Physics, 09.10.2019 04:00 rania32

Radiation from the sun reaching earth (just outside the atmosphere) has an intensity of 1.39 kw/m2. (a) assuming that earth (and its atmosphere) behaves like a flat disk perpendicular to the sun's rays and that all the incident energy is absorbed, calculate the force on earth due to radiation pressure. (b) for comparison, calculate the force due to the sun's gravitational attraction. assume that the speed of light and earth radius are 2.998 × 108 m/s and 6.37 thousand km respectively.

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Answer from: elijahworley

$F=5.8\times 10^{8}\ N$

$F=35.57\times 10^{21}\ N$

Explanation:

Given that

Intensity I

$I= 1.39\ KW/m^2$

$Speed\ of \ light = 2.99\times 10^8\ m/s$

Radius of earth,R = 6370 Km

We know that surface area of earth, A

$A=\pi R^2$

$A=\pi (6370\times 10^3)^2\ m^2$

$A=1.27\times 10^{14}\ m^2$

As we know that pressure due to intensity given as

$P=\dfrac{I}{V}$

V =Velocity of light

$V=3\times 10^8\ m/s$

$P=\dfrac{1.39\times 1000}{=3\times 10^8}$

$P=4.6\times 10^{-6}\ Pa$

We know that force F

F = P .A

$F=4.6\times 10^{-6}\times 1.27\times 10^{14}\ N$

$F=5.8\times 10^{8}\ N$

b)Gravitational force F

$F=G\dfrac{m.M}{r^2}$

$M = mass\ of\ sun = 2\times 10^{30} kg\\m = mass\ of\ earth = 6\times 10^{24}kg$

$r =1.5\times 10^{11}\ m$

$G =6.67\times 10^{-11}Nm^2/kg^2$

So F

$F=6.67\times 10^{-11}\times \dfrac{2\times 10^{30}\times 6\times 10^{24}kg}{1.5\times 10^{11}}$

$F=35.57\times 10^{21}\ N$

Answer from: cbaublitz

(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

$\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}$

(ii) Area of Earth's disc

$\begin{array}{rcl}A & = & \pi r^{2}\\& = & \pi \times (6.37 \times 10^{6} \text{ m})^{2}\\& = & 1.275 \times 10^{14} \text{ m}^{2}\\\end{array}$

(iii) Radiation force

$\begin{array}{rcl}p & = & \dfrac{F}{A}\\\\F & = & pA\\ & = & 4.636 \times 10^{-6}\text{ N$\cdot$m}^{-2} \times 1.275 \times 10^{14} \text{ m}^{2}\\ & = & 5.91 \times 10^{8}\text{ N}\\\end{array}$

(b) Gravitational Force

$\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}$

Answer from: Quest

answer: the correct answer is 1.

explanation: there are various process in which a radioactive nuclei decays:

1) alpha decay: in this process, a heavier nuclei decays into lighter nuclei by releasing alpha particle. the mass number is reduced by 4 units.

$_a^z\textrm{x}\rightarrow _{a-2}^{z-4}+_2^4\alpha$

2) electron capture: in this decay process, a parent nuclei absorbs an electron and gets converted into a neutron. simply, a proton and an electron combines together to form a neutron. mass number does not change in this process.

$_a^z\textrm{x}+_{-1}^0\textrm{e}\rightarrow _{z-1}^a\textrm{y}$

3) gamma ray emission: it is a decay process in which an unstable nuclei gives excess energy by a spontaneous electromagnetic process. this decay releases $\gamma -radiations$ . this process does not change the mass number.

$_a^z\textrm{x}^*\rightarrow _a^z\textrm{x}+_0^0\gamma$

4) positron emission: it is a type of decay process, in which a proton gets converted to neutron and an electron neutrino. this is also known as $\beta ^+$ -decay. in this the mass number remains same.

$_a^z\textrm{x}\rightarrow _{z-1}^a\textrm{y}+_{+1}^0e$

from the above information, we see that only alpha-decay is producing a change in the mass number of the nucleus.

Answer from: Quest

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