Question

An astronaut in her space suit has a total mass of m, = 90.0 kg, including suit and oxygen tank. Her tether line loses its attachment to her spacecraft while she's on a spacewalk. Initially at rest with respect to her spacecraft, she throws her oxygen tank of mass m, - 12.0 kg away from her spacecraft with a speed v = 7.50 m/s to propel herself back toward it (see figure). (a) Determine the maximum distance she can be from the craft and still return within 1.80 min (the amount of time the air in her helmet remains breathable). (b) Explain in terms of Newton's laws of motion why this strategy works. This answer has not been graded yet.

Answer 1

(a) Mass of the astronaut m1 = 90 -12 = 78 kg

Mass of the Oxygen cylinder, m2 = 12 kg

Forward momentum of the cylinder, p1 = 12x7.5 = 90 kg.m/s

Backward momentum of the astronaut, p2 = 78xv

Total momentum after throwing, p1 + p2.

Total p before throwing = 0

Conservation of momentum: p1 + p2 = 0

             P1 = - p2

         78v =90

             V= 1.15 m/s

Max distance,

         S = v.t =1.15x(1.8x60) = 124.62 m

(b) The force exerted by the astronaut on the cylinder = the force exerted by the cylinder on the astronaut

From Newton’s 2nd law:

Total momentum of a system remains conserved when there is nonet external force acting on it.

Total momentum of the astronaut + cylinder before throw

= Total momentum of the astronaut + cylinder after throw.

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