A-50-g-lead-bullet-sp-heat-0-02-is-initially-at-30-C-It-is-fired-vertically-upwards-with-a-speed-of-840-m-s-and-on-returning-to-the-starting-level-strikes-a-cake-of-ice-at-0-C-How-much-ice-is-melt

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Question Number 23361 by Tinkutara last updated on 29/Oct/17

$$\mathrm{A}50\mathrm{g}\mathrm{lead}\mathrm{bullet},\mathrm{sp}.\mathrm{heat}0.02\mathrm{is}$$$$\mathrm{initially}\mathrm{at}30°\mathrm{C}.\mathrm{It}\mathrm{is}\mathrm{fired}\mathrm{vertically}$$$$\mathrm{upwards}\mathrm{with}\mathrm{a}\mathrm{speed}\mathrm{of}840\mathrm{m}/\mathrm{s}\mathrm{and}$$$$\mathrm{on}\mathrm{returning}\mathrm{to}\mathrm{the}\mathrm{starting}\mathrm{level}\mathrm{strikes}$$$$\mathrm{a}\mathrm{cake}\mathrm{of}\mathrm{ice}\mathrm{at}0°\mathrm{C}.\mathrm{How}\mathrm{much}\mathrm{ice}\mathrm{is}$$$$\mathrm{melted}?\mathrm{Assume}\mathrm{that}\mathrm{all}\mathrm{energy}\mathrm{is}$$$$\mathrm{spent}\mathrm{in}\mathrm{melting}\mathrm{only}(L=80\mathrm{cal}/\mathrm{g}).$$

Answered by ajfour last updated on 29/Oct/17

$$(Iassumespecificheat=\frac{0.02cal}{gC°})$$$$mL+Mc△T+△K=0$$$$m(80\times 4.182)+50\times 0.02\times 4.2\times 30$$$$-\frac{1}{2}\times \frac{50}{1000}\times {\left(840\right)}^2=0$$$$\approx \Rightarrow m\left(42\times 8\right)=3\times 42+42\times 420$$$$orm=\frac{423}{8}g\approx 53g.$$

Commented by Tinkutara last updated on 29/Oct/17

$$\mathrm{Thank}\mathrm{you}\mathrm{very}\mathrm{much}\mathrm{Sir}!$$

Commented by ajfour last updated on 29/Oct/17

$$m:massoficemelted$$$$L:Latentheatofice$$$$M:massofbullet$$

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