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(II) Show that if two nonparallel vectors have the same magnitude, their sum must be perpendicular to their difference.

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$A_{x}^{2}-B_{x}^{2}+A_{y}^{2}-B_{y}^{2}+A_{z}^{2}-B_{z}^{2}=\left(A_{x}^{2}+A_{y}^{2}+A_{z}^{2}\right)-\left(B_{x}^{2}+B_{y}^{2}+B_{z}^{2}\right)=0$

Physics 101 Mechanics

Chapter 7

Work and Energy

Work

Kinetic Energy

Potential Energy

Energy Conservation

Charles W.

October 13, 2020

If the hill in Example 7-2 (Fig. 7-4) was not an even slope but rather an irregular curve as in Fig. 7-23, show that the same result would be obtained as in Example 7-2: namely, that the work done by gravity depends only on the height of the hill and not

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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.

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.

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Show that if two nonparal…

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Prove that two vectors mus…

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Show that each pair of vec…

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In order to show that two …

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The sum of two vectors, $\…

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01:07

So they're saying if the graph of thie magnitude of a equals the magnitude of B and so we know that a X squared plus B plus a y squared plus a sub z squared equals piece of X squared plus it Piece of war I squared plus piece of z squared. If that relationship is true, which is given, we can find the doc product between the some of them and the difference of them. Now we can find the sum of these vectors. This would simply be equal. Teo ace of expose piece of X. I had plus a sub. Why, plus beasts of why Jay hadn't close a subsidy close. Be subsea. Okay. Ah, vector A minus factor be would be the exact same thing Accepted will be the difference of a mix A ace of X minus bisa Becks I had plus ace of y minus B supply Jay had plus a sub z minus be subsea K hat. So at this point, we can solve for the dark products. We can say that Ah, the dark product a factor plus the vector the dock party Between the sum and difference, it is going to be equal tio a X plus bx times X minus B x and then plus a right plus B. Why time's a wine? Linus, do you? Hi! Plus a subzero plus B C C Time's a sub z minus b subsea. And so we know that this is going to be equal to a X squared minus B x squared plus a Why squared minus b Why squared plus a Z squared minus B z squared. And we can say that this is going to be equal to a X square plus a lie squared close a sub z squared minus bce of X squared plus piece of y squared plus B subsea squared. And because these are both equal to each other, this legal zero. So that's how we prove that that is the end of the solution. Thank you for watching

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