Vacuum Cleaner

# Vacuum Cleaner - Vacuum cleaners and rockets In class 10 I...

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Vacuum cleaners and rockets In class 10 I very rapidly discussed a “giant vacuum cleaner” as a rocket working in reverse. Here are more of the details. At time t , the vacuum cleaner has mass M and is moving with velocity v . As time goes on, its mass increases, and its velocity increases also. t ´¿ "! - - - v + v ex v v + Δ v Δ M M M + Δ M = Time t Time t + Δ t The “vacuum cleaner” M is sucking in a stream of tiny particles. The velocity of the particles relative to the vacuum cleaner is v ex . In time Δ t the mass of these particles that arrives is Δ M . In terms of the rate of arrival, R particles per second, and the mass of each particle, m , we have Δ M = Rm Δ t Thus, in time Δ t , the mass of M changes to M + Δ M , and we would expect that its velocity changes also. Let the change – which will be small – be Δ v . Since momentum is conserved each time that a particle arrives, the momentum at time t and at time t + Δ t is the same: Δ M ( v + v ex ) + Mv

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## This note was uploaded on 04/29/2008 for the course PHYS 230 taught by Professor Harris during the Fall '07 term at McGill.

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Vacuum Cleaner - Vacuum cleaners and rockets In class 10 I...

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