Friction Probs

# Friction Probs - 182 PROS 5.9 PROB 5.14 FRICTION H O M 5.9...

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Unformatted text preview: 182 PROS. 5.9 PROB. 5.14 FRICTION H O M 5.9 5.12 U] {— ’JI EWORK PROBLEMS Determine the force F required to cause motion in the system shOWn. At which surfaces will sliding occur? The coefﬁcient of static friction between the 2 kg block A and the 8 kg block B is p5 = 0.2 and the coefﬁcient of static friction between block B and the horizontal plane is [,ts = 0.1. The coefﬁcient of static friction between the person and the ﬂoor is 0.50, and the coefﬁcient of static friction between the crate and the ﬂoor is 0.25. Determine the largest mass for the crate that the person can move by pulling on the cable if the person’s mass is 70 kg. PROB. 5.10 PROB. 5.11 The coefﬁcient of static friction between each block and the surface it contacts is 0.2. Block A weighs 41b and block B weighs 6 lbs. Determine the largest angle (9 of the incline for which the blocks will remain at rest. The masses of blocks A and B are 5 and 10kg, respectively. The coefﬁcient of static friction between block A and its incline is 0.20. Determine the minimum coefﬁcient of static friction between block B and its incline required to maintain equilibrium. If this coefﬁcient is not sufﬁciently large, in which direction will the blocks slide? Solve Problem 5.12 if block A has a mass of 10 kg and block B has a mass of 5 kg. The masses of blocks A and C are 10 and 20 kg, respectively. These blocks are interconnected by cords AB and BC. Knowing that the system is in equilibrium, determine (a) the friction force acting on each block, (b) the minimum allowable coefﬁcient of static friction between each block and its surface for static equilibrium. Two 3 kg collars are connected by a cord and are in equilibrium in the position shown. The coefﬁcient of static friction between collar A and its inclined guide is 0.30. Determine the minimum allowable value of the coefﬁcient of static friction between collar B and its guide. PROB. '5.15 PROB. 5.16 2ft B 0 __L PROBS. 5.20 AND 5.21 PROB. 5.22 A. DRY FRICTION “ 183 *5.16 *5.17 5.18 5.20 5.21 Three suitcases A, B, and C are placed on a chute. Their weights are wA = wB = 30 lb, wc = 45 lb. The coefﬁcients of static_ friction between the suitcases and the chute are [1,, = MB = 0.40, pc 2 0.20. Determine which, if any, of the suitcases will slide down the chute. Hint: Succes- sively consider the possibility of impending motion of suitcase A ' alone, then of both suitcases A and B, and finally of all three suitcases. A 10 lb block resting on a plane inclined at 20" above the horizontal is subjected to a horizontal force F parallel to the plane, as shown. It is observed that the block will start to move if the magnitude of I—3 exceeds 3 lb. Determine (a) the coefﬁcient of static friction between the block and the inclined plane, (b) the direction in which the block starts to slide if the magnitude of F exceeds 3 lb. B y . A gr ,1: A o ‘ PROB. 5.17 PROBS. 5.18 AND 5.19 The uniform 80 kg bar rests against the rough vertical wall. The horizontal force I-3 is 400 newtons acting to the right. Determine (a) the friction force at end B, and (b) the minimum coefﬁcient of static friction between the bar and the wall for which static equilibrium is possible. The coefﬁcient of static friction between the 80 kg uniform bar and the rough vertical wall is 0.3. Determine the smallest horizontal force I3 at end A for which static equilibrium is possible. The uniform 20 lb bar is supported by a roller on the inclined wall and by the rough horizontal surface. The bar is in static equilibrium and 0 = 30°. Determine (a) the friction force acting on end A, and (b) the minimum coefﬁcient of static friction between the bar and the horizontal surface. The coefﬁcient of static friction between the uniform 20 lb bar and the horizontal surface at end A is 0.40. The inclined‘surface at end B is smooth. Determine the maximum angle 0 for which static equilib- rium is possible. The 3 ft diameter cylinder weighs 500 lb. The coefﬁcient of friction between the cylinder and both surfaces is it, = 0.32. Determine the maximum magnitude of the counterclockwise couple A7! for which sliding will not occur. 