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(I) Show that $$\vec { \mathbf { A } } \cdot ( - \vec { \mathbf { B } } ) = - \vec { \mathbf { A } } \cdot \vec { \mathbf { B } }$$

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$\overrightarrow{\mathbf{A}} \cdot \overrightarrow{\mathbf{B}}$

Physics 101 Mechanics

Chapter 7

Work and Energy

Work

Kinetic Energy

Potential Energy

Energy Conservation

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

University of Washington

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.

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Show that $\mathbf{u}=\matβ¦

04:57

00:54

$$\text { Prove that } \maβ¦

02:13

$$\text { Show that } \matβ¦

01:17

Show that $\left(\mathbf{Aβ¦

7.19. So you want to show that the dot product of a negative B is equal just the negative of the dot product of A and B. So if we assume that A and B can be written as having, you know, components a X b b x, a white B y et cetera, then they're not Product is going to be X times negative B X plus a Y times negative B y plus, um ese times negative. Easy. Now we see that these are all just real numbers multiplied together. We can factor negative one out of the entire thing. So we know this is the dot product of A and B. Okay, so then this expression is the negative of that.

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