Confusion over 2nd law and conservation of momentum

AI Thread Summary
Adding weight to a moving cart affects its momentum, but the cart's speed can change depending on how the weight is added. If the weight is introduced at zero speed relative to the ground, the cart will experience a backward acceleration as the weight accelerates forward to match the cart's speed. The interaction between the cart and the weight creates a force that accounts for this change. When removing the weight by lifting it straight up, the method of removal can influence the cart's motion, suggesting that careful handling is crucial. Understanding these dynamics clarifies the relationship between momentum conservation and acceleration in both linear and rotational motion.
steven george
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Hi everybody, I apologize if something like this has been asked before but I have been unable to find an answer through searching.

If a weight is carefully added to a moving cart then the cart should slow down due to conservation of momentum. How is it that the cart has accelerated without a horizontal force?

This issue originally came up while discussing rotational motion. If a figure skater is spinning and brings his hands in he will speed up. How can he accelerate without any torque?

There must be something very basic that I am missing here, so thank you to anybody who can help with an answer.
 
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steven george said:
If a weight is carefully added to a moving cart then the cart should slow down due to conservation of momentum.
It depends on how the weight is added. I'll guess: You add things at zero speed relative to the ground.
steven george said:
How is it that the cart has accelerated without a horizontal force?
There is a force between cart and new weight, speeding up the weight to match the speed of the car. The new weight accelerates forwards, the remaining cart accelerates backwards..
 
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mfb said:
It depends on how the weight is added. I'll guess: You add things at zero speed relative to the ground.There is a force between cart and new weight, speeding up the weight to match the speed of the car. The new weight accelerates forwards, the remaining cart accelerates backwards..

I knew there must be a simple answer. Thanks for that. Now, what if that weight is taken off by carefully lifting it straight up?
 
What do you mean by "carefully"? The answer may depend on this.
 
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