# Essentials of Mechanical Engineering (LA1210) Tutorial sheet

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Essentials of Mechanical Engineering (LA1210) Tutorial sheet No 1 (Concurrent Coplanar Force system) Don’t copy from others. Do discuss with others including me.

Submit by January 16, 2015 by 4 PM

1. Write short notes on the following: (a) Active force and reactive force (b) Transmissibility of force (c) Coplanar, collinear and concurrent force (d) Lami’s theorem (e) Static equilibrium (f) Rigid body and deformable body

2. Draw FBD and find all unknown forces in figures ‘a’ to ‘e’

Fig (d)

Fig (a)

Fig (b)

Fig (c) Fig (e)

3. A weight of 2000N is supported by two chains AC and BC as shown in figure 1. Determine the tension in each chain.

Figure 1

Figure 2

Figure 3

4. An electric light fixture weighing 50 N hangs from point C by two strings AC and BC as shown in figure 2.

The string AC is inclined at 60° to the horizontal and string BC is inclined at 45° to the vertical plane.

Determine the forces in the strings AC and BC. [Ans: 36.6 N and 25.88 N]

5. A smooth circular cylinder of radius 1.5m is lying in a triangular groove, one side of which makes 15° angle and the other 40° angle with the horizontal as shown in figure 3. Find the reactions at the surfaces of contact if there is no friction and the cylinder weighs 1000 N. [Ans. RA = 784.7 N, RB = 315.9 N]

6. A circular roller of weight 5000N rests on a smooth inclined plane and is held in position by a cord AC as shown in figure 4. Find the tension in the cord if there is a horizontal force of magnitude 1000 N acting at C. [Ans: T=3950.8N]

Prepared by: Dr Gopal Nandan

Section ECE-(B)

Essentials of Mechanical Engineering (LA1210) Tutorial sheet No 1 (Concurrent Coplanar Force system)

7. Find the value of F1 and F2 if the value of α lies between 90 to 170 degree as shown in figure 5. 8. Figure 6 shows a sphere resting in a smooth V shaped groove and subjected to a spring force. The spring is

compressed to a length of 100 mm from its free length of 150 mm. if stiffness of spring is 2N/mm. Determine the contact reactions atA and B.

P = 1000N

Figure 4

Figure 5

Figure 6

Figure 7

9. A sphere of 500N is hanging against an inclined plane as shown in figure 7. Find the contact force between inclined plane and sphere.

10. A circular roller of weight 400N rests on a vertical smooth plane and is held by chord as shown in figure 8. Find the reaction force offered by vertical plane and tension in the string. Assume the angle between string and vertical plane is 25o.

11. The sphere of a mass of 6 kg and is supported as shown in figure 9. Draw a FBD of the sphere, the chord CE and knot at C. Calculate the tension developed in the chords if pulley is smooth. The spring constant is 10 N/mm and the spring is elongated by 2mm.

12. Determine the force in each cable and the force F needed to hold the 4 kg lamp in the position shown in figure 10.

Figure 8

Figure 9

Figure 10

13. Calculate the tensile force in the cables AB and BC as shown in figure 10. Assume the pulleys are smooth. [Ans: 206.21N, 53.45N]

14. Two persons lift a mass of 100 kg by cables passing over two pulleys as shown in Fig. 11. Determine the forces P and Q that must be applied by the two persons if the body is in equilibrium at the position shown.

Prepared by: Dr Gopal Nandan

Section ECE-(B)

Essentials of Mechanical Engineering (LA1210)

Tutorial sheet No 1 (Concurrent Coplanar Force system)

15. Two smooth spheres each of weight 250N and of radius 0.2m are in equilibrium in a horizontal channel of width 0.5 m and vertical sides as shown in figure 13. Find the three reactions from the sides of channel which are all smooth. Also find the force exerted by each sphere on the other.

Figure 11

Figure 12

Figure 13

16. Two identical rollers each of weight 50 N rest on an inclined plane (Figure 13) which makes an angle 60° with the vertical wall. Find reactions at all points of contact supports assuming all surfaces to be smooth. [Ans: Ra = 43.3N, RB=72N, Rc =57.5N]

17. Three cylinders are piled in a rectangular ditch as shown in figure 14. If the radius of cylinder A, B is 5 cm and radius of C is 8 cm. The weight of cylinder C is 500 N and weight of A and B is negligible. Find all contact forces if MN=25 cm. Neglecting frictional force.

Figure 14

Figure 15

Figure 16

18. Three cylinders are placed on two inclined planes MN and PQ as shown in figure 15. If the radius of cylinder A, B is 10 cm and radius of C is 15 cm. The weight of cylinder A, B and C is 200N, 200N and 300 N respectively. Draw neat and clean FBD of A, B and C and find contact forces on body A if MP=50 cm. Neglecting frictional force.

19. Three cylinders A, B and C having weight 100 N, 200 N and 100 N respectively, are piled in a rectangular ditch as shown in figure 16. If the radius of cylinder A, C is 5 cm and radius of B is 8 cm. Find all contact forces if MN=25 cm. Neglecting frictional forces.

