A 15° wedge is forced under a 50-kg pipe as shown. The coefficient of static friction at all surfaces is 0.20. (a) Show that slipping will occur between the pipe and the vertical wall. (b) Determine the force P required to move the wedge.
Fig. P8.64 and P8.65
(a)
Show that the slipping will occur between the pipe and the vertical wall.
Explanation of Solution
Given information:
The mass of the pipe is
The value of angle
The coefficient of static friction at all surfaces is
Calculation:
Find the weight (W) of the pipe using the relation.
Here, the acceleration due to gravity is g.
Consider the acceleration due to gravity is
Substitute 50 kg for m and
Show the free-body diagram of the pipe as in Figure 1.
Find the friction force at point A using the relation.
Here, the normal force at point A is
Find the normal force at point A by taking moment about point B.
Substitute 490.5 N for W, 0.20 for
Find the friction force at point B
Substitute 490.5 N for W, 0.20 for
Find the normal force at point B
Substitute 490.5 N for W, 0.20 for
Find the maximum friction force at point B using the relation.
Substitute 0.20 for
The friction force at point B is less than the maximum friction force at point B.
Therefore, the slipping will not occur at point B and the slipping will occur between the pipe and the vertical wall.
(b)
Find the force P required to move the wedge.
Answer to Problem 8.64P
The force P required to move the wedge is
Explanation of Solution
Given information:
The mass of the pipe is
The value of angle
The coefficient of static friction at all surfaces is
Calculation:
Show the free-body diagram of the wedge as in Figure 2.
Find the normal force
Substitute 554.155 N for
Find the force P by resolving the horizontal component of forces.
Substitute 554.155 N for
Therefore, the force P required to move the wedge is
Want to see more full solutions like this?
Chapter 8 Solutions
VECTOR MECHANICS FOR ENGINEERS: STATICS
- Solve Prob. 8.62 assuming that the wedge is to be forced under the machine base at B instead of A.(Reference to Problem 8.62):A 5° wedge is to be forced under a 1400-lb machine base at A . Knowing that the coefficient of static friction at all surfaces is 0.20, (a) determine the force P required to move the wedge, (b) indicate whether the machine base will move.arrow_forwardThe double pulley shown is attached to a 10-mm-radius shaft that fits loosely in a fixed bearing. Knowing that the coefficient of static friction between the shaft and the poorly lubricated bearing is 0.40, determine the magnitude of the force P required to start raising the load.arrow_forwardA slender steel rod with a length of 225 mm is placed inside a pipe as shown. Knowing that the coefficient of static friction between the rod and the pipe is 0.20, determine the largest value of 0 for which the rod will not fall into the pipe.arrow_forward
- The double pulley shown is attached to a 10-mm-radius shaft that fits loosely in a fixed bearing. Knowing that the coefficient of static friction between the shaft and the poorly lubricated bearing is 0.40, determine the magnitude of the force P required to maintain equilibrium.arrow_forwardA recording tape passes over the 20-mm-radius drive drum B and under the idler drum C . Knowing that the coefficients of friction between the tape and the drums are μs= 0.40 and μk= 0.30 and that drum C is free to rotate, determine the smallest allowable value of P if slipping of the tape on drum B is not to occur.arrow_forwardBlock A supports a pipe column and rests as shown on wedge B . Knowing that the coefficient of static friction at all surfaces of contact is 0.25 and that 0 = 45°, determine the smallest force P required to raise block A.arrow_forward
- A cable is placed around three parallel pipes. Two of the pipes are fixed and do not rotate; the third pipe is slowly rotated. Knowing that the coefficients of friction are μs= 0.25 and μk= 0.20, determine the largest weight W that can be raised (a) if only pipe A is rotated counterclockwise, (b) if only pipe C is rotated clockwise.arrow_forwardSolve Prob. 8.124 assuming that the idler drum C is frozen and cannot rotate.(Reference to Problem 8.124):A recording tape passes over the 20-mm-radius drive drum B and under the idler drum C . Knowing that the coefficients of friction between the tape and the drums are μs= 0.40 and μk= 0.30 and that drum C is free to rotate, determine the smallest allowable value of P if slipping of the tape on drum B is not to occur.arrow_forwardA block with weight W is pulled up a plane forming an angle a with the horizontal by a force P directed along the plane. μ If is the coefficient of friction between the block and the plane, derive an expression for the mechanical efficiency of the system. Show that the mechanical efficiency cannot exceed 1/2 if the block is to remain in place when the force P is removed.arrow_forward
- A 12° wedge is used to spread a split ring. The coefficient of static friction between the wedge and the ring is 0.30. Knowing that a force P with a magnitude of 120 N was required to insert the wedge, determine the magnitude of the forces exerted on the ring by the wedge after insertion.arrow_forwardKnowing that the coefficient of static friction is 0.30 between the rope and the horizontal pipe and that the smallest value of P for which equilibrium is maintained is 80 N, determine (a) the largest value of P for which equilibrium is maintained, (b) the coefficient of static friction between the rope and the vertical pipe.arrow_forwardTwo slender rods of negligible weight are pin-connected at C and attached to blocks A and B , each with a weight W . Knowing that P = 1.260 W and that the coefficient of static friction between the blocks and the horizontal surface is 0.30, determine the range of values of 0 between 0 and 180° for which equilibrium is maintained.arrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY