Force vs Time Graph: Impulse & Momentum

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The area under a force vs. time graph represents the impulse applied to an object, which is equal to the change in momentum. If the initial momentum is zero, the area under the curve directly corresponds to the final momentum of the object. This relationship highlights the fundamental connection between force, time, impulse, and momentum in physics. Understanding this concept is crucial for analyzing motion and the effects of forces over time. The discussion confirms that the area under the graph indeed reflects changes in momentum.
gauss44
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Regarding the question here, https://www.physicsforums.com/threads/force-vs-time-graph-impulse.665936/ Would it be correct to say that the area under the plotted line equals momentum if the initial momentum were zero?

(This is NOT a homework question. I am posting here since this was the location of the original thread.)
 
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The area under the F-t graph is the change in momentum ... yes.
 

Thread 'Mousetrap Car Energy efficiency'

For simple comparison, I think the same thought process can be followed as a block slides down a hill, - for block down hill, simple starting PE of mgh to final max KE 0.5mv^2 - comparing PE1 to max KE2 would result in finding the work friction did through the process. efficiency is just 100*KE2/PE1. If a mousetrap car travels along a flat surface, a starting PE of 0.5 k th^2 can be measured and maximum velocity of the car can also be measured. If energy efficiency is defined by...
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