How Much Ice Melts When a Bullet Penetrates It?

[BuBbLeS01]

Please help...How much ice melts?

Homework Statement

A 70 gram bullet traveling at 250 m/s penetrates a block of ice at 0 degrees Celsius 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 Attempt at a Solution

I don't know where to start on this?

 

[G01]

Questions to get you started:

How much energy is needed to melt a gram of ice?

How much energy does the bullet give to the block of ice when it slows down?

 

[ogb p]

Hello,

Thank you for reaching out for help. As a scientist, it is my job to provide evidence-based explanations and solutions to problems. In order to determine how much ice melts in this scenario, we need to consider the principles of energy conservation and heat transfer.

The bullet has kinetic energy due to its motion, and when it collides with the ice block, this energy is transferred to the ice in the form of heat. This heat causes the ice to melt. We can calculate the amount of heat transferred using the equation Q = mcΔT, where Q is the heat transferred, m is the mass of the ice, c is the specific heat capacity of ice, and ΔT is the change in temperature.

Since the bullet comes to rest within the ice, we can assume that all of its kinetic energy is transferred to the ice. We can calculate the kinetic energy of the bullet using the equation KE = 1/2mv^2, where m is the mass of the bullet and v is its velocity. Plugging in the values given in the problem, we get KE = 1/2(0.07 kg)(250 m/s)^2 = 2187.5 J.

Now, we need to determine the change in temperature of the ice. We know that the ice starts at 0 degrees Celsius and ends up at some final temperature, which we will call Tf. We also know that the specific heat capacity of ice is 2.09 J/g°C. Using the equation Q = mcΔT, we can rearrange to solve for ΔT, giving us ΔT = Q/mc. Plugging in the values we have calculated, we get ΔT = (2187.5 J)/(0.07 kg)(2.09 J/g°C) = 156.8°C.

This means that the final temperature of the ice is 156.8 degrees Celsius. However, since water freezes at 0 degrees Celsius, we know that the ice will not remain at this temperature. Instead, it will continue to absorb heat until it reaches 0 degrees Celsius and then start to melt. Therefore, we can conclude that the amount of ice melted is equal to the mass of the ice, since all of it will eventually melt.

I hope this explanation helps you understand how to approach this problem. If you have any further questions, please don't hesitate to ask. Good luck with your studies!