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(II) A vertical spring (ignore its mass), whose spring constant is 875 $\mathrm{N} / \mathrm{m}$ , is attached to a table and is compressed down by 0.160 $\mathrm{m} .$ (a) What upward speed can it give to a 0.380 -kg ball when released? (b) How high above its original position (spring compressed) will the ball fly?

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A) 7.47 $\mathrm{m} / \mathrm{s}$B) 3.01 $\mathrm{m}$

Physics 101 Mechanics

Chapter 8

Conservation of Energy

Work

Kinetic Energy

Potential Energy

Energy Conservation

Moment, Impulse, and Collisions

Hope College

University of Winnipeg

McMaster University

Lectures

04:05

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.

04:30

In classical mechanics, impulse is the integral of a force, F, over the time interval, t, for which it acts. In the case of a constant force, the resulting change in momentum is equal to the force itself, and the impulse is the change in momentum divided by the time during which the force acts. Impulse applied to an object produces an equivalent force to that of the object's mass multiplied by its velocity. In an inertial reference frame, an object that has no net force on it will continue at a constant velocity forever. In classical mechanics, the change in an object's motion, due to a force applied, is called its acceleration. The SI unit of measure for impulse is the newton second.

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so according to this problem is vertical spring is attached to a table. So we have. This is the level of the table here and attach a vertical spring to the table and there is a ball which is kept just in contact with that. It is not like your dash to the spring. So what is happening is that the spring is compressed and the ball comes in this location and when it is compressed, more likely happens is that the spring comes to the UN stress length. You know, our dislocation and the ball goes up in the air after goods here. So I liberated as one too, and three So it says that what upward speed can be given to a 0.380 kilogram both. So the mass this point three kilogram and board upward speed can be given, which means that we need to find out the value of the two at this location. So this is the problem here when released. So to solve this problem, what were you going to do is that in our system we have this whole system. We have the conservative forces acting so the energy is conserved So we're going to quit the energies at even at level one and level two at level one, the total energy of the object is half and the one squared place MG Y one. Let's half gay X one squared and, um, at level do the total energy is equals to have and V two squared less mg Why do less half gay extra square? So we're just considering all three energies at both the locations and then we'll see which energy is president. Address location So less first of all, See at level one which energies are present at this location here. So where dislocation as you can see clearly that the object is at rest. So in this equation here we have this one zero and sense no object is president from this level here for our simplicity we are going to take are zero g p at this level, which means at this level X equals zero and vice equal to zero. Now you can solve by taking this reference wanted any level but I prefer this way. So therefore at this location one we have the kinetic energy zero But there is a potential energy are dislocation. So therefore all right, mg. Why one note? It's negative. Let's have gay X one squared now for this location here. What level do the bullet just in the middle and it just about to release from the spring. So our dislocation, we'll have the kinetic energy half and Vito squared on. We'll have the potential energy also where dislocation as you can see, which is zero. Because this is our resumes dealer reference level and send the string is north stress. At this level, the elastic potential energy is also zero. So if you solve this equation and the rearrange, you know we're going to get an equation. We do use equals two. Okay, x one squared. Let's do MG y one divided by and just plug in the values in this equation, you know, and you'll be getting the answer of 7.47 meters per second. So which means the velocity is at this point is 7.47 meters per second, and then it stays for the part B that how high above its own personal position, spring is compressed when the ball will fly. So in this case, we liquid energies at even Andy three. So at e one, the total energy is half and even squared less mg y one. Let's have gay X one squared and at the third location and then had the number three location We'll have the energy is half and Vetri squared, less mg Valtteri less half okay, X three squared. So our location one we have already seen at this location the kinetic energy zero and we have the potential energies. Mg y one note. It's negative when you're planning and afterwards, and the Gnostic credential energies half g x one squared at the location. Three however there is, the ball is addressed to the highest point. There is no candidate. The ball will only have the G P E, which is empty 53 and the spring ist just a stressed. And that location there is no elastic pretension is in the system, which is zero. See if you saw that you will get vie to minors. Wire one is equals two k x one squared, divided by two mg. And if you plug in the equation and the values of X one, we just 0.16 meters and this is 8 75 and this is two times mass and gravity. You will get three point or one meters, and that is our answer for the be part.

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