184 PROB. 5.23 FRICTlON 5.23 5.25 *5.26 5.27 A 2 kN load is applied to the linkage, as shown. Knowing that the system is in equilibrium, determine (a) the friction force acting on bar AB at end A, (b) the minimum value of the coefﬁcient of static friction for which static equilibrium is possible. The mass of the bars is negligible. The semicylinder of mass m and radius R is in a condition of impending motion. The coefﬁcient of static friction between the semicylinder and the inclined planes are the identical values p, and point G is the center of mass of the semicylinder. Determine u. PROB. 5.24 PROB. 5.25 The masses of the bars and the collar are negligible, and the system is in static equilibrium. Determine (a) the friction and normal forces acting on the collar, and (b) the minimum possible coefﬁcient of static friction between the collar and the guide for which the system will remain in static equilibrium. Solve Problem 5.25 if the mass of each bar is 20 kg. A cable is wrapped around the 50kg stepped drum and a tensile force 1’3 is applied to the free end of the cable, as shown. The drum is in static equilibrium. Determine (a) the magnitude of I3 and of the friction force acting on the drum, (b) the direction in which the point on the drum in contact with the inclined surface is tending to move, and (c) the minimum value of the coefﬁcient of static friction for which static equilibrium is possible. PROB. 5.27 PROB. 5.28 I PROB. 5.32 re————1ﬂ———>' A. DRY FRICTION 5.28 185 The 1000 lb stepped drum is held in static equilibrium by the tensile force I5 applied to the cable. The drum is supported on its inner radius by two rails (only one is visible in the side view shown). Determine (a) the magnitude of 13, (b) the friction force exerted by each rail on the drum, and (c) the minimum allowable coefﬁcient of static friction between the drum and a rail. The coefﬁcients of static friction between the ladder and the wall, and the ladder and the ground, are 0.2 and 0.3, respectively. Determine the minimum horizontal distance d between the center of mass G of the 60 kg worker and the wall for which the ladder will not slide. The mass of the ladder is negligible. Solve Problem 5.29 if the mass of the ladder is 10 kg. PROB. 5.29 PROB. 5.31 The coefﬁcient of friction between the uniform 30 kg bar and both surface is ,u: = 0.20. Is the system in static equilibrium? The coefﬁcient of friction between the uniform 5 lb bar and both inclined walls is 0.30. Is the bar in static equilibrium in the horizontal position shown? Point G is the center of mass of the 10 kg semicylinder. If the system is in static equilibrium, determine (a) the angle 6, and (b) the minimum allowable coefﬁcient of static friction between the semicylinder and the ground. 4r/37r ‘<’ PROB. 5.33 186 200mm PROBS. 5.34 AND 5.35 Hydraulic cylinder PROBS. 5.40 AND 5.41 FRICTION 5.34 The adjustable bracket is supported on the vertical guide by collars at A and B. The coefﬁcient of static friction between each collar and the guide is 0.20, and mass of the bracket is negligible. Determine the magnitude of the vertical force F required to move the bracket upward from rest. ’ 5.35 In Problem 5.34, determine the magnitude and sense of the vertical force F required to move the bracket downward from the rest position. 5.36 The 200 lb-in. couple is applied to rod AB in order to resist the 70 lb force applied to piston C. Knowing that the linkage is in static equilib- rium at the position where 9 = 90°, determine (a) the friction force acting on the piston, and (b) the minimum coefﬁcient of static friction between the piston and its cylinder for which this situation is possible. 5.37 Solve Problem 5.36 for the position where 9 = 135°. 200mm PROBS. 5.36 AND 5.37 5.38 The coefﬁcient of static friction between collar B and bar CD is 0.25. The bars have negligible mass. Determine the magnitude of the couple IV! A for which bar AB will rotate clockwise from rest. 5.39 In Problem 5.38, determine the magnitude and sense of the couple M A for which bar AB will rotate counterclockwise from rest. 5.40 A couple MC is applied to the brake drum C. Determine the smallest force exerted by the hydraulic cylinder on brake arm AB for which the brake drum will not rotate if MC is 300 N-m clockwise. The coefﬁcient of static friction between the drum and the arm is 0.75. 