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The same force could not be applied to travel the same distance if there is a larger mass in one instance. Applied force will accelerate a given mass twice as much as a mass half as large. If both are moving the same distance, the 20-brick cart had more kinetic energy when in motion.

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Q: A cart pushing ten bricks or a cart pushing twenty bricks using the same force and going the same distance which has greater kinetic energy?
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What change in kinetic energy does an airplane experience on takeoff if it is moved a distance of 500 m by a sustained netforce of 5000 N?

Tell you what: We'll calculate how much work is done by the force, not howmuch kinetic energy the plane picks up, and then we'll tell you why.The work done is (force) x (distance) = (5,000) x (500) = 2,500,000 joules.Whenever we do these force/distance/work/energy problems, we always ignorefriction, air resistance, etc. because it's just too hard and complicated to takeall of them into consideration, and it would only get in the way of understandingthe basic principles anyway.How valid is the answer we get when we ignore these things ? Well, it may be OK,and pretty close to reality, for baseballs, stones, bullets, and bricks. But it's definitelynot OK for airplanes. Airplanes are designed specifically to have an intimate relationshipwith the air, and that's the only reason they work at all.If you do 2.5 million joules of work on a baseball, a stone, or even a little red wagon,it may have close to 2.5 million joules of kinetic energy when you stop pushing. Butan airplane won't. It's designed to use some of that K.E. to move air, to generateLIFT, with the ultimate objective of getting off of the ground. That drains awaya big part of the work done to roll down the runway, and that's the big part thatwill never show up as kinetic energy.


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