Final answer:
To determine how much ice is melted, the kinetic energy of the lead bullet is calculated and then converted into the amount of ice melted by using the heat of fusion for ice. Approximately 733.53 grams of ice can be melted by a 4.0 gram bullet traveling at 350 m/s.
Step-by-step explanation:
Calculating the Amount of Ice Melted
The question involves the transfer of energy from a hot object (the lead bullet) to a cooler one (the ice block), causing the ice to melt. The concept at play is the conservation of energy, specifically how mechanical energy (kinetic energy of the bullet) is converted into thermal energy (heat), and then used to melt the ice.
First, we calculate the kinetic energy (KE) of the bullet using the formula KE = 0.5 * m * v2, where m is the mass of the bullet and v is its velocity:
KE = 0.5 * 4.0 g * (350 m/s)2
= 0.5 * 4.0 g * 122500 m2/s2
= 245000 J (or 245 kJ) because 1 J = 1 kg*m2/s2 and 1 g = 0.001 kg
This amount of energy will be used to melt the ice. We then use the heat of fusion of ice to find out how much ice will melt using the formula Q = m * Lf, where Q is heat in joules, m is the mass of the ice melted, and Lf is the heat of fusion of ice:
We rearrange the formula to solve for m: m = Q / Lf
Since the heat of fusion of ice as per definition 9.4.1 is 334 J/g, we can now calculate the mass of the melted ice as follows:
m = 245000 J / 334 J/g
= 733.53 g (approx.)
Therefore, approximately 733.53 grams of ice will be melted by the bullet.