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(a) If a volcano spews a $450-\mathrm{kg}$ rock vertically upward a distance of $320 \mathrm{m},$ what was its velocity when it left the volcano? $(b)$ If the volcano spews 1000 rocks of this size every minute, estimate its power output.

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A) 79 $\mathrm{m} / \mathrm{s}$B) $2.4 \times 10^{7} W$

Physics 101 Mechanics

Chapter 8

Conservation of Energy

Work

Kinetic Energy

Potential Energy

Energy Conservation

Moment, Impulse, and Collisions

Rutgers, The State University of New Jersey

University of Washington

McMaster University

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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 in this case we have a wall. Kano, which is spewing rocks vertically, upwards from the mountain and the rocks are like going upwards and rises vertically upwards a distance off 3 20 meters. And we need to find words the velocity when it left the volcano. Which means that this location so again we have a level one and level two and we can equate the energies of these two locations even as equals to you too. Because they're only conservative forces acting on the system. And we have I want is equal to zero. And why do ISS equals two, 320 meters? It required the energies of these provocations. You will get half M V. One squared is equals two mg. Why too? Because a dislocation that is no GP and a dislocation that is no kinetic energy. If you saw that he will get everyone squared is equals to two g. Why do V one is equals to approximately 79 meters per second? The volcano spews out of rocks that achieves the height of 3 20 meters for the beep are going to calculate the power output and the part output is the energy transferred to the loans rocks per unit. Time, basically so far is equals. Two. The energy transferred, the energy transferred for unit time. So the launching off energy of a single rock for one drug, the energy is half and even squared. So for 1000 rocks it's going to be 1000 times half M V. One squared. And if you divide this by one minute, you should get the par. So, therefore, the answer is 1000 times half times for 50 time, 79.2 divided by 60 seconds. That should give you 2.4 times 10 to the par off seven. What's so? That's the power output?

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