Package: Loose Leaf For College Physics With Connect Access Card (1 Semester)
Package: Loose Leaf For College Physics With Connect Access Card (1 Semester)
5th Edition
ISBN: 9781260699166
Author: GIAMBATTISTA, Alan
Publisher: McGraw-Hill Education
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Chapter 2, Problem 27P
To determine

Rank the objects according to the magnitude of net force from smallest to largest value.

Expert Solution & Answer
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Answer to Problem 27P

The objects ranked according to the magnitude of net force from smallest to largest value is Fnet,C<Fnet,A=Fnet,B<Fnet,E<Fnet,D.

Explanation of Solution

The figure 1 shows the resultant magnitude of the net force.

Package: Loose Leaf For College Physics With Connect Access Card (1 Semester), Chapter 2, Problem 27P , additional homework tip  1

Write the expression for the resultant force by using Pythagoras theorem.

  Fnet,A=F12+F22        (I)

Here, Fnet is the magnitude of net force, F1 and F2 is the force of the objects.

The figure 2 shows the resultant magnitude of the net force.

Package: Loose Leaf For College Physics With Connect Access Card (1 Semester), Chapter 2, Problem 27P , additional homework tip  2

Write the expression for the resultant force.

  Fnet,B=F12+F22+2F1F2cosθ        (II)

The figure 3 shows the resultant force.

Package: Loose Leaf For College Physics With Connect Access Card (1 Semester), Chapter 2, Problem 27P , additional homework tip  3

Write the expression for the resultant force.

  Fnet,C=F2F1        (III)

The figure 4 shows the resultant net force.

Package: Loose Leaf For College Physics With Connect Access Card (1 Semester), Chapter 2, Problem 27P , additional homework tip  4

Write the expression for the resultant force.

  Fnet,D=F1+F2        (IV)

The figure 5 shows the resultant force.

Package: Loose Leaf For College Physics With Connect Access Card (1 Semester), Chapter 2, Problem 27P , additional homework tip  5

Write the expression for the force along x axis.

  Fx=F1+F2cosθ        (V)

Write the expression for the force along y axis.

  Fy=F2sinθ        (VI)

Write the expression for net magnitude of the force.

  Fnet,E=Fx2+Fy2        (VII)

Conclusion:

Substitute 2000N for F1 and 3000N for F2 in equation (I) to find Fnet,A.

  Fnet,A=(2000N)2+(3000N)2=3605N

Substitute 2000N for F1, 90° for θ, and 3000N for F2 in equation (II) to find Fnet,B.

  Fnet,B=(2000N)2+(3000N)2+2(2000N)(3000N)cos(90°)=3605N

Substitute 2000N for F1 and 3000N for F2 in equation (III) to find Fnet,C.

  Fnet,C=3000N2000N=1000N

Substitute 2000N for F1 and 3000N for F2 in equation (IV) to find Fnet,D.

  Fnet,D=2000N+3000N=5000N

Substitute 2000N for F1, 45° for θ, and 3000N for F2 in equation (V) to find Fx.

  Fx=2000N+(3000N)cos(45°)=4121N

Substitute 2000N for F1, 45° for θ, and 3000N for F2 in equation (V) to find Fx.

  Fy=(3000N)sin(45°)=2121N

Substitute 2121N for Fy and 4121N for Fx  in equation (VII) to find Fnet.

  Fnet,E=(2121N)2+(4121N)2=4635N

Therefore, the objects ranked according to the magnitude of net force from smallest to largest value is Fnet,C<Fnet,A=Fnet,B<Fnet,E<Fnet,D.

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Chapter 2 Solutions

Package: Loose Leaf For College Physics With Connect Access Card (1 Semester)

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