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$\bullet$ The speed of hailstones. Although the altitude may varyconsiderably, hailstones sometimes originate around 500 $\mathrm{m}$(about 1500 $\mathrm{ft} )$ above the ground. (a) Neglecting air drag, howfast will these hailstones be moving when they reach theground, assuming that they started from rest? Express youranswer in $\mathrm{m} / \mathrm{s}$ and in mph. (b) From your own experience, arehailstones actually falling that fast when they reach theground? Why not? What has happened to most of the initialpotential energy?

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a) 221 $\mathrm{mph}$b) The hailstone's formation and fall is usually hindered during a thunderstorm as a result of the thunderstorm's updraft and collisions with other hailstones or water droplets. This slows the hailstone's fall.

Physics 101 Mechanics

Chapter 7

Work and Energ

Physics Basics

Applying Newton's Laws

Kinetic Energy

Potential Energy

Energy Conservation

Rutgers, The State University of New Jersey

University of Winnipeg

McMaster University

Lectures

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In physics, a conservative force is a force that is path-independent, meaning that the total work done along any path in the field is the same. In other words, the work is independent of the path taken. The only force considered in classical physics to be conservative is gravitation.

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so since the house hailstone is 500 meters above ground. So let's say this is our ground on DH. We call it if we market F as the final position of the headstone, and that's saying his Tony's around here and we mark the point is I which is just so you know that it's the initial position, and the distance between ground to the headstone is 500 meters. Now. If we use the energy conservation equation here, we see that at this point, the whole image is that at this point should be called that old energy a tte that point when the hailstone reaches. So let's see, let's say the headstone is now here, so that whole energy around here should be, well, do that old energy around here When the hell stone was 500 meters about the ground. Let's write that formally, so we'll have the kind of energy at point I plus differential energy a point. I should be equal to the kind of energy and the final point, plus the potential energy on defining point. So one more notation that we introduce here is let's say the position over here is why f and the position over here is why I just do not that that's the initial position and that's the final position. So if we say so, then a defining position. We see that this is if if if we said the origin around here and go towards up on said a poor direction as our y axis and said this where's our exact is although we don't need exactly so if we just consider that this is our origin, then we can set why f 20 and why I would be the height are the distance from ground toe, the hailstones. Let's call it eight. Now One more thing that we have to set here is the velocity. So when the hailstone reaches the ground, there will be some form of velocity. And let's call that the F just ridin on the final velocity. Initially, the velocity will be zero because at this point, the hailstone is us static and then it starts free, falling to the ground due to the gravity. So here then, if we call it the initial, the initial point will be zero, right? So if we write, combine all those together another we see that First of all, we know that kind of energy is nothing about half times and be squared, and potential energy is m times, G times height. So are, let's say, the final position of the initial position, minus the final position. So if we combine all this together, first of all, we see that the kind of energy at point I will be zero because, as we mentioned that, the zero there. So if he's, you know at this find there's no point off keeping the kinetic energy over here. But the potential energy will be see right for the final point because, as we mentioned that, why F is considered a zero. So if we use md, um, nd times why f at this point since y f zero. So this part become zero now. So actually, let's write that mg y to avoid confusion. So mg y means that the potential energy at a certain point So when it's in the final position, then this time goes away so we can ignore the potential energy part. So now we have the potential energy at this point is equal to the Canary Energy at the final points we can write that down. And since we say that the political the distance from here to here is a JJ or, in other words, why I is equal to eight so we can write m times g times age That's that being called toe half em um, the finest cleared right? And we can get it off the ends of both sides on then the final should be called do square of price gh We know that G is 9.8 meters per seconds squared and ages 500 meters. So let's move the calculation to next page. So these 9.8 meters per seconds squared and height is 500 meters. Using that, you see, the final velocity is 99 meters per second are in miles. It's 2 20 miles for are so as you can see, that's a huge speed and ah, that can hurt anyone. No. So that's why but technically you and we see his song Hail Stones. They're not that Ah, they don't have that much speed. And one of the most important reasons is that this in the first. But we actually ignored the air direct. But there is indeed a lot off air drag. Well, the hell stone is dropping down to the ground. So most of their initial potential energy is converted to a thermal energy due to that it. So the potential energy has been converted toe thermal energy. Um, you do and drag. So that's why you know, the speed reduces significantly. Thank you.

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