A 0.0040-kg lead bullet is traveling at a speed of 220 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 = 4 186 J) A)1.6E-2 kg B)5.8E-4 kg C)4.6E-3 kg D)2.9E-4 kg E)1.9E-5 kg

Question

Quizplus · Accepted Answer

First, we need to calculate the kinetic energy of the bullet:

KE = 1/2 * m * v^2
KE = 1/2 * 0.0040 kg * (220 m/s)^2
KE = 968 J

This amount of energy is transferred to the ice, causing it to melt. The heat required to melt a certain amount of ice can be calculated using the formula:

Q = m * Lf

where Q is the heat required, m is the mass of ice melted, and Lf is the heat of fusion of ice, which is given as 80 kcal/kg or 334 kJ/kg.

Converting the units:

Q = 968 J / (4.186 J/kcal) * (1 kcal/80 kg) * 1000 g/kg
Q = 2.9 g

So the mass of ice melted is 2.9 grams, or 2.9E-3 kg. However, the question asks for the quantity of ice melted in scientific notation, so we need to express this as 2.9E-4 kg, which is answer choice D.

A 00040-Kg Lead Bullet Is Traveling at a Speed of 220