5.41 Solve Problem 5.40 if MC is 300 N-m counterclockwise. *5.42 The coefﬁcient of static friction between the 2 kg bar and both surfaces it contacts is 0.20. Determine the largest and smallest values of the angle 6 for which the bar is in static equilibrium. PROBS. 5.38 AND 5.39 PROB. 5.42 PROB. 5.43 *5.43 The 3 lb bar AB is supported by the 2 lb bar CD. Determine the minimum values of the coefﬁcients of static friction between each pair of contact surfaces for which static equilibrium is possible. A. DRY FRICTION 1 87 50mm 40mm *5.44 A 50 mm diameter rod is being gripped by the Stilson wrench shown. Members A ~and B may be regarded as a single rigid body connected to member C only by pin D. It is observed that, regardless of the magnitude of the force 13, the wrench does not slip over the rod (the wrench is said to be self-locking). Determine the minimum coefficients of static friction at both points of contact between the wrench and the pipe. *5.45 A 5ft long bar is connected to the ﬂoor by a ball-and-socket joint that is 4 ft from the vertical wall supporting the other end of the bar. The bar weighs 20 lb and the coefficient of static friction between the bar and the wall is 0.35. Determine the maximum value of the angle 8 for which static equilibrium is possible. Hint: Because of the support at end A, end B tends to move tangent to the dashed circle. PROB. 5.44 PROB. 5.45 PROB. 5.46 5.46 A 30 kg plank is resting on two horizontal joists, perpendicular to the axis of the joists in the horizontal plane. The coefﬁcient of static friction between the plank and the joists is 0.40. Determine the force 1—), parallel to the joists, required to move the plank when d = 2 m. H int: The friction forces acting on the plank may be considered to be parallel to the joists. 3. Sliding or Tipping The impending motion we have considered thus far originated from the tendency of the pair of contacting surfaces to slide over each other. Another type of impending motion that is possible is the tendency of the external forces acting on a body to overturn (that is, tip over) the body. This type of motion arises whenever the frictional and normal reactions cannot exert a moment that is sufﬁcient to balance the moment of the external forces. As an example, consider the horizontal force that the person in Figure 63 must apply to the ﬁle cabinet in order to move the cabinet. If the person exerts a sufﬁciently large force close to the ground, as in Figure 6b, the 190 PROBS. 5.47 AND 5.48 FRICTION The value of P for tipping is smaller than that required to slide the crate. Thus, we conclude that the crate will tip and P ax = 503 newtons . A m Additional Remarks It “Q11 be noted that we solved the case of impending slipping without em- ploying the moment equilibrium equation. This is a consequence of the coefﬁcients of static friction at skids A and B being equal. If these coefficients were diﬁerent, we would have needed 2 F , and Z M A, to ﬁnd the individual values of NA and NB. An interesting aside to this problem is its similarity to the problem posed in part (c) of Example 1. It can be seen that concern about the possibility of impending tipping, which always requires that we consider moment equilibrium, complicates the solution of problems involving impending motion. HOMEWORK PROBLEMS 5.47 The coefﬁcient of static friction between the 1 ton granite block and the ﬂoor is 0.35, and h = 2.5 ft. Determine the largest horizontal force F that will not move the block. 5.48 The coefﬁcient of static friction between the 1 ton granite block and the ﬂoor is 0.35. Determine the largest distance h for the horizontal force F for which slipping will occur before tipping. 5.49 A 60 kg refrigerator, having center of mass G, is mounted on four casters. The coefﬁcient of static friction between a locked caster and the ﬂoor is 0.50, and the frictional resistance of a rolling caster is negligible. Determine the magnitude of the horizontal force 15 required to move the refrigerator when h = 1.0 m if all casters are locked. 5.50 Solve Problem 5.49 if only casters B are locked. mm mm PROB. 5.49 A. DRY FRICTION 191 r 5.51 In Problem 5.49, determine the largest value of h-for which the re- frigerator will not tip (a) if all casters are locked, (b) if only casters B are locked. (c) Explain why it is impossible to tip the refrigerator over with the force P when only casters A are locked. 