R.M.K ENGINEERING COLLEGE, Kavaraipettai - 601 206.R.M.K ENGINEERING COLLEGE, Kavaraipettai - 601 206.

DEPARTMENT OF MECHANICAL ENGINEERINGDEPARTMENT OF MECHANICAL ENGINEERING

ME 2151-Engineering Mechanics-TutorialsME 2151-Engineering Mechanics-Tutorials

UNIT I - Coplanar Concurrent forcesUNIT I - Coplanar Concurrent forces

1.1. DeterDetermine thmine the resule resultant of tant of the concthe concurrent urrent force sforce system ystem shown ishown in fig 1.n fig 1.

2.2. DetDetermermine the resine the resultultant of the forcant of the force systee system shown in fig 2.Nm shown in fig 2.Note thaote that the slope of thet the slope of the

action line of each force action line of each force is indicated in the figure.is indicated in the figure.

3.3. The 100 N The 100 N resresultultant of four forant of four forces togces togethether with threr with three of those fouee of those four forcer forces is shown ins is shown infig3. Determine the fourth force.fig3. Determine the fourth force.

4.4. ThThreree e wiwireres s exexerert t ththe e tetensnsioion n inindidicacateted d on on ththe e riring ng in in fifig g 4.4.AsAssusume me a a coconcncururrerentnt

system ,Determine the force system ,Determine the force in a single in a single wire which will rwire which will replace the three wires.eplace the three wires.

5.5. FigFigure 5 showure 5 shows a 10 KG lamp supps a 10 KG lamp supportorted by two cabed by two cables AB and AC .Fles AB and AC .Find thind the tense tension inion in

each cable.each cable.

6. 6. DeterDetermine the fmine the force P requorce P required tired to hold a mass o hold a mass 10kg in equi10kg in equilibrlibrium utiium utilizinlizing the systg the system of em of 

 pulleys shown in fig 6.Assume that all pulleys are of same size. pulleys shown in fig 6.Assume that all pulleys are of same size.

3030°°

4545°°

3030°°

6060°°

180N180N

150N150N

80N80N

200N200N

60N60N

nn

20N20N

nn

40N40N

nn

6868°°

fig. 4fig. 4

4545°°

4545°°

6060°°

6060°°50N50N

100N100N

120N120N

70N70N

fig. 3fig. 3

30N30N100N100N

50N50N

113311

131311131311

232311

131311

fig. 2fig. 2

fig. 1fig. 1

10kg10kg

PP

fig. 6fig. 6

BB

AA

CC

AA

1.5m1.5m 2m2m

0.75m0.75m

fig. 5fig. 5

7.7. A rubber bA rubber band has an unsand has an unstrettretched lengtched length of 200mm.h of 200mm.It is pulIt is pulled untiled until its lel its length is 250 mngth is 250 mmm

as shown in fig 7,The horizontal force P is 1.75N.What is the tension in the band?as shown in fig 7,The horizontal force P is 1.75N.What is the tension in the band?

8.8. TwTwo go guy uy wiwireres as are re fafaststeneened td to ao an an ancnchor hor bobolt lt in in a fa fououndandatition aon as ss showhown in in n fifig 8g 8..What pull does the bolt exert on What pull does the bolt exert on the foundation?the foundation?

9.9. Body A of mBody A of mass 15kg ass 15kg rest on a rest on a smootsmooth surfah surface. Body B ice. Body B is of mass of mass 6.5 kg. Ds 6.5 kg. Determetermine theine the

tension in Stension in S11 and Sand S22 and the normal reaction of the and the normal reaction of the horizontal surface on A.horizontal surface on A.

10.10. WhaWhat t is the is the nornormal reactmal reaction betweion between en the mass shown in the mass shown in figfig.10 and .10 and the grounthe ground? Thed? The

 pulley is assumed mass less and in fricti pulley is assumed mass less and in frictionless bearingsonless bearings

11.11. In fig11. three spheres In fig11. three spheres each with 2 kg maseach with 2 kg mass and each 350 mm in s and each 350 mm in diameter rest in box diameter rest in box 760760mm mm wiwidede.. FiFind nd a. a. rereacactition on of of B B on on A A b. b. ThThe e rereacactition on of of ththe e wawall ll on on C C anand 3d 3. T. Thehe

reaction reaction of of the the floor floor on on B.B.

12.12. The rolleThe roller shown in fig is of mass 150 kg. What force T is necessary to starr shown in fig is of mass 150 kg. What force T is necessary to start the roller t the roller 

over the block A?over the block A?

13.13. A 600N crate is A 600N crate is supported by several rsupported by several rope and pulley arrangements as ope and pulley arrangements as shown. Determineshown. Determine

for each arrangement the tension in the rope.for each arrangement the tension in the rope.

AA

CC

AABB

DD

CC

AAfig.11fig.11

100mm100mm

2525°°

AA

TT

350mm350mm

200mm200mmMMMMMM

MM

PP

44

33

44

fig. 7fig. 7

AABB3030°°

SS22

SS11

3600 N3600 N6650N6650N

2525°°1515°°

fig. 8fig. 8

fig. 9fig. 9

fig. 10fig. 10

40 KG40 KG110 N110 N

14. A string of length 24cm is attached to a point on a smooth vertical wall and to a point on

the surface of a sphere of radius 12cm.The sphere whose weight is 400N hangs in

equilibrium against the wall. Find the tension in the string and the reaction of the wall.

15. A string ABCD is attached to two fixed point A & D has two equal weights of 500Nattached to it at B and C. The weight rest with portions AB and CD inclined at angles of 

45° and 50°respectively to the vertical. Find the tension in the portion AB,AC,CD of the

string if the inclination of the portion BC to the vertical is 100°.

