Question

Momentum and Impulse Physics

1. An astronaut is performing EVA (extra-vehicular activity–this is NASA-speak for a space walk) near the International Space Station (ISS) when her jet pack malfunctions. There are two objects within her reach that she can use to propel herself back to the safety of the ISS. Object A has her mass M, and object B has a mass of 10·M (ten times greater). Which object should she push on to achieve a given momentum towards the ISS – that is, which one requires less work to get the same impulse? Assume the astronaut and both objects are initially at rest with respect to the ISS. Explain your reasoning. (Remember that work is force times distance and think about how the two objects move when pushed.)

2. Two particles, particle A and particle B, are pushed across a frictionless, horizontal surface by equal forces F for the same length of time, ∆t. Particle A has less mass than particle B: mA < mB. a) Compare the work done on each particle (that is, is the work done on A less than, equal to, or greater than, the work done on B). b) Compare the impulses delivered to the two particles. c) Compare the final speeds of the two particles. Explain your answers.

Thanks!

Answer 1

Lesser amount of work requires lesser amount of change in kinetic energy. This requires lesser amounts of velocities.

As initially both are at rest and hence momentum of system is 0 hence after the event again due to momentum conservation momentum need to be zero. That means m_av_a + M_oV_o = 0 or v_a =-M_oV_o/m_a

clearly v_a (velocity of astronaut) will be equal in magnitude to the velocity of object if m_a = M_o = M. but for the same value of velocity of astronaut the velocity of object can be reduced 10 times if it’s mass rises by 10 times. So in this case the net change in kinetic energies will be minimum. So she must push the heavier object, the object B.

The objects will move in opposite directions.