An astronaut comes loose while outside the spacecraft and finds himself floating away from the spacecraft with only a big bag of tools. In desperation, the astronaut throws his bag of tools in the direction of his motion (away from the space station). The astronaut has a mass of 102 kg and the bag of tools has a mass of 10.0 kg. If the astronaut is moving away from the space station at 1.20 m/s initially, what is the minimum final speed of the bag of tools (with respect to the space station) that will keep the astronaut from drifting away forever?
I wonder how the astronaut is going to throw the tools without starting to spin like a top?
action = reaction
toolmass*V=102*1.20
To solve this problem, we need to apply the principle of conservation of momentum. The total momentum of the system (astronaut + bag of tools) before the tools are thrown must be equal to the total momentum after the tools are thrown.
The momentum of an object is given by the product of its mass and velocity: momentum = mass * velocity.
Let's denote the initial velocity of the astronaut as v_astronaut, the initial velocity of the bag of tools as v_tools, and the final velocity of the bag of tools as v_final.
Initially, the momentum of the astronaut is given by:
momentum_astronaut_initial = mass_astronaut * v_astronaut
Initially, the momentum of the bag of tools is given by:
momentum_tools_initial = mass_tools * v_tools
After throwing the bag of tools, the astronaut's momentum will remain the same, but with a different velocity:
momentum_astronaut_final = mass_astronaut * v_astronaut
The total initial momentum is the sum of the individual momenta:
initial_total_momentum = momentum_astronaut_initial + momentum_tools_initial
The total final momentum is also the sum of the individual momenta:
final_total_momentum = momentum_astronaut_final + (mass_tools * v_final)
Since momentum is conserved, the initial total momentum must be equal to the final total momentum:
initial_total_momentum = final_total_momentum
Plugging in the given values, we have:
(mass_astronaut * v_astronaut) + (mass_tools * v_tools) = (mass_astronaut * v_astronaut) + (mass_tools * v_final)
We can rearrange the equation to solve for v_final:
mass_tools * v_final = (mass_astronaut * v_astronaut) + (mass_tools * v_tools) - (mass_astronaut * v_astronaut)
v_final = [(mass_astronaut * v_astronaut) + (mass_tools * v_tools) - (mass_astronaut * v_astronaut)] / mass_tools
Plugging in the given values:
v_final = [(102 kg * 1.20 m/s) + (10.0 kg * 0 m/s) - (102 kg * 1.20 m/s)] / 10.0 kg
Simplifying, we can calculate the minimum final speed of the bag of tools that will keep the astronaut from drifting away forever.