Physics 100 Chapter 3

Physics 100A Chapter 3 • Vector Magnitude and Direction (All vectors have the same length) A) [\vec{D}{AB}] [\vec{b}{cw}] [\vec{b}_{BA}] None are equal to each other B) (\vec{D}{AB}) Equal to (\vec{D}{CD}^{\prime}) as seen above Adding and Subtracting Vectors A) (A_{x}=2) The maximum [B_{x}=-1] [C_{x}=2] [D_{x}=2] [E_{x}=-1] [C_{x}+B_{x}=2+2=4] [F_{x}=0] for B) (A_{y}=-3) [B_{y}=-2] The maximum occurs for [C_{y}=1] [D_{y}=1] [E_{y}=2] [E_{y}+F_{y}=2+3=5] [F_{y}=3] C) A and F have the largest magnitudes overall. Subtracted: R It can be seen by inspection that R is the largest vector possible. Vector addition ranking tutt \[i^{2}\] ご F \[\vec{a}+\vec{c}\] \[\vec{f}+\vec{c}\] \[\vec{a}+\vec{b}\] + order \[|\vec{a}+\vec{b}|=\sqrt{(2)^{2}+(z)^{2}}=2.8\] \[|\vec{a}+\vec{i}|=\sqrt{(2)^{2}+(2)^{2}}=2\cdot8\] \[|\vec{f}+\vec{c}|=\sqrt{2)^{2}+(i)^{2}}=2.2\] \[|\vec{i}|=2\] ② ① 4 \[\theta_{Aw}=+5^{-0}\] a \[{\sigma_{ac}}=0^{\circ}\] \[\theta_{*v}=3.60^{\prime\prime}-45^{\prime\prime}=315^{\circ}\] \[\sigma_{AE}=0^{\circ}\] resultant \[F_{FC}=90^{\circ}\] 74 OFC X \[\theta_{b}=90^{\circ}\] ہے 15 157 76 7 BAD 3.25) Each person gets a different set of values for the magnitudes. In all cases |A|=5 and |B|=10. I am using a) C=A+B Cx=Ax+Bx=0+10=10 Cy=Ay+By=-5+0=-5 |C|=C=sqrt((10)^2+(-5)^2)=11 Calculating: 6=tan()=63° Reporting: From the x-axis it is 23° below or simply with respect to the positive x-axis the angle is 27°+63°=33° b) C=A-B Cx=Ax-Bx=0-10=-10 Cy=Ay-By=-5-0=-5 |C|=11 as before Q=63° The angle with respect to the positive x-axis is 270°-63°=207° c) C=B-A Cx=Bx-Ax=10-0=10 Cy=By-Ay=0-(-5)=5 |C|=11 as before Q=tan^(-1)(5/10)=27° with respect to the positive x-axis From the x-axis it is 27° below or simply with respect to the positive x-axis the angle is 27°+63°=33° From Ike x-axis it is 27° below JO Simply with respect to the positive x-axis the angle is 27°+63°=33° 3. Picture the Problem: Compare the magnitudes of the components of the vectors depicted in the figure. Strategy: Concentrate on the value of the component of each vector. A vector that is oriented vertically in the diagram has an component of zero, whereas horizontal vectors have s components with large magnitudes, either positive (to the right) or negative (to the left) Solution: Note that the component of D is large and negative. The value of its component is therefore the smallest even though the magnitude of its a component is the largest. By comparing the values of the components of the vectors as drawn we can arrive at the ranking: D, C,