun = 2\times 10^{30} kg\\m = mass\ of\ earth = 6\times 10^{24}kg[/tex]
[tex]r =1.5\times 10^{11}\ m[/tex]
[tex]G =6.67\times 10^{-11}Nm^2/kg^2[/tex]
So F
[tex]F=6.67\times 10^{-11}\times \dfrac{2\times 10^{30}\times 6\times 10^{24}kg}{1.5\times 10^{11}}[/tex]
[tex]F=35.57\times 10^{21}\ N[/tex]
Answer:
(a) 5.91 × 10⁸ N; (b) 3.542 × 10²² N
Explanation:
Data:
I = 1.39 kW/m² = 1.39 × 10³ N·m⁻³s⁻¹
c = 2.998 × 10⁸ m/s
r = 6370 km = 6.37 × 10⁶ m
G = 6.674 ×10⁻¹¹ N⋅m²kg⁻²
M = 1.989 × 10³⁰ kg = mass of Sun
m = 5.972 × 10²⁴ kg = mass of Earth
d = 1.496 × 10¹¹ m = distance from Earth to Sun
Calculations:
(a) Force exerted by the radiation pressure
(i) Radiation pressure
All the incident radiation is absorbed, so
[tex]\begin{array}{rcl}p & = & \dfrac{I}{c}\\\\& = & \dfrac{\text{1.39 $\times$ 10$^{3}$ N$\cdot$ m$^{-3}$s$^{-1}$}}{2.998 \times 10^{8}\text{ m$\cdot$ s}^{-1}}\\\\& = & 4.636 \times 10^{-6}\text{ N$\cdot$m}^{-2}\\\end{array}[/tex]
(ii) Area of Earth's disc
[tex]\begin{array}{rcl}A & = & \pi r^{2}\\& = & \pi \times (6.37 \times 10^{6} \text{ m})^{2}\\& = & 1.275 \times 10^{14} \text{ m}^{2}\\\end{array}[/tex]
(iii) Radiation force
[tex]\begin{array}{rcl}p & = & \dfrac{F}{A}\\\\F & = & pA\\ & = & 4.636 \times 10^{-6}\text{ N$\cdot$m}^{-2} \times 1.275 \times 10^{14} \text{ m}^{2}\\ & = & 5.91 \times 10^{8}\text{ N}\\\end{array}[/tex]
(b) Gravitational Force
[tex]\begin{array}{rcl}F & = & \dfrac{GMm}{r^{2}}\\\\& = & \dfrac{\text{6.674 $\times$ 10$^{-11}$ N $\cdot$ m$^{2}$kg$^{-2}\times$ 1.989 $\times$ 10$^{30}$ kg $\times$ 5.972 $\times$ 10$^{24}$ kg}}{(\text{1.496 $\times$ 10$^{11}$ m})^{2}}\\\\& = & 3.542 \times 10^{22} \text{ N}\\\end{array}[/tex]
