A 3.00- g lead bullet at 30.0^∘ C is fired at a speed of 2.40 ×10^2 m / s into a large, fixed bl

A 3.00- g lead bullet at 30.0^∘ C is fired at a speed of...

A $3.00-$ g lead bullet at $30.0^{\circ} \mathrm{C}$ is fired at a speed of 2.40 $\times 10^{2} \mathrm{m} / \mathrm{s}$ into a large, fixed block of ice at $0^{\circ} \mathrm{C}$ , in which it becomes embedded. (a) Describe the energy transformations that occur as the bullet is cooled. What is the final temperature of the bullet? (b) What quantity of ice melts?

A $3.00-$ g lead bullet at $30.0^{\circ} \mathrm{C}$ is fired at a speed of 2.40 $\times 10^{2} \mathrm{m} / \mathrm{s}$ into a large, fixed block of ice at $0^{\circ} \mathrm{C}$ , in which it
becomes embedded. (a) Describe the energy transformations that occur as the bullet is cooled. What is the final temperature of the bullet? (b) What quantity of ice melts?

Key Concepts

Latent Heat of Fusion

Latent heat of fusion is the amount of energy required to change a substance from a solid to a liquid at its melting point without a change in temperature. In problems involving phase changes, such as melting ice due to energy input, this concept is crucial to determine the quantity of material that undergoes the transition.

Energy Conservation

The conservation of energy principle states that energy can neither be created nor destroyed, only transformed from one form to another. In the collision described, the bullet’s kinetic energy is not lost but is redistributed as thermal energy that heats the bullet and causes some of the ice to melt.

Specific Heat Capacity

Specific heat capacity is the amount of energy required to raise the temperature of a unit mass of a substance by one degree Celsius. It is used to calculate how much the temperature of the bullet or any substance changes when a given amount of energy is absorbed or released.

Thermal Energy

Thermal energy refers to the internal energy in an object due to the random motion of its particles, which manifests as temperature. When the bullet is fired into the ice, a portion of its kinetic energy is converted into thermal energy, thereby causing a rise in temperature or even phase changes in the materials involved.

Kinetic Energy

Kinetic energy is the energy an object possesses due to its motion, defined mathematically as one-half the mass times the square of its velocity. In this context, the bullet’s kinetic energy, determined by its mass and speed, is the initial form of energy that is later transformed during the collision.

Transcript

00:01 So for part a, we can say that bullet loses all kinetic energy as it is stopped by that block of ice.

00:16 So stopped by ice.

00:19 And we can say that thermal energy from bullet transfers to ice.

00:36 And this would be as the bullet cools from 30 degrees celsius to the final temperature.

00:42 Now, we could say that the kinetic energy plus thermal energy from bullet melts part of the ice.

01:13 And because not all of the ice melts, so when the bullet is embedded in this ice block, it's not, the entire ice block does not melt, of course.

01:23 So we can say that the final temperature of the bullet is zero degrees celsius because this would be the temperature of that ice.

01:43 So that would be the final temperature and this is a quick summary of the energy transformations that are in play here.

01:51 So we can then say that the total energy transferred from the bullet to the ice for part b, this would be the energy transferred would be.

02:04 Equal to the initial kinetic energy plus the mass of the bullet times the specific heat capacity of lead which is what the bullet is made out of multiplied by the absolute value of zero degrees celsius minus 30 degrees celsius and so we can then say that the energy transfer would be equaling one half times the mass of the bullet times the velocity initial squared plus the mass of the bullet the specific heat of lead multiplied by 30 degrees celsius.

02:43 And so we can then say that this would be one half multiplied by the mass of the bullet, 3 .00...

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