- #1

Glenn G

- 113

- 12

- Homework Statement
- Mechanics question, olympiad style

- Relevant Equations
- f = ma

Hello all, this is an adaptation of a question i saw some time ago (can't find the original now). There are two forces acting on two masses both 1kg. The masses are joined by an inextendable rope and going over a frictionless pulley of negigible mass. In blue I have written in some working out to show that IF the pulley was tethered to a wall (say) the difference in accelerations of the two masses was the same as the difference in the two forces SO as I'd imagine if force f1 was larger than f2 then m1 would be accelerating to the right and m2 would be accelerating to the left. IN this situation imagine this was in outer space where everything is free to move AND in this case the pulley is attached to a third mass m3 via another rope.

The main question IS what is happening to mass 3? Clearly there must be a tension force that m3 is experiencing causing it to accelerate. Does m3 experience the sum of the two forces (f1 + f2) OR the average of the two forces (f1 + f2)/2 and of course everything is connected together and so if the acceleration of m3 is greater than m1 or m2 then it is going to smash into the pulley but if it's acceleration is less than that of either m1 or m2 then it is going to lag behind BUT if the cables can't extend then this can't happen. My guess is that m3 has to have the same acceleration as the larger acceleration out of m1 and m2. If m1 and m2 have different accelerations then that doesn't bother me as the pulley can rotate so the cable either side of the pulley can change length (initially).

ANYWAY I have realized that my mechanics is lacking here and would appreciate help with this analysis please.

cheers,

Glenn.

ps in blue are bits of analysis that I think would be true if the pulley was tethered not sure how this all applies IF everything is dynamic and in 'outer space'.

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