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Chapter 1, Problem 52P

(a)

To determine

The components of E in unit vector notation directed along positive x axis.

(a)

Expert Solution
Check Mark

Answer to Problem 52P

The components of E in unit vector notation directed along positive x axis is E=(15.1i^+7.72j^)cm.

Explanation of Solution

The figure 1 shows the vector notation of the following magnitudes.

Bundle: Principles of Physics: A Calculus-Based Text, 5th + WebAssign Printed Access Card for Serway/Jewett's Principles of Physics: A Calculus-Based Text, 5th Edition, Multi-Term, Chapter 1, Problem 52P

Write the expression for the vectors E along x axis.

  E=E1cosθi^+E1sinθj^        (I)

Here, E is the vector along x axis, θ is the direction of the vector, and E1 is the vector component along x axis and y axis.

Conclusion:

Substitute 17.0cm for E1 and 27.0° for θ in the equation (I) to find E.

  E=(17.0cm)cos(27.0°)i^+(17.0cm)sin(27.0°)j^=(15.1i^+7.72j^)cm

Therefore, the components of E in unit vector notation directed along positive x axis is E=(15.1i^+7.72j^)cm.

(b)

To determine

The components of F in unit vector notation directed along positive y axis.

(b)

Expert Solution
Check Mark

Answer to Problem 52P

The components of F in unit vector notation directed along positive y axis is F=(7.72i^+15.1j^)cm.

Explanation of Solution

Write the expression for the vectors F along positive y axis.

  F=F1cos(90+θ)i^+F1sin(90+θ)j^        (II)

Here, F is the vector along y axis, θ is the direction of the vector along positive x axis, and F1 is the vector component along x axis and y axis.

Conclusion:

Substitute 17.0cm for F1 and 27.0° for θ in the equation (II) to find F.

  F=(17.0cm)cos(90°+27.0°)i^+(17.0cm)sin(90°+27.0°)j^=(17.0cm)cos(117.0°)i^+(17.0cm)sin(117.0°)j^=(7.72i^+15.1j^)cm

Therefore, the components of F in unit vector notation directed along positive y axis is F=(7.72i^+15.1j^)cm.

(c)

To determine

The components of G in unit vector notation directed along negative y axis.

(c)

Expert Solution
Check Mark

Answer to Problem 52P

The components of G in unit vector notation directed along negative y axis is G=(7.72i^15.1j^)cm.

Explanation of Solution

Write the expression for the vectors G along negative y axis.

  G=G1cos(θ270)i^+G1sin(θ270)j^        (III)

Here, G is the vector along negative y axis, θ is the direction of the vector along negative y axis, and G1 is the vector component along x axis and y axis.

Conclusion:

Substitute 17.0cm for G1 and 27.0° for θ in the equation (III) to find G.

  G=(17.0cm)cos(27.0°270°+)i^+(17.0cm)sin(27.0°+270°)j^=(17.0cm)cos(243°)i^+(17.0cm)sin(243°)j^=(7.72i^15.1j^)cm

Therefore, the components of G in unit vector notation directed along negative y axis is G=(7.72i^15.1j^)cm.

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Chapter 1 Solutions

Bundle: Principles of Physics: A Calculus-Based Text, 5th + WebAssign Printed Access Card for Serway/Jewett's Principles of Physics: A Calculus-Based Text, 5th Edition, Multi-Term

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