1. A 54 kg crate rests on the 27 kg pickup tailgate. Calculate the tension T

in each of the two restraining cables, one of which is shown. The centers of

gravity are at G1 and G2. The crate is located midway between the two

cables.

2. As an airplane’s brakes are applied, the nose wheel exerts twoforces on the end of the landing gear as shown. Determine thehorizontal and vertical components of reaction at the pin C and theforce in strut AB.

Solution: Two-force member : link AB

FBD of member CA

2 kN

6 kN

A

C Cx

Cy

FAB50o

20o

1tan20

0.4tan20

0.4

m0

.6 m

kNCC

F

kNCC

F

kNF

FF

M

yy

y

xx

x

AB

ABAB

C

56.60650cos8637.0

0

66.20250sin8637.0

0

8637.0

020tan4.050cos4.050sin20tan1612

0

+

3. The 500-kg uniform beam is subjected tothe three external loads shown. Compute thereactions at the support point O. The x-y planeis vertical.

FBD of beam

GOx

Oy

Wbeam=500(9.81) N

30o

1.4 kN

mNMM

MO

766.756208.430cos3000150004.281.95002.11400

0

M

+

3 kNA

B2.4 m

15 kN.m

(ccw)

NOOF xxx 1500030sin30000

NOOF yyy 07.6103030cos300081.950014000

4. The pin A, which connects the 200-kg steel beam with center of gravity at G to the

vertical column, is welded both to the beam and to the column. To test the weld, the 80-kg

man loads the beam by exerting a 300 N force on the rope which passes through a hole in

the beam as shown. Calculate the torque (couple) M supported by the pin.

FBD of beam

GAx

Ay

Wbeam=200(9.81) N

Wman=80(9.81) N

300 N300 N

mNM

M

M A

04.4937

01.23008.13002.181.92008.181.980

0

M

+

5. A large symmetrical drum for drying sand is operated by the geared motor

drive shown. If the mass of the sand is 750 kg and an average gear-tooth force of

2.6 kN is supplied by the motor pinion A to the drum gear normal to the

contacting surfaces at B, calculate the average offset of the center of mass G

of the sand from the vertical centerline. Neglect all friction in the supporting

rollers.

x

FBD of Drum

G

N1

20o

mmmx

x

MO

2.1991992.0

081.97506.020cos106.2

0

3

+

Tangent to circle N81.9750

x2.6 kN

N2 N3

N4

6. It is desired that a person be able to begin closing the van hatch from the open

position shown with a 40-N vertical force P. As a design exercise, determine the

necessary force in each of the two hydraulic struts AB. The center of gravity of

the 40-kg door is 37.5 mm directly below point A. Treat the problem as two-

dimensional.

7. The small crane is mounted on one side of the bed of a pickup truck. For

the position q=40o, determine magnitude of the force supported by the pin

at O and the oil pressure p against the 50-mm diameter piston of the

hydraulic cylinder BC.

Two-force member: Hydraulic cylinder BC

FBD of Boom AO

O

B

C

360 mm

a

q

FBC

Ox

Oy

W

MPamm

N.

.

d

Fp

N.O

sin..O

F

N.O

cos.O

F

N.F

cosFcos.

M

.

sincos

cossintan

BC

y

y

y

x

x

x

BC

BC

O

o

222582

450

815065

4

413032

0815065819120

0

092818

0815065

0

815065

036040340785819120

0

256

4011040340

4011040340360

a

a

a

a

a

+

Oy

8. The toggle switch consists of a cocking lever that is pinned to a fixed frame at A and

held in place by the spring which has an unstretched length of 200 mm. The cocking lever

rests against a smooth peg at B. Determine the magnitude of the support force at A and

the normal force on the peg at B when the lever is in the position shown.

