EBK PHYSICS FOR SCIENTISTS AND ENGINEER
EBK PHYSICS FOR SCIENTISTS AND ENGINEER
16th Edition
ISBN: 8220100546716
Author: Katz
Publisher: CENGAGE L
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Chapter 3, Problem 70PQ

(a)

To determine

The value of m.

(a)

Expert Solution
Check Mark

Answer to Problem 70PQ

The value of m is 3.0.

Explanation of Solution

In problem it is given that F=3.3i^+6.3j^ and A=1.1i^+2.1j^.

Write the relation between F and A.

  F=mA (I)

Here, F is the force vector, A is a vector and m is a scalar quantity.

Conclusion:

Substitute 3.3i^+6.3j^ for F and 1.1i^+2.1j^ for A in equation (I) to expand the equation.

(3.3i^+6.3j^)=m(1.1i^+2.1j^)=(1.1mi^+2.1mj^)

Equate coefficient of i^ in above equation to get m.

  3.3=1.1mm=3.31.1=3

Equate coefficient of j^ in above equation to get m.

  6.3=2.1mm=6.32.1=3

Therefore, the value of m is 3.0.

(b)

To determine

To draw F and A on the same coordinate system.

(b)

Expert Solution
Check Mark

Answer to Problem 70PQ

The following figure shows the vector F and A.

Explanation of Solution

The following figure shows the vector F and A.

EBK PHYSICS FOR SCIENTISTS AND ENGINEER, Chapter 3, Problem 70PQ

(c)

To determine

The magnitude and direction of A and F .

(c)

Expert Solution
Check Mark

Answer to Problem 70PQ

The magnitude of A is 2.4 and magnitude of F is 7.1 and both vectors are at 62° with respect to x axis.

Explanation of Solution

Write the expression for the magnitude of A.

  |A|=Ax2+Ay2 (II)

Here, |A| is the magnitude of A, Ax and Ay are the x and y components of vector A.

Write the expression for the magnitude of F.

  |F|=Fx2+Fy2 (III)

Here, |F| is the magnitude of F, Fx and Fy are the x and y components of vector F.

Write the expression for the angle that F makes with x axis.

  θF=tan1(FyFx) (IV)

Here, θF is the angle that F makes with x axis.

Write the expression for the angle that A makes with x axis.

  θA=tan1(AyAx) (V)

Here, θA is the angle that A makes with x axis

Conclusion:

Substitute 3.3 for Fx and 6.3 for Fy in equation (III) to get |F|.

  |F|=(3.3)2+(6.3)2=7.1

Substitute 1.1 for Ax and 2.1 for Ay in equation (II) to get |A|.

  |A|=(1.1)2+(2.1)2=2.4

Substitute 3.3 for Fx and 6.3 for Fy in equation (IV) to get θF.

  θF=tan1(6.33.3)=62°

Substitute 1.1 for Ax and 2.1 for Ay in equation (V) to get |A|.

  θA=tan1(2.11.1)=62°

Therefore, the magnitude of A is 2.4 and magnitude of F is 7.1 and both vectors are at 62° with respect to x axis.

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Chapter 3 Solutions

EBK PHYSICS FOR SCIENTISTS AND ENGINEER

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