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A 0.800-kg ornament is hanging by a 1.50-m wire when the ornament is suddenly hit by a 0.200-kg missile traveling horizontally at 12.0 m/s. The missile embeds itself in the ornament during the collision. What is the tension in the wire immediately after the collision?

$13.6 \mathrm{N}$

Physics 101 Mechanics

Chapter 8

Momentum, Impulse, and Collisions

Section 3

Momentum Conservation and Collisions

Moment, Impulse, and Collisions

University of Michigan - Ann Arbor

Simon Fraser University

Hope College

University of Winnipeg

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problem. 8.45. We've got a ornament hanging off of a wire and a missile of some sort approaches it with the given speed and ah, embeds in it. And what we want find is what is the tension in this wire immediately after this impact occurs? So this is going to combine what we know about mo mentum with what we know about circular motion, because the ornament yeah, it's going to start moving along a circular art. And so there has to be some centripetal acceleration on the ornament that comes through the tension in the wire. So before getting to that, we even know how fast it's going because we're going to use that this a trip. It'll acceleration this v squared over R. So we would like to know what he is, and we'll call the speed of the bullet a missile. It's called bullets. We don't have too many m's. The Be even will call the speed of both combined after the impact. Just just be m o for ornament feet. So we find the speed of the ornament missile together immediately after the impact is going to be the ratio of the mass of the bullet to the total mass times the initial speed of the bullet. And this is 4.5 meters per second after. Consider um, a free body diagram for for the ornament going to have attention in the wire acting upwards and the weight of the ornament acting downwards. And so the sum of the vertical forces you call that say the tension is directed in the positive wide direction is going to be the tension. And since we have both the ornament and the bullet moving together, both of their masses contribute to the wave. And so this forms the centripetal acceleration. There's some. Is this in trip? It'll forces minus w here. Yeah, excuse because we need the mass of the bulletin ornament to make a force instead of instead of Justin acceleration and then are, of course, is just length of wire that the ornament is suspended from. And so the tension in the wire is going to be the mass of the ornament and bullet. I've done that again. I start reading be its toe and B Okay, they have a free spirit over our the centripetal acceleration, plus the acceleration due to gravity and then putting all of these numbers in, we find that our attention is 186 Newtons.

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