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Problem 150 Hard Difficulty

The fastest serve in tennis is about 150 mph. Can the kinetic energy of a tennis ball traveling at this speed be sufficient to heat $1 \mathrm{mL}$ of water by $30^{\circ} \mathrm{C} ?$

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Video Transcript

So this question asked us whether or not a serve tennis ball can provide the energy needed to heat a milliliters of water by 30 degrees Celsius. So the first step that we have to do is you have to actually find the kinetic energy of the tennis ball when it's moving. At that velocity on the kinetic energy is 1/2 M V squared, so we know the mass of a tennis ball. If you google it, it's around your point 056 kilograms, and we know the velocity 150 MPH. But this isn't a very useful unit for us because it's not in S I units, and so it will not get us jewels, which is the form or the unit of energy, that we want this. And so we need to convert this. So in 150 miles through an hour, so we know the s signing for time in seconds. We can do that pretty easily and such, and the last thing that we need to do is now that we've converted hours, two seconds, we need to convert miles two meters and you know that every one mile there is 1609 meters. So this will cancel all over units and get us meters per second, which is the S I unit for velocity. When you plug that in, you'll get it of lost e 67 meters per second. So now we could find the kinetic energy by plugging this all into the calculator and you will get that the answer will be around 125.7 jewels. So that's a kinetic energy of a tennis ball. Now we need to find how much he is required to raise the temperature of a middle leader of water by third degree. So we know that Q in this case will equal the mass of the water times. It's specific heat capacity, times change in temperature. Well, we know that it's a middle liter of water, and we know that because the density of water is one that one middle liter is equal to one gram, so mass is one gram. We know that the specific heat capacity four point wanted for Jules programmed 10 degrees Celsius, and we know that the change of temperature is going to be 30 degrees, as in the key. That's a problem and running play all of that into the calculator. We get 125 0.5 jewels. So obviously these numbers are very similar. And you find that, yes, the kinetic energy from a tennis ball is sufficient because 125.7 is greater than 125.5 very close, but it does provide enough energy.

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