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An ice cube (ha: I5 cm on each side meltingFate 01 cr" per Minute How fast Ine lengtri of Lhe sidv ducteasing?AtIhe moment wnen tne Ico cube cm on cach side ...

Question

An ice cube (ha: I5 cm on each side meltingFate 01 cr" per Minute How fast Ine lengtri of Lhe sidv ducteasing?AtIhe moment wnen tne Ico cube cm on cach side tne sid8 length decreasing (Type an integer = Dacimal rounded three decimal places naededrate of approximatelyEM per minure:

An ice cube (ha: I5 cm on each side melting Fate 01 cr" per Minute How fast Ine lengtri of Lhe sidv ducteasing? AtIhe moment wnen tne Ico cube cm on cach side tne sid8 length decreasing (Type an integer = Dacimal rounded three decimal places naeded rate of approximately EM per minure:



Answers

Ice Cube An ice cube that is 3 $\mathrm{cm}$ on each side is melting at a rate of 2 $\mathrm{cm}^{3}$ per min. How fast is the length of the side decreasing?

Here. I have an ice cube. It isn't. The shape of a perfect cubit is not a rectangular prism. It is a cube. Okay? And it is melting at the rate of two centimeters cube per minute. So that means DVD T is equal to negative two, right? What we want to know is, at what rate is the length of the side changing when this length of that side is three. So we need the formula for the volume of a cube, and that's B equals X to the third power. We're gonna take the derivative we have DVD t equals three s squared de S DT, and we're going to substitute in now what we know. Well, DVD t is negative. Two s is three and we're solving for de s DT. Okay, so negative two is gonna be evil to will. Three times 33 squared is nine times three is 27. I'm gonna divide out the 27 so I'm gonna get negative to over 27. So are the side of our ice cube is decreasing at a rate off negative to 27th centimeter for a minute decimal form. That would be 0.74 centimetres per minute

So here the heat required to melt the ice. Um It would be the mass of the ice times the latent heat of fusion, the masses equaling to the density times the volume. Sochi would then be equaling two roe V. House of F. We know that the rate of heat transfer from the rod to the water. P. Would be equaling the thermal conductivity times A. The area times T CFC minus T. Sub. I to find good bye. L. Leading here the fusion. All right brother. My apologies the length. So no subscript. Um And at this point we can say that T. C. F. C. Is the temperature of copper minus the initial temperature of the ice. The timer required to melt the ice cube. Yeah, nobody cares. T would be equaling two Q over P the power. And so substituting this in, we have the time T would be equal. And then roe v L C F divided by K A T sub c minus T. So I all divided by L. And this is giving us then row the else of F L. Divided by k a t c f c minus T. Initial. So the time to melt the ice tea with the equaling the density of 9 17 kg per cubic meter Times The volume of 10 Times 10 to the negative 3rd cubic meters. Multiplied by 334 times 10 to the third jewels per kilogram, multiplied by point 20 m. This would all be divided by the thermal connectivity of copper, 386 watts per meter per Calvin, Multiplied by .1 m2, Multiplied by 363 Calvin minus 2 73 Calvin. And the time is then calculated to be 17.6 seconds. That is the end of the solution. Thank you for

We have to determine the time taken to melting the eyes. Okay, so we know that that time the heat required to make the heat uh met the Q. Q. It will be equals to mass molecular by latent heat of fusion. So mass can be bitterness density, molecular volume molecular by latent heat of fusion. This value. Okay so now the rate of heat transfer to the roar, it will be equal to P. That is equal to K. A temperature of the water, manage temperature of liquid. Ah They were by L. And it will be equal to cuba time T. Okay, so substituting values here so we will get time. T. It will be equal to Q muscular by L. They were by K. A. T. W minus T. I. Okay so from here we get from here after solving value of Q. We can substitute this value. So we get raw density molecular bait volume molecular by latent heat of fusion. Latent heat of fusion molecular by L. They were by thermal conductivity. A thermal conductivity came particular molecular BtW minus t initial temperature. Okay so from here after solving we get substituting values in this equation. So we get time to equal student city which is 917 program per meter cube and volume which is one into 10. To the power minus three m cube. And late into heat of fusion is 3 34 into 10 to the power three jewel per Casey and length. L, which is 0.2 double zero m developed by thermal conductivity of the cooper block. It will be equals to 3 94 per meter. Kelvin replied by area this will be 0.1 double zero m. Holy square and temperature difference which is 90 C minus zero C. Okay so from here after solving we get tempt equals to 1 74.5 seconds, which is nearly equals two 1/75. Okay so this is the answer for this question. Okay

Okay, So we have this small ice cube in this hemispherical bowl, a radius art. And we want to know what the speed of the ice cube will be when it reaches the bottom. And so for this we can use conservation of energy because we release it won't have any kinetic energy. We all potential. And once it reaches the bottom it will have used up all its potential energy and will only have kinetic. So the potential energy from its gravitational position, it's going to be energy H. In this case this height here is the same as the radius in the bowl. So it's MGr and then it's kinetic energy. Once it reaches the bottom is one half mv squared or the the masses are going to cancel out here. We divide both sides by M. And then if we solve this for V. Multiply through by two and divide are sorry and then take the square root. We're going to get V. Is equal to the square root of two times. Gr If we plug in, our values will get uh answer of 2.15 m/s.


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