A 0.0030-kg lead bullet is traveling at a speed of 300 m/s when it embeds in a block of ice at 0°C.If all the heat generated goes into melting ice,what quantity of ice is melted? (L_f = 80 kcal/kg,the specific heat of lead = 0.03 kcal/kg·°C,and 1 kcal = 4186 J) A) 1.47 × 10−² kg B) 4.0 × 10−⁴ kg C) 3.2 × 10−³ kg D) 2.6 × 10−⁴ kg

Question

Quizplus · Accepted Answer

First, we need to calculate the total heat generated by the bullet as it embeds in the block of ice:

Kinetic energy of bullet = 0.5 * 0.0030 kg * (300 m/s)^2 = 1350 J

Heat generated = 1350 J / 4186 J/kcal = 0.322 kcal

Next, we need to calculate the amount of ice melted by this heat:

Heat required to melt 1 kg of ice = 80 kcal/kg

Mass of ice melted = Heat generated / Heat required = 0.322 kcal / 80 kcal/kg = 0.00402 kg

Therefore, the amount of ice melted is 4.02 g or 4.0 × 10^-3 kg, which is closest to option B.

A 00030-Kg Lead Bullet Is Traveling at a Speed of 300