ME 2151 E MECH.doc

R.M.K ENGINEERING COLLEGE, Kavaraipettai - 601 206.DEPARTMENT OF MECHANICAL ENGINEERING

ME 2151-Engineering Mechanics-Tutorials

UNIT I - Coplanar Concurrent forces

1. Determine the resultant of the concurrent force system shown in fig 1.

2. Determine the resultant of the force system shown in fig 2.Note that the slope of the action line of each force is indicated in the figure.

3. The 100 N resultant of four forces together with three of those four forces is shown in fig3. Determine the fourth force.

4. Three wires exert the tension indicated on the ring in fig 4.Assume a concurrent system ,Determine the force in a single wire which will replace the three wires.

5. Figure 5 shows a 10 KG lamp supported by two cables AB and AC .Find the tension in each cable.

6. Determine the force P required to hold a mass 10kg in equilibrium utilizing the system of pulleys shown in fig 6.Assume that all pulleys are of same size.

30

45

30

60

180N

150N

80N

200N

60Nn

20Nn

40Nn

68

fig. 4

45

45

60

6050N

100N

120N

70N

fig. 3

30N100N

50N

13

11

2

1

fig. 2

fig. 1

10kg

P

fig. 6

B

A

CA

1.5m 2m

0.75m

fig. 5

7. A rubber band has an unstretched length of 200mm.It is pulled until its length is 250 mm as shown in fig 7,The horizontal force P is 1.75N.What is the tension in the band?

8. Two guy wires are fastened to an anchor bolt in a foundation as shown in fig 8.What pull does the bolt exert on the foundation?

9. Body A of mass 15kg rest on a smooth surface. Body B is of mass 6.5 kg. Determine the tension in S1 and S2 and the normal reaction of the horizontal surface on A.

10. What is the normal reaction between the mass shown in fig.10 and the ground? The pulley is assumed mass less and in frictionless bearings

11. In fig11. three spheres each with 2 kg mass and each 350 mm in diameter rest in box 760 mm wide. Find a. reaction of B on A b. The reaction of the wall on C and 3. The reaction of the floor on B.

12. The roller shown in fig is of mass 150 kg. What force T is necessary to start the roller over the block A?

13. A 600N crate is supported by several rope and pulley arrangements as shown. Determine for each arrangement the tension in the rope.

A

CA

BDCA

fig.11

100mm

25

A

T

350mm

200mmMMMM

P

434

fig. 7

AB30

S2

S1

3600 N6650N2515

fig. 8

fig. 9

fig. 10

40 KG110 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 500N attached to it at B and C. The weight rest with portions AB and CD inclined at angles of 45 and 50respectively 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.

600Nn

600Nn

T

T

600Nn

T

600Nn

T

ABA C

ADA

500

500

A D

B

C

45 50110

Concurrent forces in space1.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 x, y & z 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

O

B

80m

A

40m

30m

y

x

z

7m6m

12m

24m

A

D

B

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 E on 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

y

x

z

3m

3m

60kNm

A

B

D

C

E

3m1.5m 6m 1.5m

2m

x

A,B,C in a horizontal plane

y

z

10

30

3030

60

O

C

9m

650 N

y

x

z

2m

4m

C

D

T1

B

6m4m3m

AT2

T3

M

10kN

+

+

6kN3kN

5kN

8kN

12kNm10kNm

30

450.5m

1.5m

0.5m

1m1.5m 1.5m

.

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 the vector expression for the tension T as a force acting on member AB. Also find the magnitude of the projection of T along line AC.

y

z

A

C

B

D

X

1m

4m2m

4m

20kN

40kN

A

Y

Z

20kN

O

D

CB

2 mAD

5 m

8kN

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 a couple M

3mx

2mO

CB

x

y

z

15m

A

B

12m9m

T=10kN

O

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


x

z

y3m

3m

3m

40kNm

30kNm

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.

UNIT III - Centre of Gravity and Moment of Inertia

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

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

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)

30

40a

40a

30(20,10)

(40,90) (100,100)

30a

(100,30)

20

45a

60a

75

50a

50a


50a

75

250

300


45a

100

75

100

100All dimension are in ‘mm’

x

y

40mm

75mm

200mm

200m

m

x

y

7.Locate the centroid of the following figures with respect to the axes shown.

A. B.

C.

8.A right circular cone of altitude 200mm and radius of base 150mm is welded to a hemisphere 300mm in diameter so that their base coincide. Locate the centroid of the total volume.

