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3 years ago

14

Estimate the smallest possible period of a satellite in a circular orbit around earth. (mass and radius of earth is 5.98 x 1024

kg and 6.37 x 106 m. the universal gravitational constant g = 6.67 x 10-11 n.m2/kg2 .)

1 answer:

myrzilka [38]3 years ago

3 0

Given: Mass of earth Me = 5.98 x 10²⁴ Kg

Radius of earth r = 6.37 x 10⁶ m

G = 6.67 x 10⁻¹¹ N.m²/Kg²

Required: Smallest possible period T = ?

Formula: F = ma; F = GMeMsat/r² Centripetal acceleration ac = V²/r

but V = 2πr/T

equate T from all equation.

F = ma

GMeMsat/r² = Msat4π²/rT²

GMe = 4π²r³/T²

T² = 4π²r³/GMe

T² = 39.48(6.37 x 10⁶ m)³/6.67 x 10⁻¹¹ N.m²/Kg²)(5.98 x 10²⁴ Kg)

T² = 1.02 x 10²² m³/3.99 x 10¹⁴ m³/s²

T² = 25,563,909.77 s²

T = 5,056.08 seconds or around 1.4 Hour

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3 years ago

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Answer:

$\dot Q=105.042\ W$ is the heat loss by conduction.

Explanation:

Given:

area of window pane, $A=1.5\ m^2$

thickness of the glass pane, $x=0.02\ mm$

thickness of the air gap, $x'=0.013\ m$

thermal conductivity of the glass, $k=0.78\ W.m^{-1}.K^{-1}$

thermal conductivity of the air, $k_a=0.025\ W.m^{-1}.K^{-1}$

inside temperature, $T_i=20^{\circ}C$

outside temperature, $T_o=-20^{\circ}C$

<u>From the Fourier's law of conduction we have the rate of heat transfer as:</u>

$\dot Q=k.A.\frac{dT}{dx}$

$\dot Q=dT\div \frac{dx}{k.A}$

where:

k = thermal conductivity of the material

A = area subjected to the conduction

$dT =$ temperature difference across the two surfaces

dx = thickness of the surface

$\frac{dx}{k.A} =$ regarded as thermal resistance on electrical analogy

According to question here the heat transfer occurs due to conduction of the air.

Here we have two surfaces with air sandwiched between them. So we find an equivalent resistance:

$R_e=2\times \frac{x}{k.A}+ \frac{x'}{k_a.A}$

$R_e=2\times \frac{0.02}{0.78\times 1.5} +\frac{0.013}{0.025\times 1.5}$

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4 years ago

During a tennis match, a player serves the ball at 27.4 m/s, with the center of the ball leaving the racquet horizontally 2.34 m

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a. The ball's horizontal and vertical positions at time $t$ are given by

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at which point the ball's vertical position would be

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