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(II) $\mathrm{A} 28$ -g rifle bullet traveling 210 $\mathrm{m} / \mathrm{s}$ buries itself in a 3.6 $\mathrm{-kg}$ pendulum hanging on a 2.8 -long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulum's maximum displacement.

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0.86 $\mathrm{m}$

Physics 101 Mechanics

Chapter 9

Linear Momentum

Motion Along a Straight Line

Kinetic Energy

Potential Energy

Energy Conservation

Moment, Impulse, and Collisions

Rutgers, The State University of New Jersey

University of Washington

University of Winnipeg

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.

03:47

In physics, the kinetic energy of an object is the energy which it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. The same amount of work is done by the body in decelerating from its current speed to a state of rest. The kinetic energy of a rotating object is the sum of the kinetic energies of the object's parts.

08:27

(II) A 28-g rifle bullet t…

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06:59

(II) A 28 -g rifle bullet …

03:11

A pendulum consists of two…

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(II) A pendulum consists o…

08:31

A Ballistic Pendulum. A 12…

01:30

An $8.0 \mathrm{g}$ bullet…

09:10

A 12.0 -g rifle bullet is …

04:48

A $12.0 \mathrm{~g}$ rifle…

01:42

A ballistic pendulum consi…

07:22

A 12.0-g rifle bullet is f…

05:09

As shown in Figure $\mathr…

02:18

will be using the results of example 11 which says that the velocity and for the pendulum will be, um, small M plus Bigham over M over small. I'm times two times two times height on DSO height is what we're interested in here we have all the other quantities. So h is just rearranging this equation. Taking the square both sides h is just envy over m plus big m squared times one over to she. And so it's plugging those values here, uh, 28 grams, which is m is 1 28 280.0 to 8 kilograms. V is to 10 meters per second over 100.0 to a plus point plus 3.6 kilograms. Um ah, quantity squared times one over two times 9.8 meters per second sweat. All right, so the height comes out to be 0.13 meters. That's the height to which the pendulum swings from its initial position. So let me draw out the scenario for what we have so far right now. Okay, So we, um Here's, um here's, uh here's where the pendulum swings from and so this is the entire length of the pendulum l It swings up to hear this. So this is also l me just raise this part to make it look more even. So that's also that's also l. And so it swings up to, uh, swings up to there on dso This love, it's not to scale, but the idea is that this whole thing is l on this part here, uh, going over there is l minus h. And so this little bit here from the, uh from the point the highest point which the pendulum swings to the original length of the pendulum. This is H Okay, so that is l minus h. So this is our minus h. This is what we want. Denoting back by green s O. This is l minus age. This is Elle. And this way Here. This right here is X. So that's the horizontal Ah, position we want. Okay, so, x, therefore Or rather, let's just do, um there's just solve Pythagoras, the protagonist. The room here used to protect a student here. L squared. The high Patna square is a horizontal square x squared plus vertical square. Vertical is l minus h squared. Therefore, X squared is just l squared minus l minus h squared. Um And so, uh or rather the square will come out here. But X is just the square. It's just the square root of that, right? So access square root of minus minus h quantity squared. And l, as we know, is 2.8 meters squid that squared minus 2.8, minus 0.1413 meters of as we just found, uh, quantity square. That was the whole point of finding each year s so that we could put that in there. On DSO the answer comes out to me 0.0.86 meters or 86 centimeters for a horizontal displacement.

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