Chapter 3: Q. 18 (page 78)

Let $\vec{B} = (5.0 m, 30^{\circ} c o u n t e r c l o c k w i s e f r o m v e r t i c a l) .$ Find the $x a n d y$ -components of localid="1651138630094" $\vec{B}$ in each of the two coordinate systems shown in FIGURE EX3.18.

Short Answer

Expert verified

(a) $\vec{B} = (- 2.5 m) \hat{i} + (4.3 m) \hat{j} .$

(b) $\vec{B} = (0 m) \hat{i} + (5 m) \hat{j} .$

Step by step solution

Part (a) Step 1. Given information

The given figure is,

and $\vec{B} = (5.0 m, 30^{\circ} c o u n t e r c l o c k w i s e f r o m v e r t i c a l) .$ We need to determine the $x$ and $y$ components of $\vec{B}$ in coordinate shown in the figure.

Step 2. Solution

The vector $\vec{B} = (5.0 m, 30^{\circ} c o u n t e r c l o c k w i s e f r o m v e r t i c a l)$ falls into the second quadrant with the magnitude of $5 m .$

$\vec{B_{x}} = \vec{B} \sin ϕ .$

$B_{x} = 5 \times \sin 30^{\circ} .$

$= 5 \times \frac{1}{2} = - 2.5 m .$

role="math" localid="1649274344760" $\vec{B_{y}} = \vec{B} \cos ϕ .$

$= 5 \times \cos 30^{\circ} .$

$= 5 \times \frac{\sqrt{3}}{2} .$

$= (4.3 m) \hat{j} .$

$\vec{B} = (- 2.5 m) \hat{i} + (4.3 m) \hat{j} .$

Part (b) Step 1. Given information

The given figure is,

and $\vec{B} = (5.0 m, 30^{\circ} c o u n t e r c l o c k w i s e f r o m v e r t i c a l) .$ We need to determine the $x a n d y$ components of $\vec{B}$ in the coordinate system.

Step 2. Solution

The vector $\vec{B} = (5.0 m, 30^{\circ} c o u n t e r c l o c k w i s e f r o m v e r t i c a l) .$ The $x a n d y$ axis are rotated $30^{\circ} . \vec{B}$ perfectly lies in the $y$ -axis.

$ϕ = 0^{\circ} .$

$\vec{B_{x}} = \vec{B} \sin ϕ .$

$= 5 m \times \sin (0^{\circ}) .$

$= (0 m) \hat{i} .$

$\vec{B_{y}} = \vec{B} \cos ϕ .$

$= 5 \times 1 .$

$= (5 m) \hat{j} .$

$\vec{B} = (0 m) \hat{i} + (5 m) \hat{j} .$

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Let $\vec{B} = (5.0 m, 30^{\circ} c o u n t e r c l o c k w i s e f r o m v e r t i c a l) .$ Find the $x a n d y$ -components of localid="1651138630094" $\vec{B}$ in each of the two coordinate systems shown in FIGURE EX3.18.

Short Answer

Step by step solution

Part (a) Step 1. Given information

Step 2. Solution

Part (b) Step 1. Given information

Step 2. Solution

One App. One Place for Learning.

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Let B→=5.0m,30∘counterclockwisefromvertical.Find the xandy-components of localid="1651138630094" B→in each of the two coordinate systems shown in FIGURE EX3.18.

Short Answer

Step by step solution

Part (a) Step 1. Given information

Step 2. Solution

Part (b) Step 1. Given information

Step 2. Solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Classical Mechanics

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Study anywhere. Anytime. Across all devices.

Let $\vec{B} = (5.0 m, 30^{\circ} c o u n t e r c l o c k w i s e f r o m v e r t i c a l) .$ Find the $x a n d y$ -components of localid="1651138630094" $\vec{B}$ in each of the two coordinate systems shown in FIGURE EX3.18.