5.52 A 60 kg cabinet whose center of mass is point G is supported by skids along edges A and B. The coefﬁcients of static friction between the skids and the incline are m = #3 = 0.75. Determine the largest force F, parallel to the incline, for which the cabinet will not move. 5.53 Solve Problem 5.52 if [AA = 0.5 and p3 = 0.90. 5.54 Determine the magnitude and sense of the force 13 for which the cabinet in Problem 5.52 is in a state of impending motion down the incline. PROB. 5.52 5.55 The center of mass of the 120 lb table is point G. The table is supported by four casters, each of which is locked. The coefﬁcient of static friction between a locked caster and the incline is 0.60. Determine the magnitude and sense of the horizontal force P for which the table is in a state of impending motion down the incline. 5.56 Solve Problem 5.55 if only caster A are locked. The friction between the unlocked casters B and the incline is negligible. PROB. 5.55 PROB. 5.57 5.57 The 25 kg door is mounted on the horizontal rail by means of runners A and B. The coefﬁcients of friction for these runners are m = #3 = 0.15. The door handle is pulled to the right to open the door. Determine (a) the maximum distance d for the door handle for which the door will not tip when it is opened, (b) the force required to open the door if d equals the value found in part (a), and (c) the force required to open the door if d equals one-half the value found in part (a). Solve Problem 5.57 if [AA = 0.20, #3 = 0.10. The 8 lb thin semicylindrical shell is to be towed to the left. The coefﬁcient of static friction between the shell and the surface is 0.35. Determine the largest angle a for which the cable tension T will cause the shell to slide to the left without tipping. What is the corre- PROB. 5.59 sponding value of T? 192 PROB. 5.60 PROB. 5.63 FRICTION 5.60 *5.61 *5.62 *5.64 The angle [3 of the incline is very gradually increased until the block of mass m moves. Develop formulas that indicate whether the block slides or tips in terms of the coefﬁcient of friction u, the ratio b/h, and the angle if at which movement occurs. The bar of mass m is supported in the vertical plane by pins A and B, which are separated by a distance d. The coefﬁcient of static friction between each pin and the bar is 0.70. Determine the largest value of d for which static equilibrium is possible. 500mm PROB. 5.61 PROB. 5.62 A 500 kg electronic computer, having center of mass G, is placed on the 20 kg dolly. The casters A of the dolly are locked. The coefﬁcients of friction between the computer and the dolly, and between the casters and the ﬂoor, are 0.50 and 0.30, respectively. Determine the maximum force F that can be applied without causing the computer to move. The 80 kg block rests against the vertical wall in the position shown. Determine the largest horizontal force 175 for which the block will not move if the coefﬁcient of friction between the ground and the block is 0.50, and the vertical wall is smooth. Solve Problem 5.63 for the case where the coefﬁcient of friction between the block and each surface it contacts is 0.5. 8. BASIC MACHINES HAVING FRICTION There are a multitude of simple mechanical devices, that we refer to as basic machines, that can be used to either move or prevent the motion of physical objects. These devices can magnify or convert the input forces applied to them into a different set of output forces that are applied to other systems. For example, a wheel ﬁxed to an axle has the capability of trans- forming a torque exerted by its axle into a forward force that can propel a vehicle. In Chapter 4, we developed the basic techniques for investigating the equilibrium of machines. The common feature of the machines we shall consider here is the important, and sometimes useful, effect of friction. ...
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## This note was uploaded on 09/08/2010 for the course ME 270 taught by Professor Murphy during the Summer '08 term at Purdue.

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Friction Probs - 182 PROS 5.9 PROB 5.14 FRICTION H O M 5.9...

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