20. Find the tension in each chord if all the pulleys are smooth as shown in figure at corner.

Prepared by: Dr Gopal Nandan

Section ECE-(B)

Submit by January 16, 2015 by 4 PM

1. Write short notes on the following: (a) Active force and reactive force (b) Transmissibility of force (c) Coplanar, collinear and concurrent force (d) Lami’s theorem (e) Static equilibrium (f) Rigid body and deformable body

2. Draw FBD and find all unknown forces in figures ‘a’ to ‘e’

Fig (d)

Fig (a)

Fig (b)

Fig (c) Fig (e)

3. A weight of 2000N is supported by two chains AC and BC as shown in figure 1. Determine the tension in each chain.

Figure 1

Figure 2

Figure 3

4. An electric light fixture weighing 50 N hangs from point C by two strings AC and BC as shown in figure 2.

The string AC is inclined at 60° to the horizontal and string BC is inclined at 45° to the vertical plane.

Determine the forces in the strings AC and BC. [Ans: 36.6 N and 25.88 N]

5. A smooth circular cylinder of radius 1.5m is lying in a triangular groove, one side of which makes 15° angle and the other 40° angle with the horizontal as shown in figure 3. Find the reactions at the surfaces of contact if there is no friction and the cylinder weighs 1000 N. [Ans. RA = 784.7 N, RB = 315.9 N]

6. A circular roller of weight 5000N rests on a smooth inclined plane and is held in position by a cord AC as shown in figure 4. Find the tension in the cord if there is a horizontal force of magnitude 1000 N acting at C. [Ans: T=3950.8N]

Prepared by: Dr Gopal Nandan

Section ECE-(B)

Essentials of Mechanical Engineering (LA1210) Tutorial sheet No 1 (Concurrent Coplanar Force system)

7. Find the value of F1 and F2 if the value of α lies between 90 to 170 degree as shown in figure 5. 8. Figure 6 shows a sphere resting in a smooth V shaped groove and subjected to a spring force. The spring is

compressed to a length of 100 mm from its free length of 150 mm. if stiffness of spring is 2N/mm. Determine the contact reactions atA and B.

P = 1000N

Figure 4

Figure 5

Figure 6

Figure 7

9. A sphere of 500N is hanging against an inclined plane as shown in figure 7. Find the contact force between inclined plane and sphere.

10. A circular roller of weight 400N rests on a vertical smooth plane and is held by chord as shown in figure 8. Find the reaction force offered by vertical plane and tension in the string. Assume the angle between string and vertical plane is 25o.

11. The sphere of a mass of 6 kg and is supported as shown in figure 9. Draw a FBD of the sphere, the chord CE and knot at C. Calculate the tension developed in the chords if pulley is smooth. The spring constant is 10 N/mm and the spring is elongated by 2mm.

12. Determine the force in each cable and the force F needed to hold the 4 kg lamp in the position shown in figure 10.

Figure 8

Figure 9

Figure 10

13. Calculate the tensile force in the cables AB and BC as shown in figure 10. Assume the pulleys are smooth. [Ans: 206.21N, 53.45N]

14. Two persons lift a mass of 100 kg by cables passing over two pulleys as shown in Fig. 11. Determine the forces P and Q that must be applied by the two persons if the body is in equilibrium at the position shown.

Prepared by: Dr Gopal Nandan

Section ECE-(B)

Essentials of Mechanical Engineering (LA1210)

Tutorial sheet No 1 (Concurrent Coplanar Force system)

15. Two smooth spheres each of weight 250N and of radius 0.2m are in equilibrium in a horizontal channel of width 0.5 m and vertical sides as shown in figure 13. Find the three reactions from the sides of channel which are all smooth. Also find the force exerted by each sphere on the other.

Figure 11

Figure 12

Figure 13

16. Two identical rollers each of weight 50 N rest on an inclined plane (Figure 13) which makes an angle 60° with the vertical wall. Find reactions at all points of contact supports assuming all surfaces to be smooth. [Ans: Ra = 43.3N, RB=72N, Rc =57.5N]

17. Three cylinders are piled in a rectangular ditch as shown in figure 14. If the radius of cylinder A, B is 5 cm and radius of C is 8 cm. The weight of cylinder C is 500 N and weight of A and B is negligible. Find all contact forces if MN=25 cm. Neglecting frictional force.

Figure 14

Figure 15

Figure 16

18. Three cylinders are placed on two inclined planes MN and PQ as shown in figure 15. If the radius of cylinder A, B is 10 cm and radius of C is 15 cm. The weight of cylinder A, B and C is 200N, 200N and 300 N respectively. Draw neat and clean FBD of A, B and C and find contact forces on body A if MP=50 cm. Neglecting frictional force.

19. Three cylinders A, B and C having weight 100 N, 200 N and 100 N respectively, are piled in a rectangular ditch as shown in figure 16. If the radius of cylinder A, C is 5 cm and radius of B is 8 cm. Find all contact forces if MN=25 cm. Neglecting frictional forces.

20. Find the tension in each chord if all the pulleys are smooth as shown in figure at corner.

Prepared by: Dr Gopal Nandan

Section ECE-(B)

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