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Question
Calculate the kinetic energy, potential energy, total energy and binding energy of an artificial satellite of mass 2000 kg orbiting at a height of 3600 km above the surface of the Earth.
Given: G = 6.67 × 10-11 Nm2/kg2
R = 6400 km, M = 6 × 1024 kg
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Solution
Given: m = 2000 kg, h = 3600 km = 3.6 × 106 m,
G = 6.67 × 10-11 Nm2/kg2,
R = 6400 km = 6.4 × 106 m,
M = 6 × 1024 kg
To find:
1. Kinetic energy (K.E.)
2. Potential energy (P.E.)
3. Total energy (T.E.)
4. Binding energy (B.E.)
Formulae:
1. K.E. = `"GMm"/(2("R + h"))`
2. P.E. = `- "GMm"/("R + h")` = - 2(K.E.)
3. T.E. = K.E. + P.E.
4. B.E. = –T.E.
Calculation:
From formula (i),
K.E. = `(6.67 xx 10^-11 xx 6 xx 10^24 xx 2 xx 10^3)/(2 xx [(6.4 xx 10^6) + (3.6 xx 10^6)])`
`= (6.67 xx 6 xx 10^16)/10^7`
= 40.02 × 109 J
From formula (ii),
P.E. = –2 × 40.02 × 109 = - 80.04 × 109 J
From formula (iii),
T.E. = (40.02 × 109) + (–80.04 × 109) = - 40.04 × 109 J
From formula (iv),
B.E. = – (–40.02 × 109) = 40.02 × 109 J
Kinetic energy of the satellite is 40.02 × 109 J potential energy is –80.04 × 109 J, total energy is -40.02 × 109 J and binding energy is 40.02 × 109 J.
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