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2. A mass is pushed up against a compressed spring which is buttressed behind by a solid block fixed permanently onto the physics lab-bench surface. The spring lies horizontally with the mass at the end opposite that of the buttressing solid block (i.e. the compressed spring lies horizontally on the lab-bench surface and this spring lies between the solid block buttressing fixture to its left side, and, there is a smooth freely moving nearly frictionless mass to the right of this same spring). Further to the right of the compressed spring and the freely moveable mass on its right side is a horizontal surface that Is frictionless and it stays this way for 1.56 m right up until it then turns into a ramp that is curved upward and away from the horizontal surface, We assume in BOTH parts (@) and (b) below that this curved ramp remains frictionless in either case. In part (&), the spring Is going to push the smooth freely moving mass down a narrow, stralght, horizontally level air-hockey track (i.e. nearly frictionless mass/track interface when the many hundreds of tiny alr-Jet holes in the track are actively emitting their many many tiny air jets) toward the beginning of the curved-up ramp. In part (b), the only difference is that the air-jets are turned off and now there actually is some non-negligible amount of kinetic friction to be also considered when solving the problem. (@) Assume the spring is compressed by 4,38 cm and has a spring constant of k= 7,92 N/em. Assume the freely moving mass is 125 grams, In part{e) we assume the 1.56 meter track that this mass travels has zero friction, (@) What is the final or 'muzzle velocity' of the mass when it leaves the end of the spring after the compressed spring is allowed to freely extend itself back to its normal 'at rest' spring length? s (@) What is the energy stored in the spring when compressed? s (ay) What is the kinetic energy of the freely moving mass after it leaves the spring behind? & (o) How high up the curved ramp does the freely moving mass travel before it stops going up (and starts to roll back down)? - (L.e. what is the maximum height achieved by the moving mass?) e (@) What Is the maximum stored gravitational potential energy of the freely moving mass when it gets to its highest point, just before it starts to roll back down? e (@) What would be the magnitude of the velocity of the freely moving mass after it has come down to half its maximurm height on the curved ramp? s (o) What is the freely moving mass velocity when it is back on the horizontal track surface just after it leaves the curved up ramp heading back toward the spring? e (o) Will the mass make it all the way back to the spring? If it does, what s its velocity just before impact? If it doesn't, prove why it doesn't make it. e (@) Assuming the mass above does make it all the way back to the spring, what would happen next? And then what would happen after that? And after that?... etc... (i.e. assume no energy losses due to friction, air resistance, mechanical energy losses internal to the spring's compression and extensions, etc... no energy lost due to any of these 'error sources'). (b;) Repeat the above analyses, sub-part by sub-part (i.e. (&) to (&) as stated above for part{a)), but now assume that the 1.56 meters of track where the ball is free of the spring and has not yet reached the still-frictionless curved-up ramp, has a mass/track interface of coefficient of kinetic friction of 0.0250. (b:) Does the maoving mass, now (i.e. with a horizontal track that now does cause friction) even make it to the curved-up ramp? If not, why not? Explain. Include labelled diagrams. (bs) If the moving mass does make it to the ramp (i.e. in spite of the friction it now encounters while crossing the 1.56 meter long horizontal track (with the airjets turned off}), then what is the velocity of this moving mass just as it enters the frictionless curved-up ramp? (bs) After the moving mass passes along the now-with-friction horizontal track to get to the ramp, and goes up and back down the frictionless curved-up ramp, and then heads back to the spring { ifit can do this (explain "why not' if it can't)) can this mass make it all the way back to the spring after going up and coming back down the curved-ramp?? {bs) What new maximum height does the moving mass achieve as it climbs the ramp, just before it stops moving up and starts to roll back down (assuming it makes it ta the ramp in the first place)? (bg) Can this mass make more than one \"complete circuit of travelling from the end of the spring, to the curved-up ramp, and then back to the end of the spring where it ariginally left the spring the first time {i.e. with its original Eastward-directed spring-induced 'muzzle velocity'), or not? Explain and prove with calculations either way. (b7) Assuming the mass can make one or more complete circuits as described above, then how many complete circuits can this moving mass make (can it even make just one complete circuit??) before the mass comes to a complete stop? [ oLease wore: Keep in mind that the only energy losses are from the "airjets off' horizontal track which now has a low but non-zero non-negligible amount of friction (see the above-stated coefficient of kinetic friction). ]] (ba) Assuming the moving mass is able to complete more than one circuit across the now-with-friction horizontal track {and this includes the mass going up and back down the curved-up ramp, and re-compressing the spring and then being shot back out again when the spring re-extends itself) then what amount of energy is lost each time from crossing the 1.56 meter length of horizontal track? Is this amount of energy loss the same amount for each time the moving mass traverses the full 1.56 meters of the track? Whether you feel it is the same amount of energy lost or not, please explain your reasoning either way and support your reasoning with some 'energy loss' calculations. (ba) Assuming the moving mass makes it all the way back to the spring the first time, how far will the moving mass compress the spring upon the first (maybe it only happens once..?...) return of the moving mass to the spring? Whether the moving mass does make it back all the way or not, please also try the following series of 3 theoretical calculations that compare how much new compression of the spring occurs, as cornpared to the original compression at the beginning of the problem (see above): (1.} if the moving mass returns with only 90.0% of its original 'muzzle velocity' magnitude? versus (2.) what if returns with 50.0% of its original ''muzzle velocity'? or (3.) what if it returns with only 10.0% of its original 'muzzle velocity'? Compare these 3 results to one another. Explain the nature of the trend you observe and relate it to the equations and calculations you performed