A spring-loaded gun is cocked by compressing a short, strong spring by a distanc

Question

A spring-loaded gun is cocked by compressing a short, strong spring by a distance d. It fires a signal flare of mass m directly upward. The flare has speed vo as it leaves the spring and is observed to rise to a maximum height h above the point where it leaves the spring. After it leaves the spring, effects of drag force by the air on the flare are significant. (Use any variable or symbol stated above along with the following as necessary: g.) (a) How much work is done on the spring during the compression? X Your answer cannot be understood or graded. More Information (b) What is the value of the force constant k? (c) Between the time of firing and the time at which maximum elevation is reached, how much mechanical energy is dissipated into thermal energy? E therm = eBook Submit Answer Save Progress

Explanation / Answer

a)

m = mass

vo = speed gained

W = work done on the spring = kinetic energy gained = (0.5) m vo2

W = (0.5) m vo2

b)

using conservation of energy

Kinetic energy gained = spring potential energy lost

(0.5) m vo2 = (0.5) k d2

k = sqrt(m) (vo/d)

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