BEDFORD ESTATICA

Problem 2.1 In Active Example 2.1, suppose that the

vectors U and V are reoriented as shown. The vector

V is vertical. The magnitudes are jUj D 8 and jVj D 3.

Graphically determine the magnitude of the vector

U C 2V.

U V

45

Solution: Draw the vectors accurately and measure the resultant.

R D jU C 2Vj D 5.7 R D 5.7

Problem 2.2 Suppose that the pylon in Example 2.2 is

moved closer to the stadium so that the angle between

the forces FAB and FAC is 50°. Draw a sketch of the

new situation. The magnitudes of the forces are jFABj D 100 kN and jFACj D 60 kN. Graphically determine the

magnitude and direction of the sum of the forces exerted

on the pylon by the cables.

Solution: Accurately draw the vectors and measure the magnitude

and direction of the resultant

jFAB C FACj D 146 kN

˛ D 32°

c 2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they

currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

7

Problem 2.3 The magnitude jFAj D 80 lb and the

angle ˛ D 65°. The magnitude jFA C FBj D 120 lb.

Graphically determine the magnitude of FB.

FB

FA

a

FC

Solution: Accurately draw the vectors and measure the magnitude

of FB.

jFBj D 62 lb

Problem 2.4 The magnitudes jFAj D 40 N, jFBj D 50 N, and jFCj D 40 N. The angle ˛ D 50° and ˇ D 80°.

Graphically determine the magnitude of FA C FB C FC.

FB

FA

a

FC

Solution: Accurately draw the vectors and measure the magnitude

of FA C FB C FC.

R D jFA C FB C FCj D 83 N

8

c 2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they

currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

Problem 2.5 The magnitudes jFAj D jFBj D jFCj D 100 lb, and the angles ˛ D 30°. Graphically determine

the value of the angle ˇ for which the magnitude

jFA C FB C FCj is a minimum and the minimum value

of jFA C FB C FCj.

FB

FA

a

FC

Solution: For a minimum, the vector FC must point back to the

origin.

R D jFA C FB C FCj D 93.2 lb

ˇ D 165°

Problem 2.6 The angle
D 50°. Graphically determine

the magnitude of the vector rAC. 60 mm 150 mm

A C

B

rAB rBC

rAC



Solution: Draw the vectors accurately and then measure jrACj.

...