An astronaut in space cannot use a scale or balance to weigh objects because the

Question

An astronaut in space cannot use a scale or balance to weigh objects because there is no gravity. But she does have devices to measure distance and time accurately. She knows her own mass is 76.6kg , but she is unsure of the mass of a large gas canister in the airless rocket. When this canister is approaching her at 3.60m/s , she pushes against it, which slows it down to 1.00m/s (but does not reverse it) and gives her a speed of 2.10m/s .

What is the mass of this canister?

How much kinetic energy is

Explanation / Answer

The mass of the astronaut m = 76.6 kg

the speed of the canister vi = 3.6 m/s

after approach the final speed of the canister vf = 1.00m/s

the speed of the astronaut v = 2.1 m/s

Let the mass of the canister be M

from law of conservation of momentum

     Mvi = Mvf + mv

   M( vi - vf) = mv

therefore the mass of the canister

     M = mv/(vi - vf)

         = (76.6)(2.1) / (3.6-1.0)

         = 61.87 kg

b)

KE initial - KE final = 0.5*61.87*3.6^2 - 0.5*61.87*1.0^2 - 0.5*76.6*2.1^2= 201.08 J

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