A 1.2-m plank with a mass of 3 kg rests on two joists. Knowing that the coefficient of static friction between the plank and the joists is 0.30, determine the magnitude of the horizontal force required to move the plank when (a) a = 750 mm, (b) a = 900 mm.
Fig. P8.37
(a)
Find the magnitude of the horizontal force required to move the plank.
Answer to Problem 8.37P
The magnitude of the horizontal force required to move the plank is
Explanation of Solution
Given information:
The length of the plank is
The mass of each plank is
The coefficient of static friction between the plank and the joists is
The distance between the points A and C in the plank is
Calculation:
Find the friction force (F) using the relation.
Show the free-body diagram of the member AB is vertical plane as in Figure 1.
Take moment about point A.
Resolve the vertical component of forces.
Show the free-body diagram of the member AB is horizontal plane as in Figure 2.
Take moment about point A.
Resolve the vertical component of forces.
Find the weight of the plank (W) using the relation.
Here, the acceleration due to gravity is g.
Consider the acceleration due to gravity is
Substitute 3 kg for m and
Substitute 29.43 N for W, 1.2 m for L, and 750 mm for a in Equation (1).
Substitute 29.43 N for W, 1.2 m for L, and 750 mm for a in Equation (2).
Substitute 1.2 m for L, and 750 mm for a in Equation (3).
Substitute 1.2 m for L, and 750 mm for a in Equation (4).
At point A, the plank to slip;
Find the horizontal force P using the relation.
Substitute 0.6P for
At point C, the plank to slip;
Find the horizontal force P using the relation.
Substitute 1.6P for
The smallest value of P will slip the plank. The plank will slip at A.
Therefore, the magnitude of the horizontal force required is
(b)
Find the magnitude of the horizontal force required to move the plank.
Answer to Problem 8.37P
The magnitude of the horizontal force required is
Explanation of Solution
Given information:
The length of the plank is
The mass of each plank is
The coefficient of static friction between the plank and the joists is
The distance between the points A and C in the plank is
Calculation:
Refer part (a) for calculation.
Substitute 29.43 N for W, 1.2 m for L, and 900 mm for a in Equation (1).
Substitute 29.43 N for W, 1.2 m for L, and 900 mm for a in Equation (2).
Substitute 1.2 m for L, and 900 mm for a in Equation (3).
Substitute 1.2 m for L, and 900 mm for a in Equation (4).
At point A, the plank to slip;
Find the horizontal force P using the relation.
Substitute 0.3333P for
At point C, the plank to slip;
Find the horizontal force P using the relation.
Substitute 1.3333P for
The smallest value of P will slip the plank. The plank will slip at C.
Therefore, the magnitude of the horizontal force required is
Want to see more full solutions like this?
Chapter 8 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
- Two 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_forwardA 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_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
- 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_forwarda 1.2-m plank with a mass of 3kg rests on two joists. knowing that the coefficient of static friction between the plank and the joists is 0.30, determine the magnitude of the horizontal force required to move the plank when a=750mm and a=900mmarrow_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
- 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 window sash weighing 10 lb is normally supported by two 5-lb sash weights. Knowing that the window remains open after one sash cord has broken, determine the smallest possible value of the coefficient of static friction. (Assume that the sash is slightly smaller than the frame and will bind only at points A and D.)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_forward
- A 16-lb spool is at rest on an inclined surface. Around its center a cable is wound which travels with the same inclination of the ramp, passes through a frictionless pulley, and is attached to a block B at its other end.The coefficient of static friction between block B and the floor is 0.25. For the position shown, with the given value of α, determine: R (in) = 11,1 in r (in) = 7 in α (°) = 16° 1. The minimum coefficient of static friction that must exist between the reel and the floor of the ramp, so that the reel does NOT slide on the ramp (does not slip). 2.The minimum weight that block B must have for the reel to NOT roll down the ramp dragging block B. Do not allow for the possibility of the block turning or tipping over.arrow_forwardTwo slender rods of negligible weight are pin-connected at C and attached to blocks A and B, each of weight W. Knowing that P =1.260W and that the coefficient of static friction between the blocks and the horizontal surface is 0.30, determine the range of values of θ,between 0 and 180°, for which equilibrium is maintained.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
- 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