While painting the top of an antenna 225 m in height, a worker accidentally lets a 1.00-L water bottle fall from his lunchbox. The bottle lands in some bushes at ground level and does not break. If a quantity of heat equal to the magnitude of the change in mechanical energy of the water goes into the water, what is its increase in temperature?

Video transcript

Welcome back everybody. We have an iron ball that is being released from the top of a building. So let me go ahead and draw our building here. We are told that it is released from a height that is 48 m off the ground and we are told that the mass of the ball is two kg. Now, when this ball hits the ground, it's actually going to stay intact with the ground, it's not going to bounce up at all. So we are tasked with finding if all of the mechanical energy is converted to heat energy, we need to determine the change in temperature or the rise in temperature of the ball. So this formula that I wrote down right here says that the mechanical energy or the kinetic plus potential energy is equal to our heat. Now we have formulas for all this. So let me just go ahead and plug in the formulas here, we have one half mv V squared is our kinetic energy plus MG H. Is our potential energy equals our heat, which is M. M. C. Which specific heat of iron times our delta T. Now we want to figure out this delta T term. So I'm going to divide both sides by M. C. You'll see that on the right hand side here, M. C cancels out and the M. In every single term cancels out over here. So we are left with delta T. Is equal to one half times V squared plus G H. All over. See, let's go ahead and plug in some values here. What is going to be our B in this case, what we are told that the ball is released from the top meaning it starts at rest so our initial velocity is just going to be zero, making this entire term zero and go away. Now we are adding a potential energy to this. So we have our acceleration due to gravity, which is 9.8 times our height of 48 m. Now this is all going to be divided by the specific heat of iron, which is 450 jewels per kilogram Celsius. When we plug all of this in your calculator, we get that. The rise in temperature of the ball is one point oh five degrees Celsius, which corresponds to answer choice. C. Thank you all so much for watching. Hope this video helped. We will see you all in the next one.