PROBLEM 1

The uniform 30-kg bar OB is secured to

the accelerating frame in the 30o

position from the horizontal by the

hinge at O and roller at A. If the

horizontal acceleration of the frame is

a=20 m/s2, compute the force FA on the

roller and the x- and y-components of

the force supported by the pin at O.

PROBLEM 2

The block A and attached rod have a combined mass

of 60 kg and are confined to move along the 60o guide

under the action of the 800 N applied force. The

uniform horizontal rod has a mass of 20 kg and is

welded to the block at B. Friction in the guide is

negligible. Compute the bending moment M exerted

by the weld on the rod at B.

SOLUTION

x

W=60(9.81) N

60o

N

FBD Kinetic Diagram

x

2/84.4

6060sin)81.9(60800

sma

amaF

x

xxx

FBD of rod

Bx

By

M

W1=20(9.81) N

KD of rod

mTax=60ax

m1ax=20ax

2/196

)60sin7.0)(94.4)(20(7.0)81.9(20

smM

MdmaM xB

The parallelogram linkage shown moves in

the vertical plane with the uniform 8 kg bar

EF attached to the plate at E by a pin which

is welded both to the plate and to the bar. A

torque (not shown) is applied to link AB

through its lower pin to drive the links in a

clockwise direction. When q reaches 60o, the

links have an angular acceleration an

angular velocity of 6 rad/s2 and 3 rad/s,

respectively. For this instant calculate the

magnitudes of the force F and torque M

supported by the pin at E.

PROBLEM 3

The uniform 100 kg log is supported by

the two cables and used as a battering

ram. If the log is released from rest in the

position shown, calculate the initial

tension induced in each cable

immediately after release and the

corresponding angular acceleration a of

the cables.

PROBLEM 4

SOLUTION

W=100(9.81) N

FBD KD

TA TB

nam

tam

+n

+t

+n

+t

When it starts to move, v=0, w=0 but a≠0 02 ran w

2

..

..

/905.430sin

57.849030cos0

smaammgamF

TTmgTTF

tttkd

t

BABAkd

n

2/45.22

905.4sradrat aa

Length of the cables

NTNT

TTTTM

BA

BABAkd

G

17.63739.212

30)5.0(60sin)5.1(60sin0..

The motion of the log is curvilinear translation.

*

*

An 18 kg triangular plate is supported by cables AB and CD. When the plate is in the

position shown, the angular velocity of the cables is 4 rad/s ccw. At this instant,

calculate the acceleration of the mass center of the plate and the tension in each of the

cables.

G 10 cm

A

B

C

D

60° 60°

24 cm

20 cm 20 cm

Answer:

NTNT

sma

CDAB 93.7811.143

/23.6 2

PROBLEM 5

PROBLEM 6

The uniform 8 kg slender bar is hinged about a horizontal axis through O and released from rest

in the horizontal position. Determine the distance b from the mass center to O which will result

in an initial angular acceleration of 16 rad/s2, and find the force R on the bar at O just after

release.

SOLUTION

FBD KD

mg Ot

On

G O

G O

aI

tam

nam

+n

+t

0

6471053601688198

0536005360

55008434878128

168162408198

24060812

1

12

1

2

222

nnn

tttt

a

to

OmaF

N.O..OmaF

m.b.

.b.b.b

bb.b.

bamIM

kgm..mlI

t

a

When it is released, w=0 (v=0, an=w2r=0) but a≠0.

PROBLEM 7

The spring is uncompressed when the uniform slender bar is in the vertical position

shown. Determine the initial angular acceleration a of the bar when it is released from

rest in a position where the bar has been rotated 30o clockwise from the position

shown. Neglect any sag of the spring, whose mass is negligible.

SOLUTION Unstrecthed length of the spring: llllo

2

5)4/2( 22

When q=30o , length of the spring: llspring2

3

When q=30o , spring force:

2

3

2

5

2

3

2

5klllkFspring

(in compression)

l

g

m

k

lamml

lF

lmg

amIM

l

tspring

tO

857.0864.0

412

1

2460cos

4

2

a

a

a

W

O

G +n

+t

On

Ot

30o

30o

l

Fspring

60o

.

lspring

G +n

+t

04

2 l

mam n w

tam

aI 60o

PROBLEM 8

In the mechanism shown, the flywheel has a mass of 50 kg and radius of gyration about

its center of 160 mm. Uniform connecting rod AB has a mass of 10 kg. Mass of the

piston B is 15 kg. Flywheel is rotating by the couple T ccw at a constant rate 50 rad/s.

When q=53o determine the angular velocity and angular acceleration of the connecting

rod AB (wAB ve aAB). What are the forces transmitted by the pins at A and B? Neglect the

friction. Take sin 53=0.8, cos 53=0.6.

PROBLEM 9

The masses of uniform bars AB and BC are mAB = 2 kg and mBC = 1 kg, respectively. Bar BC is

pin connected to a fixed support at C. Bar AB is pin connected at A to a uniform wheel of

radius R = 0.50 m and mass mw = 5 kg. At the instant shown, A is vertically aligned with O,

bar AB is horizontal and bar BC is vertical. For the given instant, bar BC is rotating with an

angular velocity of 2 rad/s and an angular acceleration of 1.2 rad/s2, both in clockwise

direction. Assuming that the wheel rolls without slipping, determine the force P that is

applied to the wheel. Also determine the coefficient of friction between the wheel and the

surface.

C

0.95 m

1.25 m

A

B

O

P

R = 0.50 m

r

wBC=2 rad/s aBC=1.2 rad/s2

m

PROBLEM 10

The 45 kg uniform flywheel shown is rotating

with an angular velocity of 30 rad/s and an

angular acceleration of 72 rad/s2 both in

counter clockwise direction. Bar AB has a

mass of 15 kg and a radius of gyration with

respect to its mass center of 325 mm. The

coefficient of friction between the pin at C and

the slot in bar AB is 0.10. When bar AB is in

the position shown, determine the force

exerted on the bar by the pin at support A and

the support reactions exerted on the flywheel

at point O.

B B

C C

G

A A

G

250 mm

300 mm

600 mm 700 mm

PROBLEM 11

The unbalanced 20 kg wheel with the mass center at G has a radius of gyration about G

of 202 mm. The wheel rolls down the 20o incline without slipping. In the position

shown. The wheel has an angular velocity of 3 rad/s. Calculate the friction force F

acting on the wheel at this position.

SOLUTION “General Motion”

FBD

N

mg

Ff

KD

=

am

aI

222816.0)202.0(20 kgmkmI

aa 25.0 raox x

y

jia

ikkikiaaa

yxaa

G

OGOG

075.0675.025.0

075.033075.025.0/

a

aa

604805

67502502020

.F

..FsinmgamF

f

fxefx

a

a

a

a

51367184

07502020

..N

.cosmgNamF yefy

aa 81602500750 .).(F).(NIM fefG N.N

N.F

s/rad.

f

971160

6172

59715 2

a