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Quiz_3_solutions_web - Group Question A spring loaded gun...

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Group Question A spring loaded gun is cocked by compressing a spring of spring constant 1000 N/m by 10cm. The gun fires a signal flare of mass 10g vertically upward. The flare rises to a height of 45m above the point where it leaves the spring. The drag force of the air is significant in slowing down the flare. a) How much work is done in compressing the spring? b) What is the velocity of the flare as it leaves the spring? c) How much mechanical energy is lost as work against the drag force of the air? d) If the drag force is assumed to be constant, what is its value? e) What form of energy is the lost mechanical energy transformed into? f) How long does it take for the flare to reach its maximum height? g) At its maximum height the flare explodes into 5 separate pieces with a release of chemical energy of 50J, what will be the total kinetic energy of the pieces immediately after the explosion? Let the spring constant be k N/m, the distance the spring is compressed d m, the mass of the flare m kg and the distance to which it rises h m. Let the velocity of the flare as it leaves the spring be v m/s and the drag force be F N a) Work done in compressing the spring = gain in PE of the spring = ½ kd 2 = ½ 1000 0.1 2 = 5J b) Gain in KE of the flare = loss of PE in the spring = ½ mv 2 ½ kd 2 = ½ mv 2 v = d k/m = 0.1 1000/0.01 = 31.6m/s There is a small gravitational PE component as the flare has risen 10cm, if they ignore it that is OK, don’t subtract any points. If they include it and get it right then give them a plus in other parts of the problem.
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Quiz_3_solutions_web - Group Question A spring loaded gun...

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