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$\bullet$ Changing mass. A railroad hopper car filled with sand is rolling with an initial speed of 15.0 $\mathrm{m} / \mathrm{s}$ on straight, horizontal tracks. You can ignore frictional forces on the railroad car. The total mass of the car plus sand is $85,000 \mathrm{kg} .$ The hopper door is not fully closed so sand leaks out the bottom. After 20 min, $13,000 \mathrm{kg}$ of sand has leaked out. Then what is the speed of the railroad car? (Compare your analysis with that used to solve Problem $16 .$ )

15 $\mathrm{m} / \mathrm{s}$

Physics 101 Mechanics

Chapter 8

Momentum

Physics Basics

Kinetic Energy

Potential Energy

Energy Conservation

Moment, Impulse, and Collisions

Cornell University

University of Washington

Hope College

McMaster University

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once again our welcome to new problem. Uh, this time we're dealing with physics, and in physics, we have Newton's laws. Eso Isaac Newton was a famous physicist, and he solved ah, lot off problems and physics using algebra and calculus. And Newton's first Law states that, ah, body but rest remains addressed or a body moving with uniforms. Motion continues to move with uniform motion unless compelled, uh, by external forces on their Newton's second law. Simply say's that force is the product off mass times acceleration, and you can extend that to mass times defining explorations. Final velocity minus initial velocity all over time. So forced times time equals two. Uh, and the final and the note. This value is called the Impulse. It's called the Impulse Off the Force, and it's a measure off. The change in momentum whereby I am the final is the final momentum, and M V note is the initial mo mentum. Um mo Mentum is the product of mass times velocity. That's just what momentum is. It's the product of most times velocity, and it does happen to be, uh, and the final envy initial. So we do have a problem and These are railroad problems. Uh, so we have a railroad hope. We have a railroad khokha, and obviously it's gonna have some opening somewhere. And all of this is just sand. This is sand on a theme. The it's filled with sand. The initial speed we not, um, is 15 leaders a second, and this is how it's rolling on the trucks and this surface. The friction on this surface zero on the friction is zero. Both the kinetic friction and static friction. So this surfaces frictionless, frictionless office, uh, the total musk off the sand, plus the mask off the car. Mm hmm. Is the same Azaz 85,000 kilograms. And so assume we have, Ah, a door that's not fully closed. So, you know, this is, like, a look an opening right here. So it's not fully closed, and then the sun starts to leak. So the sun is leaking, and after a time off, 10 minutes at the time of 10 minutes, we've lost Mm. Must off. Sand lost is equivalent to 13,000 Philip mumps. So here's the question. The question is, if that's the case Mm. If that's the case, we wanted to time in, uh, the speed off. The hope wanted to time in the speed. So we love them right here. So we'll say determine determined thing, speed. Mm. Off the This is not 10 minutes, but this is 20 minutes. It's time in this speed off the railroad. Cool. So this is what happens Are the surface is frictionless with no external forces, therefore, to move out constant velocity 15 m per second. Uh, railroad cool does not require any external forces. Well, this was standing forces does not require instead of saying does not require any external forces that does not require any push. Oh, cool. Um and so in that sense was saying Newton's first law oh, stands was valid on since there on no external forces acting on the system through the resultant false on the system is zero. The result and force on the system is zero. So if you think about the impulse, FD equals two m v final minus m v initial. This is the final momentum minus initial momentum. Uh, if f zero, that means that the change in momentum is also zero. So the final momentum is equal to the initial momentum and Mm. Since the masses. Mm, the mosque. This this would be the mosque before I would say that the total moss hmm, since the would say, since since the moss off the system. Alright, since the total most of the system on before was actually we don't even have to use the Newton's second law just by Newton's first law just by Newton's fastball. We can, uh, hypothesize. But all right, I can hypothesize that. Bye. Hughton's first Lou the Smart, you know velocity is the same. How is the initial velocity outs? 15 m per second? Because, hmm, the body is moving but constant speed on a frictionless surface with no external interference. If there's external interference, then we're gonna go into Newton's second law. So once again, we had a problem, and in this problem we had a railroad car with 85,000 kg of weight and in 20 minutes it's losing 13,000 kg. But we want to find out the speed after these losses. It just so happens that we don't have any external forces based on Newton's first of all, and therefore the velocity will stay constant since we don't have external interference. But 15 m per second. Hope you enjoy the problem. Feel free to send any questions or comments and have a wonderful day.

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