Problem 2: Space explorers discover an mA = 8.7 x 10¹7 kg asteroid that happens to have a positive charge of qA = 4400 C. They would like to place their ms = 3.3 x 105 kg spaceship in orbit around the asteroid. Interestingly, the solar wind has given their spaceship a charge of qs = -1.2 C. What speed must their spaceship have to achieve a 7500-km- diameter circular orbit?

Principles of Physics: A Calculus-Based Text
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Chapter19: Electric Forces And Electric Fields
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Problem 2: Space explorers discover an mA = 8.7 x 10¹7 kg asteroid
that happens to have a positive charge of qA = 4400 C. They would like
to place their ms = 3.3 × 105 kg spaceship in orbit around the asteroid.
Interestingly, the solar wind has given their spaceship a charge of qs =
-1.2 C. What speed must their spaceship have to achieve a 7500-km-
diameter circular orbit?
Gaima
+
0.98, ms
a) In Fig. 2, draw the vectors that represent the gravitational and
electric forces experienced by the satellite. Compute the magnitudes of
these forces. (Note: Do not use the formula |Fg| = msg, where g =
9.8 ms 2, to compute the gravitational force, because that formula is valid only at low altitudes, and only
for the gravitational field of the Earth. Instead, use Newton's law of gravity, |F| = Gmams, where G is the
gravitational constant, and R is the radius of the orbit.)
R²
FIG. 3: The scheme for Problem 2
b) For the spaseship to stay in equilibrium on the circular orbit, the total force acting on the spaceship
should provide the acceleration a = v2/R, directed inwards (remember that a circular motion is an accel-
erated motion, because the velocity keeps changing direction, even if its magnitude is constant). Using
Newton's second law of motion for the spaceship, Ftot = msa, where Ftot is the total force acting on the
spaceship, find the required velocity.
Transcribed Image Text:Problem 2: Space explorers discover an mA = 8.7 x 10¹7 kg asteroid that happens to have a positive charge of qA = 4400 C. They would like to place their ms = 3.3 × 105 kg spaceship in orbit around the asteroid. Interestingly, the solar wind has given their spaceship a charge of qs = -1.2 C. What speed must their spaceship have to achieve a 7500-km- diameter circular orbit? Gaima + 0.98, ms a) In Fig. 2, draw the vectors that represent the gravitational and electric forces experienced by the satellite. Compute the magnitudes of these forces. (Note: Do not use the formula |Fg| = msg, where g = 9.8 ms 2, to compute the gravitational force, because that formula is valid only at low altitudes, and only for the gravitational field of the Earth. Instead, use Newton's law of gravity, |F| = Gmams, where G is the gravitational constant, and R is the radius of the orbit.) R² FIG. 3: The scheme for Problem 2 b) For the spaseship to stay in equilibrium on the circular orbit, the total force acting on the spaceship should provide the acceleration a = v2/R, directed inwards (remember that a circular motion is an accel- erated motion, because the velocity keeps changing direction, even if its magnitude is constant). Using Newton's second law of motion for the spaceship, Ftot = msa, where Ftot is the total force acting on the spaceship, find the required velocity.
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