9. Located the centroid of the shaded area

10. Determine the centroidal coordinates of the area shown in fig.

x

y

10mm

40mm

40mm

50mm

10mmO

125

y

x25 50

50

25

25

25


xO

y

175

12

75

12

150

12

200

100

40R

60R

80

40

y

100mm

11. Locate the centroid coordinates for the shaded area shown

Moment of inertia

1.

2.Calculate the moment of inertia of the shade area about its centroidal axes.

3. Calculate moment of inertia of the shaded area about x axis

`

60

100

80

x

40

100

R40

10020

All dimensions are in ‘mm’

R50

30

30

100

100

2020

x


X’2mm

Y’

2mm

6mm

10mm

8mm

2

100 100

100

500

600

For the given Z section determine a. Co-ordinate of centroid with respect to x’ and

y’ axesb. Moment of inertia about centroidal x and y axesc. Moment of inertia about x’ and y’ axesd. Product of inertia about centroidal x and y axese. Product of inertia about x’ and y’ axesf. Moment of inertia about two Perpendicular

axes passing through C.G which are inclined at 30 and 120 from x and y axes respectively

g. Principal moment of inertias and the directions of principal axes.

90


R30

X

4.Calculate the moment of inertia of the shaded area about x axis.

5.Calculate the moment of inertia of the shaded area about Centroidal axis

6. Determine the mass moment of inertia of the plates shown in fig. Assume = 8000 kg/m3 and thickness 5mm.

7.Determine the mass moment of inertia of the combination of solids abouta. Centroidal x axisb. About AA axis

8.a. Find principal moment of inertia of the shaded area about centroidal axes. b. Find moment of inertia and product of inertia about x’ and y’ axes.

50

7560

x All dimension are in ‘mm’

50

150

250

R50 R50

100

100

75 75

3030

A

A

40

20

30

150

200

100

10

20

3

1.Cone2. Cylinder3.Hemisphere

9

cm

225

75

75 75

Y’





A A

9. Find moment of inertia of the section about centroidal axes.

10. Determine the moment of inertia of the shaded area about centroidal axes.

11. Determine the moment of inertia of the shaded area about AB and AD

150 150

X’

30

1050

50 50

20

40

20 20

R40

30R1200

60



10

20 20

30

10

10 10

A B

CD

UNIT IV - Dynamics of Particles

1. A particle has straight line motion according to the equation x = t3 – 3t2 - 5 with x in meters and t in seconds. What is the change in displacement while the velocity changes from 8m/s to 40 m/s?

2. A body moves along a straight line so that its displacement from a fixed point on the line is given by s = 3t2 + 2t. Find the displacement velocity and acceleration at the end of 3 seconds.

3. An automobile accelerates uniformly from rest to 72 km/h and then the brakes are applied so that it decelerates uniformly to a stop. If the total time is 15 s, what distance was traveled?

4. A stone is dropped from a balloon that is ascending at a uniform rate of 10 m/s. If it takes the stone 10 s to reach the ground, how high was the balloon at the instant the stone was dropped?

5. Boy A throws a ball vertically up with a speed of 9 m/s from the top of a shed 2.5 m high. Boy B on the ground at the same instant throws a ball vertically up with a speed of 12 m/s. Determine the time at which the two balls will be at the same height above the ground. What is the height?

6. A radar-equipped police car notes a car travelling 110 km/h. The police car starts pursuit 30 s after the observation and accelerates to 160 km/h in 20 s. Assuming the speeds are maintained on a straight road, how far from the observation post will the chase end?

7. The motion of a particle is given by the acceleration a = t3 – 2t2 + 7, where a is in m/s2

and t in seconds. The velocity is 3.58 m/s when t= 1s and the displacement is + 9.39m when t=1s. Calculate the displacement ,velocity and acceleration when t=2.

8. The motion of a particle is defined by the relation v=4t2+3t-5. Knowing the displacement x = - 2m when t=0 s, determine the displacement and acceleration when t=3s.

9. Car A is moving Northwest with a speed of 100km/hr. Car B is moving East with a speed of 60 km/hr. Determine the Velocity of A relative to B. Determine the velocity of B relative to A.

10. A Car enters a curved road ( in the form of a quarter circle) of a length 360m at a speed of 40 km/hr and leaves at 60 km/hr. If the car is travelling with constant with a constant acceleration along the curve, determine the magnitude and direction of acceleration in the Car (a) enters and (b) leaves the curve.

11. A jet of water discharging from ‘O’ hits a screen 6m away at a height of 4m above ‘O’ and when the screen is moved 4m further away, the jet hits it again at the same point. Assuming the curve described by water jet to be a parabola, find the angle at which the jet is projected .

