Conservation of Momentum with Varying Mass

AI Thread Summary
In the discussion on conservation of momentum with varying mass, a scenario is presented where a boat at rest collects balls thrown at its back, leading to an inelastic collision. The key equation used is Δmu + MV = (Δm + M)(V + ΔV), which helps in analyzing the system. Participants clarify that since no external forces act on the boat, linear momentum is conserved, allowing for the application of conservation principles. The comparison to rocket dynamics highlights the unique aspect of the boat collecting mass rather than expelling it. The overall conclusion emphasizes that the boat's motion can be analyzed using momentum conservation despite the varying mass.
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Homework Statement



A boat with mass M is at rest. Balls are thrown at the back of the boat, where each ball has mass of m, and the balls are being thrown with the mass rate of σ kg/s (the rate is continuous). The balls are being collected inside the boat (inelastic collision). Find velocity and position of the boat as a function of time.

Homework Equations



Δmu + MV = (Δm + M)(V + ΔV)

The Attempt at a Solution



I thought I could use the rocket equation for this, but I had trouble figuring it out because I wasn't sure if I can assume ƩF = 0.
 
Physics news on Phys.org
Rockets don't usually scoop up their own exhaust products. Once the exhaust mass leaves the rocket, it is assumed to be lost permanently.
 
Yes you can go ahead and use the conservation, there is no outer force acting on the system. The Boat is not fixed by some outer force so we can translate it in space and get the same dynamics meaning linear momentum is conserved (we assume the effect of water on the boat negligible).
 
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