Answer to Question #141517 in Mechanics | Relativity for Hayri

Question

An astronaut is outside her space capsule in a region where the effect of gravity can be neglected. She uses a gas gun to move herself relative to the capsule. The gas gun fires gas from a muzzle of area 160 mm^2 at a speed of 150m/s. The density of the gas is 0.800kg/m^3 and the mass of the astronaut, including her spacesuit, is 130kg. Calculate (a) the mass of gas leaving the gun per second, (b) the acceleration of the astronaut due to the gun, assuming that the change in mass is negligible.

Answer 1

A)   Since density is $\rho=\frac{m}{V}$ , then $m=\rho\times V=0.8\times160\times10^{-6}\times150$ $=1.92\times 10^{-2}$ kg.

B)    According to the law of conservation of momentum, the gas pulse is transmitted to the astronaut's pulse $m_g\times v=\Delta p_a$ , since $F=\frac{\Delta p_a}{\Delta t}=a\times M$, then $a=\frac{m_g\times v}{\Delta t \times M}= \frac{1.92\times 10^{-2}\times 150}{1 \times 130}\approx0.02$ m/s$^2$ .