Solution 3 - San Jose State University

Solution 3.11

PROBLEM STATEMENT

The tailgate of a car is supported by the hydraulic lift BC. If the lift exerts a 125-lb force directed along its centerline on the ball and socket at B, determine the moment of the force about A.

First note Then

and

Now where Then

dCB (12.0 in.)2 (2.33 in.)2 12.2241 in. 12.0 in.

cos 12.2241 in. 2.33 in.

sin 12.2241 in.

FCB FCB cos i FCB sin j

125 lb

[(12.0 in.) i (2.33 in.) j]

12.2241 in.

MA rB/A FCB

rB/A (15.3 in.) i (12.0 in. 2.33 in.) j (15.3 in.) i (14.33 in.) j

125 lb MA [(15.3 in.)i (14.33 in.)j]12.2241 in. (12.0i 2.33j)

(1393.87 lb in.)k

(116.156 lb ft)k

or MA 116.2 lb ft

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Solution 3.14

PROBLEM STATEMENT

It is known that the connecting rod AB exerts on the crank BC a 2.5-kN force directed down and to the left along the centerline of AB. Determine the moment of the force about C.

Using (a):

MC y1(FAB )x x1(FAB )y

(0.056

m)

7 25

2500

N

(0.042

m)

24 25

2500

N

61.6 N m

Using (b):

MC y2 (FAB )x

(0.088

m)

7 25

2500

N

61.6 N m

(a) MC 61.6 N m

(b) MC 61.6 N m

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Solution 3.21

PROBLEM STATEMENT

Before the trunk of a large tree is felled, cables AB and BC are attached as shown. Knowing that the tensions in cables AB and BC are 555 N and 660 N, respectively, determine the moment about O of the resultant force exerted on the tree by the cables at B.

dBA (0.75 m)2 (7 m)2 (6 m)2 9.25 m dBC (4.25 m)2 (7 m)2 (1 m)2 8.25 m

Have

TB A

TB A

BA dB A

555 N (0.75 m i 9.25 m

7

m j

6

m k

)

TBA (45 N)i (420 N)j (360 N)k

TBC

TBC

BC dBC

660 N 8.25 m

(4.25

m

i7

m

j k)

TBC (340 N)i (540 N)j (80 N)k

R TBA TBC

R 295 Ni 980 N j 440 Nk

MO rB /O R where rB /O (7 m)j

i MO 0

295

j 7 980

k 0 Nm 440

3080 Nmi 2065 Nmk

MO 3080 Nm i 2070 Nm k

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Solution 3.38

PROBLEM STATEMENT

Three cables are attached to the top of the tower at A. Determine the angle formed by cables AD and AB.

First note:

AB (16 m)i (48 m)j (12 m)k AD (14 m)i (48 m)j

AB (16 m)2 (48 m)2 (12 m)2 52.0 m

AD (14 m)2 (48 m)2 50.0 m

By definition,

AB AD (AB)(AD)cosBAD

cos

BAD

AB AD

ABAD

cos

BAD

(16

m)i

(48

m)j (12 m)k(14 52.0 m50.0 m

m)i

(48

m)j

1614 482 cosBAD 52.050.0

cos BAD 0.800

36.9

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Solution 3.55

PROBLEM STATEMENT

A force P of magnitude 520 lb acts on the frame shown at point E. Determine the moment of P about a line joining points O and D.

First develop expression for P in terms of its unit vector: EH (30 in.)i (7.5 in.)j (10 in.)k

EH (30)2 (7.5)2 (10)2 32.50 in.

EH

EH EH

30i 7.5j 10k 32.50

EH 0.92308i 0.23077j 0.30769k

P PEH 520 lb0.92308i 0.23077j 0.30770k

P (480.0 lb)i (120.0 lb)j (160.0 lb)k

The moment of P about axis OD is given by the mixed triple product Eq. (3.43):

MOD OD (rE /D P)

rE/D (30 in.)i (7.5 in.)j

OD

OD OD

30i

15j 10k 35.0

OD 0.85714i 0.42857j 0.28571k

0.85714 MOD OD (rE /D P) 30.0 in.

480 lb

0.42857 7.50 in. 120 lb

0.28571 0

160 lb

MOD 0.85714[(7.50 in.)(160 lb) 0] 0.42857[0 (30.0 in.)(160 lb)] 0.28571[(30.0 in.)(120 lb) (7.50)(480]

3085.7 lb in. MOD 3090 lb in.

Copyright ? McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

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