An astronaut in her space suit has a total mass of m1 = 74.5 kg, including suit

Question

An astronaut in her space suit has a total mass of m1 = 74.5 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 m2 = 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 1.60 min (the amount of time the air in her helmet remains breathable). m (b) Explain in terms of Newton's laws of motion why this strategy works.

Explanation / Answer

Mass of the astronaut m1 = 74.5 -12 = 62.5kg

mass of the Oxy cylinder, m2 = 12 kg

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

Backward momentum of the astronaut, p2 = 62.5xV

Total momentum after throwing, p1 + p2.

Total p before throwing = 0

Conservation of momentum: p1 + p2 = 0

             p1 = - p2

         62.5v =90

             v= 90 / 62.5 = 1.44 m/s

Max distance,

         S = v.t =1.44x1.6x60

            = 138.24 m

Explanation:

newton's 3rd law Action and reaction are equal andopposite.

The force exerted by the astronaut on thecylinder(action)

= the force exerted by the cylinder on theastronaut(reaction).

From 2nd law.

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

Total momentum of the astonaut + cylinder before throw

= Total momentum of the astonaut + cylinderafterthrow.

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