12. A projectile is fired from a point ‘O’ with an initial velocity same as it would be due to fall of 80m from rest. The projectile hits a point at a depth 40m below ‘O’ at a distance of 80m from ‘O’ along the horizontal line. So that the two possible directions of projections are at right angles.

13. Murali is a Basket ball player 1.8m tall throws the balls to the basket from a horizontal distance of 12m as shown in fig. If he shoots at 35 angle with the horizontal, at what initial speed must he throw the ball so that the ball goes through the hoop without striking the board.

14. A radar equipped police car notes a car traveling at 110km/hr. The police car starts pursuit 30 sec after the observation and acceleration to 160Km/hr in 20 sec .Assuming the speeds are maintained on a straight road, how far from the observation point will the chase end.

15. A wheel 2m diameter rotating at 1500rpm accelerate uniformly to 3000rpm in 25sec.Calculatre the number of revolution the wheel makes and tangential velocity at a point on the rim after 1 seconds.

Kinetics of Particles

1. A locomotive exerts a constant pull on a train of mass 300tonnes up an incline of 1 in 200 measured along the slope and in 4km, the speed drops from 72 km/hr to 60km/hr. If the frictional resistance is constant at 50 N/ tonne, Find the pull of the locomotive.

2. A train weighing 1800kN as a velocity 60km/hr when it is in beginning of 1.5% grade as shown in figure. If the pull exerted by the engine 50kN and the tractive resistance is 9 N per KN load find the distance which it will travel up the inclined plane before coming to rest.(fig)

3. A 25kg box is dropped on to a body of a Van moving at a speed of 60km/hr . If the coefficient of the friction is 0.5, Calculate how far the Van will move before the box stops slipping?

4. Block A and B are connected with a bar of negligible weight as shown in fig. If A and B, each weigh 300N, with A =0.25 and B =0.5, Calculate the acceleration of the system and the force in the bar.

5. Two bodies of weight WA=800N and WB=500N are Connected to the two ends of a light in extensible string which passes over a smooth pulley. The weight 800N is placed on an inclined plane of angle 15.If the coefficient of friction is 0.2, Determine the acceleration, tension in string and the distance moved by 500Nin 5 sec starting from rest.

6. Find the acceleration of the blocks and the tension in the cable for the system shown in fig (only E11.12(b)).

7. A block of mass 15kgs is pushed 3m along a frictionless horizontal table by a constant 50N force directed 35 below the horizontal. Determine the workdone by (a) applied force (b) Normal force by the table (c) Force of gravity (d) Net force on the block.

8. A spring is used to stop a 10kg package which is moving down on 25 inclined as shown in fig. The spring constant (k)=30kN/m is held by the cables so that it is initially compressed by 120mm. Knowing that the velocity of package is 3m/s. When it is 8m from the spring, determine the maximum additional deformation of the spring in bringing package to rest. Assume the surface to be smooth.(fig)

9. A ball whose weight is 2kg falls from a height of 7.5m and rebound to a height of 5.8m. Find the impulse and the average force between the ball and the floor, if the time of contact between ball and floor is (1/12) of a second.

10. A Gun of mass 2500kg fires horizontally a shell of mass 40kg with a velocity of 350m/s. What is the velocity with which the Gun will recoil? Also determine the force required to stop the Gun in 0.8m.In how much time will it stop?

11. Two cars travelling in the same straight line collide and remain locked together after impact. Car A as a mass of 2500kg and has a velocity of 15m/s due east. The Car B has a mass of 3750kg and has a velocity of 9m/s due west. Determine the velocity of cars impact. What is the loss in kinetic energy after impact.

12. Two men of mass 60kg and 90kg dive off from the end of a boat of mass 400kg so that there relative velocity with respect to the boat is 8m/s. If the boat is initially at rest determine its final velocity (a) If two men dive simultaneously. (b) the 60kg man dives first followed by 90kg man. (c) The 90kg man dives first followed by 60kg man.

13. Two identical balls B and C are at rest when ball B is struck by a ball A of the same mass moving with a velocity of 6m/s. This causes a series of collisions between various balls. Knowing that e=0.50, determine the velocity of each ball after all collisions have taken place.(fig).

14. A Spherical ball of mass 60kg moving with a velocity of 20m/s overtakes another ball of mass 45kg moving with 16m/s in the same direction. If e=0.5,find the final velocities after collision.