600N

n

600N

n

T

T

600N

n

T

600N

n

T

AB

A CA

D

A

500

500

A D

B

C

45°50°110°

Concurrent forces in space

1.Forces of 20N ,15N 30N and 50 N are concurrent at the origin and are respectively directed

through the points whose coordinates are (2,1,6),(4,-2,5),(-3,-2,1),and (5,1,-2). Determine the

resultant of the system of forces.2.Find the resultant of the forces shown in fig.

0

3.The guy wire of a tower is anchored by means of a bolt at A as shown in fig..The force in the

wire is 75KN.Determine a.) The components Fx ,Fy & Fz of the force .b) The angle θx, θy & θz

defining the direction of the force components.

4. If the tension in wire ‘AB’ is 75 kN determine the required values of tension in ‘AC’ and

‘AD’,so that the resultant of the three forces applied at ‘A’ is vertical.Find also the resultant .

2m

3m

1m

3m

2m

48kN

60kN

36kN

1m

y

x

z

y

x

z

80m

40m

30m

y

x

z

7m

12m

24m

A

D

C

5.Three wires are joined at D.Two ends A and B are on the wall and the other end C is on the

ground.The wire CD is vertical.A force of 60 kN is applied at ‘D’and it passes through a point Eon the ground as shown in fig.Find the forces in all the three wires.

6. In fig, a pole 9m high is shown supporting a wire in the xy plane, exerting a force of 650N

on the top at an angle of 10° below the horizontal .Two guy wires are affixed as shown.

Determine the tension in each guy wire and the compression in the pole assuming that the

column OC is supported by a ball and socket joint at C.

7. A mass of 6.1 kg is supported by the three wires as shown in fig,.AB and AC are in xz plane.

Determine tension T1,T2,T3

UNIT II - Equilibrium of rigid bodies

1. Find the resultant of the system shown in figure.

8m

6m

B

y

x

z

3m

3m

60kN

m

A

B

D

C

E

3m1.5m 6m 1.5m

2m

x

A,B,C in a horizontal plane

y

z

10°

30°

30°

30°

60°

O

C

     9    m

650 N

y

x

z

2m

4m

C

D

T1

B

6m4m3m

AT2

T3

M

.

2. Find the resultant of the three loads shown acting on the beam.

3. A rectangular plate is supported by brackets at A and B and by a wire CD. The

magnitude of tension in the wire CD is 200 N. Determine the moment of this tension about the

 point A.

4.Reduce the system of 

forces shown in fig to a

force couple system at O.

5. The turnbuckle is tightened until the tension in the cable AB equals 2.4kN.Determine thevector expression for the tension T as a force acting on member AB. Also find the magnitude of 

the projection of  T along line AC. z

A

C

B

X

1m

4m2m

4m

20kN

40kN

A

Y

Z

20kN

O

D

CB

2 mADO

5 m

10kN

8kN

+

+

6kN3kN

5kN

8kN

12kNm10kNm

30°

45°0.5m

1.5m

0.5m

1m

1.5m 1.5m

20t

8t10t

8m5m3m 3m

O

6. A tension T of magnitude 10kN is applied to the cable attached to the top A of the rigid mast

and secured to the ground at B. Determine the moment Mz of T about the Z axis passing through

the base O.

7. Determine the moment of the 400-N force about point A.

8.Replace the two forces that act on the 3-m cube by an equivalent single force F at A and acouple M

3m

y

x

2m

O

CB

x

y

z

15m

A

B

12m9m

T=10kN 

OB

125

X

Y

A

10050

50B

60°

Z

400N

All dimension are in ‘mm’

x

z

y3m

3m

3m

40kNm

30kNm

O

9.A square foundation mat supports the four columns shown. Determine the magnitude and

 point of application of the resultant of the four loads.

10.A 3m boom is acted upon by the 4kN force shown. Determine the tension in each cable

and the reaction at the ball and socket joint at A.

11. Determine the moment of the 400-N force about point A by using the vector cross-product

relation.

12.Replace the two forces that act on the 3-m cube by an equivalent single force F at A and a

couple M

y

z x

400kN

120kN

80kN200kN

4m

6m 5m

5m

y

x

z

1.8m

1.8m

A

B

D

C

E

2.1m

1.8m 1.2m

4kN

125

X

Y

A

10050

50B

60°

Z

400N

All dimension are in ‘mm’

x

z

y3m

3m

3m

40kN

m

30kN

m

13.A square foundation mat supports the four columns shown. Determine the magnitude and

 point of application of the resultant of the four loads.

14. A 3m boom is acted upon by the 4kN force shown. Determine the tension in each cable

and the reaction at the ball and socket joint at A.

y

z x

400kN

120kN

80kN200kN

4m

6m 5m

5m

y

x

z

1.8m

1.8m

A

B

D

C

E

2.1m

1.8m 1.2m

4kN

UNIT III - Centre of Gravity and Moment of Inertia

1.Locate the coordinates of centroid for the areas shown in fig.

2.Locate the centroid of the bent wire shown in fig.

3. Determine the centroid of a uniform rod bent into triangular shape.

4.Find the centroid of the figure built up of the lines as shown in fig.

5.Locate the centroid of the shaded area formed by removing the triangle from the semicircular 

area in fig.

6.Determine the coordinates of the centroid of the shaded area in fig.

Y

X

a)

b)

c)

d)

30a

40a

40a

30a(20,10)

(40,90) (100,100)

30a

(100,30)

20a

45

a

60

75

50

a

a

50

a

All dimension are in ‘mm’

50 a     7     5

     2     5     0

300

All dimension are in ‘mm’

45

100

75

100

100

All dimension are in ‘mm’

x

y

40mm

a

75mm

200mm

     2     0     0    m    m

x

y