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Problem 122 Hard Difficulty

The height of Niagara Falls on the American side is $51 \mathrm{m}$. (a) Calculate the potential energy of $1.0 \mathrm{g}$ of water at the top of the falls relative to the ground level. (b) What is the speed of the falling water if all of the potential energy is converted to kinetic energy? (c) What would be the increase in temperature of the water if all the kinetic energy were converted to heat? (See Problem 6.121 for suggestions.)

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Video Transcript

So this question has three parts. And for the first part we're supposed to find the potential energy of one gram of water top of Niagara Falls. So we know that in general, the expression for potential energy, it's just MGH. You know that the M is one gram, but this is not the correct unit there Correct unit that we want is kilogram and so but corrects it for us. We know that the height that's equal to 51 meters and in another G acceleration due to gravity is 9.8 meters per second squared. So when you multiply all of those things together, you get that. Your answer is approximately half a jewel. Part B Part B asks us for the speed of the falling water if all of the potential energy is converted into kinetic energy. So we know that the expression for Connecticut with you is 1/2 and he squared. And so we know that if all of the potential energy is converted to kinetic energy, that all of it will be like this and you can set that equality expressions. So then, from there we can solve it because we know the mass of the water as well. So we divide both sides by 0.1 The velocity is velocity squared is equal to 1000. And then from there you get that when you take the square root of both sides that one rounded to the once digit the velocity is 32 meters per second. The last part access for what? The increase in temperature the water be if all of the kinetic energy is converted to heat. So once again we know that in terms of jewels, that kinetic energy is 0.5 and we know that he can be expressed his mass times keep capacity, times change in temperature. And we know that the mass the water was your 0.1 kilograms. You know that the specific Matthew Water is for put money for Jules program over centigrade and then so all we have to do is simply divide by the mass and the specific heat capacity, and that will give us a change in temperature, which, if you put in your calculator, turns out to be 0.12 degrees Celsius and that is the final answer

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