A 49-g bullet traveling at 290m/s penetrates a block of ice at 0∘C and comes to rest within the ice.Assuming that the temperature of the bullet doesn't change appreciably, how much ice is melted as a result of the collision? The heat of fusion of water is 333 kJ/kg.
Equate energy with the heat of fusion of water.
(1/2)mv²=MH
m=mass of bullet(kg)
H=heat of fusion (J/kg)
M=mass of ice melted (kg)
Make sure the heat of fusion of water is converted to J/kg for your calculations.
To determine the amount of ice melted as a result of the collision, we need to consider the energy transferred from the bullet to the ice.
The bullet has a mass of 49 g, which is 0.049 kg, and it is traveling at 290 m/s. The initial kinetic energy (KE) of the bullet can be calculated using the formula:
KE = (1/2) * mass * velocity^2
Let's calculate the initial kinetic energy:
KE = (1/2) * 0.049 kg * (290 m/s)^2
Next, we need to calculate the amount of energy required to melt a certain amount of ice. The heat of fusion of water is given as 333 kJ/kg. The bullet will transfer its energy to the ice, causing it to melt.
The amount of ice melted can be calculated using the formula:
Amount of ice melted = Energy transferred / Heat of fusion
Let's calculate the energy transferred from the bullet to the ice:
Energy transferred = Initial kinetic energy of the bullet
Finally, let's substitute the values into the formula to find the amount of ice melted:
Amount of ice melted = Energy transferred / Heat of fusion
Remember to convert the units appropriately to ensure consistency.
Thus, by following these steps, you can calculate the amount of ice melted as a result of the collision.