Chapter 15: Homework Problems 15-61

10.1 A force P acts on a block having a mass of m with the block resting on a rough incline.The coefficients of static and kinetic friction between the block and the incline are µsand µk, respectively.

(a) Determine the minimum force P required to hold the block in equilibrium.

(b) Determine the minimum force P required to initiate motion of the block up theincline.

Use the following parameter values: m = 10kg, µs = 0.2, µk = 0.1 and θ = 30◦.

15-62 Chapter 15: Homework Problems

10.2 A L-shaped bar is pinned to ground at end B. End A of the bar rests on a block thatsits on a rough horizontal surface C. A vertical force F acts downwardly on the bar, asshown in the figure below. Let µsAand µsC represent the coefficients of static frictionat A and C, respectively. A horizontal force P acts to the right on the block. Let mbe the mass of the block, and consider the mass of the bar to be negligible.

Determine the minimum force P required to initiate motion of the block to the right.

Use the following parameter values: m = 40kg, F = 100N , µaA = µsC = 0.3, L =2meters and h = 1meter.

Chapter 15: Homework Problems 15-63

10.3 Blocks A and B (having masses of mA and mB, respectively) are connected by thecable-pulley system shown. Block A rests on a rough, horizontal surface with µs beingthe coefficient of static friction between A and the horizontal surface. A horizontalforce P acts to the left on block A, as shown below in the figure. Consider the pulleysto be ideal.

(a) Determine the minimum force P required to hold the system in equilibrium.

(b) Determine the minimum force P required to initiate motion of block A to the left.

Use the following parameter values: mA = mB = 80kg and µs = 0.25.

15-64 Chapter 15: Homework Problems

10.4 A truck of weight W is parked on a hill. The center of mass of the truck is at point G.

(a) Determine the minimum coefficient of static friction µs for the truck to remain atrest if the brakes on only the rear wheels are activated (that is, with no frictionon the front wheels).

(b) Determine the minimum coefficient of static friction µs for the truck to remain atrest if the brakes on only the front wheels are activated (that is, with no frictionon the rear wheels).

Use the following parameter values: W = 6000lb, b = 10ft, h = 4ft and θ = 25◦.

Chapter 15: Homework Problems 15-65

10.5 A block having a mass of m is pinned to ground at corner B. Corner A is supported bya wedge with the wedge resting on a rough inclined surface. The coefficient of staticfriction at A and at the incline is µs. Assume that the weight of the wedge is negligible.

Is the wedge self-locking?

Use the following parameter values: m = 100kg, θ = 10◦, h = 2meters, b = 1meterand µs = 0.4.

15-66 Chapter 15: Homework Problems

10.6 A homogeneous disk of radius R and weight W rests on a rough horizontal surface. Awedge is placed between the right side of the disk and a smooth incline, as shown inthe figure below. A horizontal force F acts to the right at the center G of the disk. Avertical force P acts downwardly on the wedge. Assume that the weight of the wedgeis negligible.

(a) Determine the minimum force P required to initiate motion of the disk to the left.

(b) At which surface of the disk (B or C) does the disk slip? Justify your answer withyour calculations.

Use the following parameter values: W = 50lbs, R = 0.5meters, θ = 20◦, F = 100lbsand µs = 0.5.

Chapter 15: Homework Problems 15-67

10.7 A block having a mass of m is at rest on a rough horizontal surface. A wedge is placedbetween the right side of the block and a rough inclined surface. A vertical force P actsdownwardly on the wedge, as shown in the figure below. Determine the minimum forceP required to initiate motion of the block to the left. The coefficient of static frictionat all surfaces is µs. Ignore the weight of the wedge.

Use the following parameter values: m = 10kg, θ = 10◦, and µs = 0.4.

15-68 Chapter 15: Homework Problems

10.8 A simple refrigerator problem. If the refrigerator (when full) weights 265 lbs., whatforce, P is required to initiate motion? You may assume that h = 4.5ft.,H = 5.75ft.,and b = 1.35ft.. Does the refrigerator slip or tip?

P

h

b b

H

Chapter 15: Homework Problems 15-69

10.9 A semi-cylindrical shell of weight W and center of mass at point G rests on a roughhorizontal surface. A horizontal force P acts at the end of a cable that is attached tothe shell, as shown in the figure below. The coefficient of static friction between thehorizontal surface and the shell at A and B is µs.

(a) Determine the minimum force P required to initiate motion of the shell.

(b) Is the impending motion of the shell slipping or tipping on the horizontal surface?Justify your answer with your calculations.

Use the following parameter values: W = 200lbs, R = 2feet, h = 1.5feet and µs = 0.4.

15-70 Chapter 15: Homework Problems

10.10 A block of mass m and center of mass at G rests on a rough incline. The coefficientof static friction between the block and the incline is µs.

(a) Determine the maximum angle θ for the incline for which the block remains inequilibrium.

(b) Is the impending motion of the block slipping or tipping on the incline? Justifyyour answer with your calculations.

Use the following parameter values: m = 90kg, b = 2meters, h = 3meters and µs = 0.6.

Chapter 15: Homework Problems 15-71

10.11 A pulley of radius R is attached to the output shaft of a motor at O. A belt connectingparticles A and B is supported by the pulley, as shown in the figure below. A torqueMO acts on the output shaft of the motor.

(a) Determine the torque MO required to keep the system in equilibrium.

(b) Determine the minimum value of the coefficient of static friction between the beltand the pulley to prevent slipping of the belt on the pulley.

Use the following parameter values: mA = 10kg, mB = 20kg and R = 0.2meters.

15-72 Chapter 15: Homework Problems

10.12 The coefficient of static friction between the belt and the drum is µs. The coefficientof static friction between block A (of weight W) and the rough horizontal surface onwhich block A rests is also µs. Determine the minimum force P required to initiatemotion of block A to the left.

Use the following parameter values: W = 80lbs, µs = 0.5 and θ = 40◦.

Chapter 15: Homework Problems 15-73

10.13 A smooth disk is allowed to slide along the smooth horizontal guide BC, as shown inthe figure below. A belt is attached to a fixed wall on the left side and supports blockA (of weight W). The coefficient of static friction between the belt and the disk is µs.A horizontal force P acts to the right on the disk.

(a) Determine the minimum force P required to keep the system in equilibrium.

(b) Determine the minimum force P required to lift block A.

Use the following parameter values: W = 50lbs and µs = 0.3.

15-74 Chapter 15: Homework Problems

10.14 A block of mass m and center of mass at G rests on a rough horizontal surface. BlockC (of mass M) is supported by a belt that is attached to the block and is pulled overa rough stationary drum.

(a) Determine the minimum force P required to keep the block in equilibrium.

(b) Is the impending motion of the block slipping or tipping on the horizontal surface?Justify your answer with your calculations.

Use the following parameter values: M = 800kg, m = 100kg, b = 2meters, h =3meters and µs = 0.1.