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University of New Mexico

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Problem 97

The kinetic energy of a rolling billiard ball is given by KE = 12 mv2. Suppose a 0.17-kg billiard ball is rolling down a pool table with an initial speed of 4.5 m>s. As it travels, it loses some of its energy as heat. The ball slows down to 3.8 m>s and then collides head-on with a second billiard ball of equal mass. The first billiard ball completely stops, and the second one rolls away with a velocity of 3.8 m>s. Assume the first billiard ball is the system and calculate w, q, and E for the process.

Answer

$$

-1.2 \mathrm{J}

$$

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## Discussion

## Video Transcript

We know that the internal energy off a system is some off its kinetic along with potential energy off all the particles that composed the system. The Indo no energy is this state function. The internal energy value depends on the state off the system. So we are given with the moss off billiard ball. So the mask is equal to 0.17 kilograms On the initial speed in issue will be 4.5 meters per second on the collision speed. Wait a minute on Dhe the collision speed will be 3.8. Medios was second so the expression for kind of taken Oh Gee, is he called who? Half m V square. The final energy off the system e do is equal to zero the initial energy off the system that this e one is equal to kind of take energy which is also equal to half every square. Substituting in the values we have half my deployed by 0.17 on velocities 4.5 square. We have even equals to hunt one point 72 kilogram meter square. Second square on even is equal to 1.72 Jules from that we can find the difference between an OD state that is e to minus. You won. Did you give this? Zero minus 1.72 gives us the difference off energy as negative one point seven. Tow Jules from the given condition, the believe ball loose some off its energy as a heat using K equals half empty square. We can deter mined the kind of take energy as 1.7 to Jules the ball involved in collision. Then we have mass and velocity again. The kind of take energy off the system can be determined as half empty square. This is the second kinetic energy which turns out to be 1.2 poodles. They are two difference between an energy levels which can be determined by formula Kato minus Okay, one that is kind of dick energy off second system minus the kinetic energy of the first system, which gives us the loss off energy as heat is equal to negative 0.5 jewels from the first law of thermodynamics. Voke done is equal to there's a guy in my nest heat bitches minus 1.7 to Jules minus 0.5 jewels. It gives us the vogue done as negative 1.2 jewels

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