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There is a worked example in this book on P168-169 titled "Chain on a scale". Two different ways of obtaining the solution are shown. I am confused about the 2 different methods.

Method 1 equates the rate of change of momentum of the chain to the net force on the chain giving F.

Method 2 equates the rate of change of momentum to part of the force called ##F_(dp/dt)## which is then added to ##F_(weight)## to give F.

I am confused about why method 2 needs the addition of the weight already on the table but method 1 doesn't even though both methods equate forces to rates of change of momentum.

Any help would be appreciated.

Thanks