k=50 N/m300 mm

100 mm

300 mm30o

k=50 N/m300 mm

100 mm

300 mm30o

Ax

Ay

D

C

A

30o

30

0 m

m

oo .,.sinsinsin

CD

mm.CDcosCD

19178112400300

150

46761504003002400300 222

aa

N.AAA

N.AcosFsinFA

F

N.AsinFcosFA

F

N.FFsinF

M

yx

yspringBy

y

xspringBx

x

BBspring

A

1328

1991203030

0

3472503030

0

136210100400

0

22

N..lkF

mm..l

spring 8322847664050

6447620064676

FBD of lever

a

30o

B

A FB

D

Fspring

+

9. The bracket and pulley assembly has a mass of 40 kg with combined center of

gravity at G. Calculate the magnitude of the force supported by the pin at C and

roller at A when a tension of 400 N is applied in the vertical plane of the cable.

75 mm

D

G

B

400 N

30o

450 mm

375 mm

75 mm

100 mm

C

A

75 mm

D

G

B

400 N

30o

450 mm

375 m

m

75 mm

100 mm

C

A

30oAx

FBD of bracket

W=mg=40(9.81) N

Cx

Cy

NAsinAC

F

xxx

x

800030400

0

N.Ccos.C

F

yy

y

8173803040081940

0

NC

CC.

M

x

xy

B

600

03754507540035081940

0

Cx

10. Pulley A delivers a steady torque of 100 N.m to a pump through its shaft at C. The

tension in the lower side of the belt is 600 N. The driving motor B has a mass of 100

kg and rotates clockwise. As a design consideration, determine the magnitude of the

force on the supporting pin at O.

FBD of motor (B)FBD of pulley (A)

30o

Cx

CyT

600 N100 N.m

N.T

.T.

MC

6155

10022502250600

0

T=155.6 N

600 N

mg=100.9.81=981 N

Ox

OyFD

N.OORN.O

Ocos.

F

N.O

.O.sin..sin.cos..cos..

M

yxox

x

x

y

y

D

55116675734

0600306155

0

08906

025012506003007501250306155300750203061551250981

0

22

11. The winch consists of a drum

of radius 30 cm, which is pin

connected at its center C. At its

outer rim is a ratchet gear having a

mean radius of 60 cm. The pawl

AB serves as a two force member

(short link) and holds the drum

from rotating. If the suspended

load is 500 N, determine the

horizontal and vertical components

reaction at the pin C.

60 cm

20 cm

70 cm

30 cm

NCCF

F

NCCF

F

NF

F

M

yyAB

y

xxAB

X

AB

AB

C

43.5710500sin

0

2500cos

0

260

03050060cos

0

a

a

a

+

Two-force member : Pawl AB

FBD of winch

C

a

500 N

FAB

Cx

Cy

a20 cm

70 cm

B

A

Correct sense

60 cm

20 cm

70 cm

30 cm

12. Determine the support reactions of roller A and the smooth collar B on the

rod. The collar is fixed to the rod AB, but is allowed to slide along rod CD.

45o

NBMB

Ax

FBD of rod AB

Equations of equilibrium;

mNM

Mcos

M

NA

Acos.

F

N.N

sinN

F

B

B

B

x

x

x

B

B

y

227

04529001900

0

900

045791272

0

791272

090045

0

13. Plate AB contains a smooth parabolic slot. Fixed pins B and C are

located at the positions shown in the figure. The equation of the parabolic

slot is given as y = x2/160 , where x and y are in mm. If it is known that the

force input P = 4 N, determine the forces applied to the plate by the pins B

and C and also the force output Q.

Q

Px

B

Cy

A

140 mm 60 mm 40 mm

20 mm

46 mm

120 mm

Q

P=4 kNx

B

Cy

A

140 mm 60 mm 40 mm

20 mm

46 mm

120 mm

By

C

aa

Tangent to the parabolic slot

o

x

.

tan

tanx

dx

dyy

mm.yx

y

6812

4060140

2046120

4

3

160

2

522160

60

160

60

22

a

N.ByN.QN.C

Q.B

.tansinQB.PM

Q.C.B

cosQcosCBF

Q.C.

sinQsinCPF

y

yC

y

yy

x

20729554944

9013760

05224046605220

0975080

00

4219060

00

a

a