Respuesta :
Answer:
U = G m M / R1 , U = 18.95 10¹⁴ J
Explanation:
The law of universal gravitation is
F = G m M / r²
Force is related to potential energy
F = - dU / dr
dU = - F dr
Let's replace and integrate
∫dU = - G m M ∫ dr / r²²
Uf - U = - G m M (-1 / r)
It tells us to take zero potential (U = 0) for a distance inf (r = ∞) this is the end point
0 - U = - G mM (- 1 /∞ + 1 / r)
U = G m M / r
Let's calculate the potential energy of the meteor with the data
U = G m M / R1
m = 0.86 10 kg
M = 7.6 10²⁵ kg
R1 = 2.3 10⁷ m
U = 6.67 10⁻¹¹ 0.86 10 7.6 10²⁵ / 2.3 10⁷
U = 18.95 10⁸ J
R1 = 2.3 10 m
U = 6.67 10⁻¹¹ 0.86 10 7.6 10²⁵ / 2.3 10
U = 18.95 10¹⁴ J
The expression for the gravitational potential energy PE1 of the meteoroid at R1 in terms of defined quantities and the gravitational constant G is :
- U = G m M / R1 , U = 18.95 10¹⁴ J
"Gravity"
The law of universal gravitation is
F = G m M / r²
Force is related to potential energy
F = - dU / dr
dU = - F dr
replace and integrate
∫dU = - G m M ∫ dr / r²²
Uf - U = - G m M (-1 / r)
0 - U = - G mM (- 1 /∞ + 1 / r)
U = G m M / r
The potential energy of the meteor with the data :
U = G m M / R1
m = 0.86 10 kg
M = 7.6 10²⁵ kg
R1 = 2.3 10⁷ m
U = 6.67 10⁻¹¹ 0.86 10 7.6 10²⁵ / 2.3 10⁷
U = 18.95 10⁸ J
The potential energy of the meteor with the data is 18.95 10⁸ J.
R1 = 2.3 10 m
U = 6.67 10⁻¹¹ 0.86 10 7.6 10²⁵ / 2.3 10
U = 18.95 10¹⁴ J
The gravitational potential energy PE1 of the meteoroid at R1 is 18.95 10¹⁴ J.
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