15. The velocity of 2 balls before collision on a horizontal surfaces are shown in fig. knowing that ball A of 9kg rebound to the left with a velocity 9m/s. Determine the rebound velocity of ball B of mass 13.5kg.(fig)

16. Two equal balls moving along with equal speeds impinge, their directions being inclined at 30 and 60 to the line of centers at the time of impact as shown in fig. Show that the balls move in parallel directions at 45 to the line of centers after impact if e=1.(fig)

UNIT V – FRICTION and RIGID BODY DYNAMICS

1. Determine the smallest angle for equilibrium of the homogeneous ladder of length l. The coefficient of friction for all surface is .

2. What horizontal force P on the wedge B and C is necessary to raise the 20kN resting on A. Assume between the wedge and the ground is 0.25 and between the wedge and A is 0.2.Also assume symmetry of loading.

3. Block B rests on block A and is attached by a horizontal rope BC to the wall as shown in fig. What force P is necessary to cause motion of A to impend? The coefficient of friction between A and B is 1/4 and between A and the floor is 1/3 .A has a mass of 14kg and B has a mass of 9kg.

4. Determine the necessary force P acting parallel to the plane to cause motion to impend .Assume the coefficient of friction is0.25 and the pulley smooth.

5. The mean diameter of the threads of a square threaded screw is 50mm.The pitch of the thread is 6mm.The coefficient of friction =0.15 .What force must be applied at the end of a 600mm lever which is perpendicular to the longitudinal axis of the screw to raise a load of 17.5kN? Determine the force required to lower the same load?

6. Two equal pulleys, of diameter 750mm,are connected by a belt .The tension in the tight side of the belt is 200N.If the coefficient of friction is 0.25,determine the tension in the slack side when the belt is about to slip.

7. What force is necessary to hold a mass of 900kg suspended on a rope wrapped twice around a post ? Assume the coefficient of friction = 0.20.

20kN

101 A

B C10

1

P P

A

BBB

PPPP

45B

C

135 kg

45

750 mm 750 mm

P

8. A homogeneous ladder 5m long and having a mass of 55 kg rests against a smooth wall. The angle between it and the floor is 70.The coefficient of friction between the floor and the ladder is 0.25.How far up the ladder can a 80 kg man walk before the ladder slips?

9. The clamp exerts a normal force of 100N on the three pieces held together as shown in fig. What force P may be exerted before motion impends? The coefficient of friction between the pieces is.0.3

10. What force P is needed to drive the 5 wedge to raise the 500 kg mass shown in fig. The coefficient of friction for all surface is 0.25.

11. Block A of mass 27 kg rest on block B of mass 36 kg .Block A is restrained from moving by a horizontal rope tied to the wall at C. What force P parallel to the plane inclined 30 with the horizontal is necessary to start B down the plane? Assume for all surface to be 0.33.

12. The mass of A is 23kg;the mass of B is 36kg .The coefficient of friction are 0.06 between A and B, 0.2 between B and the plane and 0.3 between the rope and the fixed drum. Determine the maximum mass of M before motion impends.

13. Determine the load that can be raised with a single threaded jack- screw having a pitch of 10mm and a mean diameter of 75mm,when a force of 900N is exerted on a bar 750mm long.

14. A vertical force P exerted on lever AB holds the 20kg mass M from falling as shown in fig. The coefficients of friction between the lever ad the 300mm drum is ¼.Neglect the mass of the drum and lever, and determine the force P to hold the mass.

P/2

P/2 P

Clamp

M

B M

A

M

BA

P380 mm

530 mm

All dimension are in mm

P

B

A

30

C

PB

15. In fig M1 and M2 are two masses of 22.5 and 14kg respectively. A rope ties them together parallel to the plane. The coefficient of friction between M1 and the plane is 0.25, and between M2 and the plane it is 0.5.Determine the value of the angle at which sliding will occur. what is the tension in the rope?

16. Determine the force P to cause motion to impend if the coefficient of friction for both blocks and the plane shown in fig is 0.25.The force P and the rope are parallel to the plane .The pulley is frictionless.

17. The uniform bar has a mass of 35kg.What rightward force P is needed to start the bar moving? The coefficient of friction for all surfaces is 0.3.

18. The mass of A is 225 kg and mass of B is 45kg .What force P must be exerted perpendicular to the arm of the jack and 500mm from the jack center line to raise A? The jack-screw has a lead of 8mm and a mean diameter of 50mm.The coefficient of friction between the jack and the screw is 0.15.

