Physics
Physics
3rd Edition
ISBN: 9780073512150
Author: Alan Giambattista, Betty Richardson, Robert C. Richardson Dr.
Publisher: McGraw-Hill Education
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Chapter 3, Problem 30P

(a)

To determine

The x and y component of B.

(a)

Expert Solution
Check Mark

Answer to Problem 30P

The x component of B is 6.9 and y component of B is 1.7.

Explanation of Solution

Since angle is below x axis, take it as negative.

Write the expression for x component of B

Bx=Bcosθ (I)

Here, Bx is the x component of B , B is the magnitude of B and θ is the angle that B makes below the x axis .

Write the expression for y x component of B

By=Bsinθ (II)

Here, By is the y component of B and θ is the angle that B makes below the x axis.

Conclusion:

Substitute 14° for θ and 7.1 for B in equation (I) to get Bx.

Bx=7.1cos(14°)=6.9

Substitute 14° for θ and 7.1 for B in equation (II) to get By.

By=7.1sin(14°)=1.7

Negative sign for By indicate that it lies along negative y axis.

Therefore, the x component of B is 6.9 and y component of B is 1.7.

(b)

To determine

The magnitude and direction of C.

(b)

Expert Solution
Check Mark

Answer to Problem 30P

The magnitude of C is 6.9 and it is 225° counterclockwise from the +x axis.

Explanation of Solution

Write the expression for the magnitude of C.

C=Cx2+Cy2 (III)

Here, C is the magnitude of vector C , Cx is the x component of C and Cy is the y component of C.

Write the expression for direction of C.

θc=tan1(CyCx) (IV)

Here, θc is the angle than C makes with x axis.

Conclusion:

Substitute 6.7 for Cy and 1.8 for Cx in equation (III) to get C.

C=(1.8)2+(6.7)2=6.9

Substitute 6.7 for Cy and 1.8 for Cx in equation (IV) to get θc.

θc=tan1(6.71.8)=75°

The x component and y component are negative. Therefore, C lies at 180°+75°=255° counterclockwise from the x axis.

Therefore, the magnitude of C is 6.9 and it is 225° counterclockwise from the +x axis.

(c)

To determine

The magnitude and direction of C+B.

(c)

Expert Solution
Check Mark

Answer to Problem 30P

The magnitude of C+B is 9.8 and it is directed 59° clockwise from the +x axis.

Explanation of Solution

Write the expression for the magnitude of C+B.

|C+B|=(Cx+Bx)2+(Cy+By)2 (V)

Here, |C+B| is the magnitude of vector C+B , Cx is the x component of C and Cy is the y component of C.

Write the expression for direction of C+B.

θC+B=tan1(Cy+ByCx+Bx) (VI)

Here, θC+B is the angle than C+B makes with +x axis.

Conclusion:

Substitute 6.9 for Bx, 1.7 for By, 6.7 for Cy and 1.8 for Cx in equation (V) to get |C+B|

|C+B|=(1.8+6.9)2+(6.7+1.7)2=9.8

Substitute 6.9 for Bx, 1.7 for By,6.7 for Cy and 1.8 for Cx in equation (VI) to get θC+B.

θC+B=tan1(6.7+1.71.8+6.9)=59°

Therefore, the magnitude of C+B is 9.8 and it is directed 59° clockwise from the +x axis.

(d)

To determine

The magnitude and direction of CB.

(d)

Expert Solution
Check Mark

Answer to Problem 30P

The magnitude of CB is 10 and it is directed 210° counterclockwise from the +x axis.

Explanation of Solution

Write the expression for the magnitude of CB.

|CB|=(CxBx)2+(CyBy)2 (V)

Here, |CB| is the magnitude of vector CB , Cx is the x component of C and Cy is the y component of C.

Write the expression for direction of CB.

θC-B=tan1(CyByCxBx) (VI)

Here, θCB is the angle than CB makes with +x axis.

Conclusion:

Substitute 6.9 for Bx, 1.7 for By, 6.7 for Cy and 1.8 for Cx in equation (V) to get |C+B|

|C+B|=(1.86.9)2+(6.7(1.7))2=10

Substitute 6.9 for Bx, 1.7 for By,6.7 for Cy and 1.8 for Cx in equation (VI) to get θC+B.

θC+B=tan1(6.7(1.7)1.86.9)=30°

Since x component of CB is negative , it lies at 180°+30°=210° counterclockwise from the +x axis.

Therefore, the magnitude of CB is 10 and it is directed 210° counterclockwise from the +x axis.

(e)

To determine

The x and y components of CB.

(e)

Expert Solution
Check Mark

Answer to Problem 30P

The x components of CB is 8.7 and y component of CB is 5.0.

Explanation of Solution

Write the expression for the x component of CB.

|CB|x=CxBx (VII)

Here, |CB|x is the x component of vector CB.

Write the expression for the y component of CB.

|CB|y=CyBy (VII)

Here, |CB|y is the y component of vector CB.

Conclusion:

Substitute 6.9 for Bx and 1.8 for Cx in equation (VII) to get |C+B|x.

|CB|x=1.86.9=8.7

Substitute 1.7 for By and 6.7 for Cy in equation (VI) to get θC+B.

|CB|y=6.7(1.7)=5.0

Therefore, the x components of CB is 8.7 and y component of CB is 5.0.

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