Problems for Practice

PROBLEMS FOR PRACTICE

On Horizontal and Inclined Planes

1. A body, resting on a rough horizontal plane required a pull of 180 N inclined at 30° to the plane just to move it. It was found that a push of 220 N inclined at 30° to the plane just moved the body. Determine the weight of the body and the coefficient of friction.

[Ans. 3971.47 N; 0.097]

2. An effort of 200 N is required to just move a certain body up an inclined plane of angle 15°, the force acting parallel to the plane. If an angle of inclination of the plane is made 20°, then the effort required parallel to the plane is found to be 230 N. Determine the weight of the body and the coefficient of friction. 

[Ans. 397.5 N; 0.253]

3. A body of weight 450 N is pulled up along an inclined plane with 30° inclination to the horizontal at a steady speed. If the coefficient of friction between the body and the plane is 0.25 and the force is applied parallel to the inclined plane, find the force required. Find, also, the work done on the body, if the distance travelled by the body is 10 m along the plane. 

[Ans. 322.42 N; 3224.2 N.m]

On Square Threaded Screws

4. A bolt with sequence threads has outer diameter of 27.5 mm and pitch of 5 mm. It is tightened by screwing a nut whose mean diameter of bearing surface is 50 mm. The coefficient of friction for nut and bolt is 0.10 and for nut and bearing is 0.15. The nut is tightened by a spanner whose effective lever arm is 400 mm. The load on the bolt' is 10 kN. Determine the force required at the end of the spanner. 

[Ans. 145.25 N]

5. A square threaded bolt of root diameter 22.5 mm and pitch 5 mm is tightened by screwing a nut whose mean diameter of bearing surface is 50 mm. If coefficient of friction for nut and bolt is 0.1 and for nut and bearing surface is 0.16, find the force required at the end of a spanner 500 mm long when the load on the bolt is 10 KN.

 [Ans. 121.15 N].

6. A turn buckle, with right and left hand single start threads is used to couple two wagons. Its thread pitch is 12 mm and mean diameter 40 mm. If μ = 0.16,

(i) Determine the work done in drawing the wagons together a distance of 240 mm, against a steady load of 2500 N. 

(ii) If the load increases from 2500 N to 6000 N over the distance of 240 mm, what is the work to be done? 

[Ans. 815.3 N.m; 1141.4 N.m]

7. A vertical screw with single start square threads 50 mm mean diameter and 12.5 mm pitch is raised against a load of 10 kN by means of a hand wheel, the boss of which is threaded to act as a nut. The axial load is taken up by a thrust collar which supports the wheel boss and has a mean diameter of 60 mm. If the coefficient of friction is 0.15 for the screw and 0.18 for the collar and the tangential force applied by each hand to the wheel is 100 N; find the suitable diameter of the hand wheel. 

[Ans. 1.222 m]
8. A 150 mm diameter valve, against which a steam pressure of 2 MN/m2 is acting, is closed by means of a square threaded screw 50 mm in external diameter with 6 mm pitch. If the toefficient of friction is 0.12; find the torque required to turn the handle.

[Ans. 134.07 N.m]

On Screw Jack

9. The pitch of 50 mm mean diameter threaded screw of a screw jack is 12.5 mm. The coefficient of friction between the screw and the nut is 0.13. Determine the torque required on the screw to raise a load of 25 kN, assuming the load to rotate with the screw. Determine the ratio of the torque required to raise the load to the torque required to lower the load and also the efficiency of the machine.

[Ans. 132.625 N.m; 4.3; 37.7%] 

10. A screw jack has a square thread, 75 mm mean diameter and 15 mm pitch. The load on the jack revolves with the screw. The coefficient of friction at the screw threads is 0.05. 

(i) Find the tangential force to be applied to the jack at 360 mm radius so as to lift a load of 600 N.

(ii) State whether the jack is self-locking. If it is, find the torque necessary to lower the load. If not, find the torque, which must be applied to keep the load from descending. 

[Ans. (i) 7.126 N; (ii) Not self-locking; 0.306 N.m]

On V-threads

11. A bolt is having Y-threads. The pitch of the threads is 5 mm and the V-angle is 55°. The mean diameter of the bolt is 20 mm. The bolt is tightened by screwing a nut. The mean radius of the bearing surface of the nut is 25 mm. The load on the bolt is 5000 N. The coefficient of friction for nut and bolt is 0.1 whereas for nut and bearing surface is 0.16. Determine the force required at the end of a spanner 0.6 m long. 

[Ans. 49.533 N]

On Flat Pivot Bearing

12. A vertical shaft of 140 mm diameter rotating at 120 rpm rests on a flat end footstep bearing. The shaft carries a vertical load of 30 kN. The coefficient of friction is 0.06. Estimate the power lost in friction assuming (i) uniform pressure and (ii) uniform wear. 

[Ans. (i) 1055.88 W; (ii) 294.56 W]

On Conical Pivot Bearing

13. A conical pivot supports a load of 25 kN, the cone angle being 120°, and the intensity of pressure does not exceed 0.25 MPa. The external diameter is twice the internal diameter. Find the outer and inner radii of the bearing surface. If the shaft rotates at 180 rpm and the coefficient of friction is 0.15, find the power lost in friction assuming uniform pressure. 

[Ans. 103 mm; 206 mm; 13.08 kW]

On Thrust Bearing

14. In a thrust bearing the external and internal radii of the contact surfaces are 210 mm and 160 mm respectively. The total axial load is 60 kN and coefficient of friction = 0.05. The shaft is rotating at 380 rpm. Intensity of pressure is not to exceed 350 kN/m2. Calculate: (i) Power lost in overcoming the friction, and (ii) Number of collars required for the thrust bearing. 

[Ans. (1) 22.2 kW; (ii) 3]