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A 1 036-kg satellite orbits the Earth at a constant altitude of 98-km. (a) How much energy must be added to the system to move t

Veronika [31]

Answer:

a) The Energy added should be 484.438 MJ

b) The Kinetic Energy change is -484.438 MJ

c) The Potential Energy change is 968.907 MJ

Explanation:

Let 'm' be the mass of the satellite , 'M'(6× $10^{24}$ be the mass of earth , 'R'(6400 Km) be the radius of the earth , 'h' be the altitude of the satellite and 'G' (6.67× $10^{-11}$ N/m) be the universal constant of gravitation.

We know that the orbital velocity(v) for a satellite -

v= $\sqrt{\frac{Gmm}{R+h} }$ [(R+h) is the distance of the satellite from the center of the earth ]

Total Energy(E) = Kinetic Energy(KE) + Potential Energy(PE)

For initial conditions ,

h = $h_{i}$ = 98 km = 98000 m

∴Initial Energy ( $E_{i}$ ) = $\frac{1}{2}$ m $v^{2}$ + $\frac{-GMm}{(R+h_{i} )}$

Substituting v= $\sqrt{\frac{GMm}{R+h_{i} } }$ in the above equation and simplifying we get,

$E_{i}$ = $\frac{-GMm}{2(R+h_{i}) }$

Similarly for final condition,

h= $h_{f}$ = 198km = 198000 m

∴Final Energy( $E_{f}$ ) = $\frac{-GMm}{2(R+h_{f}) }$

a) The energy that should be added should be the difference in the energy of initial and final states -

∴ ΔE = $E_{f}$ - $E_{i}$

= $\frac{GMm}{2}$ ( $\frac{1}{R+h_{i} }$ - $\frac{1}{R+h_{f} }$ )

Substituting ,

M = 6 × $10^{24}$ kg

m = 1036 kg

G = 6.67 × $10^{-11}$

R = 6400000 m

$h_{i}$ = 98000 m

$h_{f}$ = 198000 m

We get ,

ΔE = 484.438 MJ

b) Change in Kinetic Energy (ΔKE) = $\frac{1}{2}$ m[ $v_{f} ^{2}$ - $v_{i} ^{2}$ ]

= $\frac{GMm}{2}$ [ $\frac{1} {R+h_{f} }$ - $\frac{1} {R+h_{i} }$ ]

= -ΔE

= - 484.438 MJ

c) Change in Potential Energy (ΔPE) = GMm[ $\frac{1}{R+h_{i} }$ - $\frac{1}{R+h_{f} }$ ]

= 2ΔE

= 968.907 MJ

3 0

2 years ago

Consider each of the electric- and magnetic-field orientations given next. In each case, what is the direction of propagation of

vodka [1.7K]

The route of the propagation of the wave in every case are; A) +z route B) +z route C) -y route D) -x route .

vec Ein is the Electrical area vector and vec Bin is the Magnetic area vector, due to the fact the sphere vectors are continually perpendicular to every different the propagation of the wave is perpendicular to the 2 vectors. The route of the propagation of the wave may be observed with the aid of using vec Ein X vec Bin (Cross made from vectors). This also can be achieved with the aid of using the usage of the RIGHT HAND RULE.

Cross product may be observed with the aid of using

i x j = okay and j x i = - okay

j x okay=i and okay x j = - i

okay x i=j and that i x okay = - j

wherein i represents the +x route, j represents the +y route and okay represents the +z route

The RIGHT HAND RULE may be used to demonstrate the move product with the aid of using the usage of the proper hand and pointing the index finger withinside the route of the primary vector and the center finger alongside the second one vector, the move product is withinside the route of the thumb.

A) vec Ein the +xdirection,vec Bin the +ydirection,

Finding the move made from the 2 vectors (i x j = okay) might provide a vector withinside the +z route

B) vec Ein the -y route,vec Bin the +x route

Finding the move made from the 2 vectors (- j x i = okay) might provide a vector withinside the +z route

C) vec Ein the +z route,vec Bin the -x route

Finding the move made from the 2 vectors (okay x - i = - j) might provide a vector withinside the -y route

D) vec Ein the +y route,vec Bin the -z route

Finding the move made from the 2 vectors (j x - okay = - i) might provide a vector withinside the -x route

The complete question is- Consider each of the electric- and magnetic-field orientations given next. In each case, what is the direction of propagation of the wave?A)\vec Ein the +xdirection,\vec Bin the +ydirection.Please Choose+ x direction- x direction+ y direction- y direction+ z direction- z directionB)\vec Ein the -y direction,\vec Bin the +x directionPlease Choose+ x direction- x direction+ y direction- y direction+ z direction- z directionC)\vec Ein the +z direction,\vec Bin the -x direction.Please Choose+ x direction- x direction+ y direction- y direction+ z direction- z directionD)\vec Ein the +y direction,\vec Bin the -z direction.Please Choose+ x direction- x direction+ y direction- y direction+ z direction- z direction.

Learn more about vector here-

brainly.com/question/13966790

#SPJ4

3 0

3 months ago

The potential difference between the plates of an air-filled parallel-plate capacitor with a plate separation of 4 cm is 51 V. W

Salsk061 [2.6K]

Answer:

Explanation:

Electric field between plates of a parallel plate capacitor is uniform .

In a uniform electric field , relation between electric field and potential gradient is as follows

electric field = potential gradient [ E = - dV / dl ]

in the given case ,

dV = 51 V ,

dl = 4 cm

= 4 x 10⁻² m

E = 51 / 4 x 10⁻²

= 12.75 x 10² V / m

= 1275 V / m

6 0

2 years ago

Would it be m/s or kg?

Nesterboy [21]

Answer:

m.s

Explanation:

3 0

2 years ago

What is the jet stream and how does it separate cold air to warm air?

docker41 [41]

Jet stream<span>ˈjet ˈˌstrēm/</span>noun1.a narrow, variable band of very strong, predominantly westerly air currents encircling the globe several miles above the earth. There are typically two or three jet streams in each of the northern and southern hemispheres.
(credit to google)

4 0

3 years ago