Webwork and MasteringPhysics Homework Help: MasteringPhysics Hints and Tips (Sections 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8)

In vector notation the sum is represented by

$\vec{C}=\vec{A} + \vec{B}$ .

Addition using geometry

Which of the following procedures will add the vectors and ?

ANSWER:

Put the tail of $\vec{B}$ on the arrow of $\vec{A}$ ; $\vec{C}$ goes from the tail of $\vec{A}$ to the arrow of $\vec{B}$

Put the tail of $\vec{A}$ on the tail of $\vec{B}$ ; $\vec{C}$ goes from the arrow of $\vec{B}$ to the arrow of $\vec{A}$

Put the tail of $\vec{A}$ on the tail of $\vec{B}$ ; $\vec{C}$ goes from the arrow of $\vec{A}$ to the arrow of $\vec{B}$

Calculate the magnitude as the sum of the lengths and the direction as midway between $\vec{A}$ and $\vec{B}$ .

Correct

It is equally valid to put the tail of $\vec{A}$ on the arrow of $\vec{B}$ ; then $\vec{C}$ goes from the tail of $\vec{B}$ to the arrow of $\vec{A}$ .

Part B

Find , the length of , the sum of and .

Hint B.1 Law of cosines

Hint not displayed

Hint B.2 Interior and exterior angles

Hint not displayed

Express in terms of , , and angle , using radian measure for known angles.

ANSWER:

= $sqrt\left(A^{2}+B^{2}+2{\cdot}A{\cdot}B{\cdot}{\cos}\left(theta\right)\right)$
Correct

Part C

Find the angle that the vector makes with vector .

Hint C.1 Law of sines

Hint not displayed

Express in terms of and any of the quantities given in the problem introduction ( , , and/or ) as well as any necessary constants. Use radian measure for known angles. Use asin for arcsine

ANSWER:

= ${\asin}\left(\frac{\left({\sin}\left(pi-theta\right){\cdot}B\right)}{C}\right)$
Correct

Part D

To manipulate these vectors using vector components, we must first choose a coordinate system. In this case choosing means specifying the angle of the x axis. The y axis must be perpendicular to this and by convention is oriented $\pi/2$ radians counterclockwise from the x axis. Indicate whether the following statement is true or false:
There is only one unique coordinate system in which vector components can be added.

ANSWER:

true

false

Correct

Part E

The key point is that you are completely free to choose any coordinate system you want in which to manipulate the vectors. It is a matter of convenience only, and so you must consider which orientation will simplify finding the components of the given vectors and interpreting the results in that coordinate system to get the required answer. Considering these factors, and knowing that you are going to be required to find the length of and its angle with respect to , which of the following orientations simplifies the calculation the most?

ANSWER:

The x axis should be oriented along $\vec{A}$

The x axis should be oriented along $\vec{B}$

The x axis should be oriented along $\vec{C}$

Correct

Part F

Find the components of in the coordinate system shown.

Express your answer as an ordered pair: x component, y component ; in terms of and . Use radian measure for known angles.

ANSWER:

$B_x,B_y$ = $\left(B{\cdot}{\cos}\left(theta\right),B{\cdot}{\sin}\left(theta\right)\right)$

Part G

In the same coordinate system, what are the components of ?
Express your answer as an ordered pair separated by a comma. Give your answer in terms of variables defined in the introduction ( , , and ). Use radian measure for known angles.

ANSWER:
$\left(A+B{\cdot}{\cos}\left(theta\right),B{\cdot}{\sin}\left(theta\right)\right)$

Webwork and MasteringPhysics Homework Help

Sunday, January 30, 2011

MasteringPhysics Hints and Tips (Sections 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8)

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