M1

M2

30

P

9kg

4.5kg

5m

3m

4m

P

0.5m

B

A

0.5mR 0.25mm

19.The three flat blocks are positioned on the 30 incline as shown, and a force P parallel to the incline is applied to the middle block. The upper block is prevented from moving by a wire, which attaches it to the fixed support. The coefficient of static friction for each of the three pairs of mating surfaces is shown. Determine the maximum value, which P may have before any slipping takes place.

19. The horizontal position of the 500kg rectangular block of concrete is adjusted by the 5 wedge under the action of the force P .If the coefficient of static friction for both pairs of wedge surface is 0.30 and if the coefficient of static friction between the block and the horizontal surface is 0.60,determine the least force P required to move the block.

20. A cord is attached to a block of 50kg mass, the block is positioned on a 20 inclined as shown in fig. the other end of the cord is supporting a cylinder. If the coefficient of friction between the block and the incline is 0.2 and co-efficient of friction between the cord and the cylindrical support surface is 0.3,determine the range of mass of cylinder for which the system is in equilibrium.

21. A clamp is used to hold two piece of wood together as shown. The clamp has double square thread of mean diameter equal to 10mm with a pitch of 2mm.The coefficient of friction between threads is =0.3.If a maximum torque of 40N-m is applied in tightening the clamp, determine (a)The force exerted on the pieces of wood (b). the torque required to loosen the clamp.

22. A force of 360N pulls a body of weight 600N up on a rough plane inclined at 300 to horizontal. The force is applied parallel to the plane. If the weight of the body is increased by 840N, determine the additional pull to be applied parallel to the plane to move the body up the plane.

30

P =0.45

50kg

40kg

30kg=0.30

=0.40

P

500Kg

20

50kg

BLOCKM

=0.2

=0.3

CYLINDER

23. An effort of 500N is required to just move a body up an inclined plane of angle 150

with horizontal. The force is applied parallel to the plane. If the inclination of the plane is increased to 200, the effort applied parallel to the plane is 575N. Find the weight of the body and the coefficient of friction.

24. A 6.5m ladder weighting 200N is placed against a smooth vertical wall with its lower end placed at a distance of 2.5m away from the wall. If the coefficient of friction between the ladder and the floor is 1/3, show that the ladder is in equilibrium at this position. What is the frictional force acting on the ladder at the point of contact between the ladder and the floor?

25. A uniform ladder 700N and 12m long resting on rough horizontal floor is inclined at an angle of 450 with rough vertical wall (w = 0.5). The ladder would just about to slip if a man of weight 1120N reaches a point 9.75m from the lower end of the ladder. Find the coefficient of friction between the ladder and the floor.

26. Find the tension in the cable and the force ‘P’ required to move the blocks towards the right as shown in fig.

Coefficient of friction between ‘B’ and plane = B = 0.2 Coefficient of friction between ‘A’ and plane = A = 0.3

27. A block weighing 10kN is to be raised against a surface inclined at 600 to the horizontal by means of a 150 wedge as shown in fig. Find the horizontal force which will just start the block to move if the coefficient of friction between all contact surfaces is 0.2.

28. A rope is wrapped three turns around a cylinder as shown. Determine the force required to just support a weight of 1kN. Coefficient of friction between the rope and the cylinder is 0.30.

29. Find the power transmitted by a cross belt drive connecting two pulleys of 45.0cm and 20.0cm diameters which are 1.95 apart. The maximum permissible tension in the belt is 1kN, coefficient of friction is 0.20 and the speed of larger pulley is 100 r.p.m.

30. In a flat belt, the maximum tension is 1160N and the angle of lap is 1700. The coefficient of friction between the belt and pulley is 0.25. Diameter of the pulley is 90cm and it runs at 540 rpm. Find the power transmitted at the above speed. Neglect the effect of centrifugal tension.

32. Determine the maximum value of the mass of block B, so that the system remains in equilibrium.

33. A wheel 2m diameter rotating at 1500rpm accelerate uniformly to 3000rpm in 25sec.Calculatre the number of revolution the wheel makes and tangential velocity at a point on the rim after 1 seconds.

34. Find the acceleration and the tension in the cable for the system shown in fig.

35. Determine the velocities of the masses shown in fig after the impact. Assume coefficient of restitution as 0.6.

36. A 150kg stepped pulley with radius of gyration 0.5m is connected to two blocks as shown. Determine the position of the block 10 seconds after starting from rest.

B

A

30

=0.3=0.2

WA=100Kg

WA = 20kgWB = 30kg = 0.3

A

B30

A B

30 60

Line of impact

A = 10 Kg B = 20Kg20 m/sec

30 m/sec

30kg

50kg

0.4m

0.6m

ME 2151 E MECH.doc

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