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(II) An object at rest is suddenly broken apart into two fragments by an explosion. One fragment acquires twice the kinetic energy of the other. What is the ratio of their masses?

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$\frac{1}{2}$

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 Michigan - Ann Arbor

Simon Fraser University

University of Sheffield

Lectures

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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.

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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.

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because very instructor nine problem 50 says an object at rest is suddenly broken apart into two fragments by in this boat, one fragment requires twice the kinetic energy of the other. What is the ratio of their masses? Look So the important concept years momentum is concerned and says that initially everything's at rest. Okay, so the initial momentum here is committed to the room and we can now just say or less Let A and B represented two fragments of our our on the object. You and we can write the final moment, Um, as the sum of these fragments numbers. So that's in a V A plus in the B B. Okay, so from this but some more, babe me, we do that. We see this is negative and a the over awesome. So with this in mind, we can now look at how they're kinetic Energies are related because they should tell us that one of them has a larger connect committed in the other. So say kinetic energy of a equals C Times critic of D. So now let's write beats by Hughes, but Connecticut. So this is one have in a be a square miss equals to come one perhaps that cancels out. And b baby squid Okay, in here for trying to find the ratio in their masses, we can you just divine they. So if we want to find the ratio in their masses that could be in a over and be in Italy rearranged this equation right here we bring the two over divide by the Hayes. This is too V v squared over the square. And now let's plug in what v b squared this. So this is too in a squared Be a square over he a squared in the square You can sew these cancel and we're left with in a over in times in the squared over in any squared equals two and miss implies if he canceled things out in a over m B equals 1/2. That's the ratio of their masses we wanted to find in the first place. Cool. So it's a little bit out of tricks here, but overall pretty simple. Just apply conservation of momentum and just ride out the equations for kinetic energy with the relations that were given awesome

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