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(II) Car A hits car $\mathrm{B}$ (initially at rest and of equal mass) from behind while going 35 $\mathrm{m} / \mathrm{s} .$ Immediately after the collision, car $\mathrm{B}$ moves forward at 25 $\mathrm{m} / \mathrm{s}$ and car $\mathrm{A}$ is at rest. What fraction of the initial kinetic energy is lost in the collision?

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0.49

Physics 101 Mechanics

Chapter 9

Linear Momentum

Motion Along a Straight Line

Kinetic Energy

Potential Energy

Energy Conservation

Moment, Impulse, and Collisions

University of Washington

Simon Fraser University

Hope College

University of Winnipeg

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right. So, um, very simply, we're not even gonna do anything like Memento of energy conservation. All we want this fraction of Katie that is lost. So faction lost will be the change in kinetic energy from initial the final. So how you gonna do initially? Minors cannot manage final connect energy over initial connect Cannady times 100% on. So this would be, uh, 1/2 times. Ah m a massive, eh? Times V A squared minus 1/2 and beauty. Massive beauty times V b prime squared The velocity which be starts moving afterwards. And initially you have 1/2 may tons via squared times 100% on. So, uh, m a is equal to m being raped. Uh, so you have 1/2 times mass. Let's take that common times V A squared minus B b prime squared over 1/2 em, Uh, times the a square. And so the 1/2 and factor cancels out. This is what you're multiplying by 100%. And so, uh, you have V A, which is 35 meters per second quantity squared. Okay, let's go to the the next page here. Out of here on dso fraction F is, uh, V A, which is 35 meters per second, quietly squared minus B B, which is 25 years per second. Quantity squared over, um V a squared 35 meters per second quantity squared, um, and so that's equal to 0.49 and that's it.

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