dry friction

Problem 532
In Fig. P-532, two blocks each weighing 1.5 kN are connected by a uniform horizontal bar which weighs 1.0 kN. If the angle of friction is 15° under each block, find P directed parallel to the 45° incline that will cause impending motion to the left.
 

Problem 531
A uniform plank of weight W and total length 2L is placed as shown in Fig. P-531 with its ends in contact with the inclined planes. The angle of friction is 15°. Determine the maximum value of the angle α at which slipping impends.
 

Problem 530
A plank 10 ft long is placed in a horizontal position with its ends resting on two inclined planes, as shown in Fig. P-530. The angle of friction is 20°. Determine how close the load P can be placed to each end before slipping impends.
 

Problem 529
As shown in Fig. P-529, a homogeneous cylinder 2 m in diameter and weighing 12 kN is acted upon by a vertical force P. Determine the magnitude of P necessary to start the cylinder turning. Assume that μ = 0.30.
 

Problem 527
A homogeneous cylinder 3 m in diameter and weighing 30 kN is resting on two inclined planes as shown in Fig. P-527. If the angle of friction is 15° for all contact surfaces, compute the magnitude of the couple required to start the cylinder rotating counterclockwise.
 

Problem 528
Instead of a couple, determine the minimum horizontal force P applied tangentially to the left at the top of the cylinder described in Prob. 527 to start the cylinder rotating counterclockwise.
 

Problem 526
A ladder 6 m long has a mass of 18 kg and its center of gravity is 2.4 m from the bottom. The ladder is placed against a vertical wall so that it makes an angle of 60° with the ground. How far up the ladder can a 72-kg man climb before the ladder is on the verge of slipping? The angle of friction at all contact surfaces is 15°.
 

Problem 525
A uniform ladder 4.8 m ft long and weighing W lb is placed with one end on the ground and the other against a vertical wall. The angle of friction at all contact surfaces is 20°. Find the minimum value of the angle θ at which the ladder can be inclined with the horizontal before slipping occurs.
 

Problem 524
A horizontal arm having a bushing of 20 mm long is slipped over a 20-mm diameter vertical rod, as shown in Fig. P-524. The coefficient of friction between the bushing and the rod is 0.20. Compute the minimum length L at which a weight W can be placed to prevent the arm from slipping down the rod. Neglect the weight of the arm.
 

Problem 523
A force of 400 lb is applied to the pulley shown in Fig. P-523. The pulley is prevented from rotating by a force P applied to the end of the brake lever. If the coefficient of friction at the brake surface is 0.20, determine the value of P.
 

Problem 522
The blocks shown in Fig. P-522 are separated by a solid strut which is attached to the blocks with frictionless pins. If the coefficient of friction for all surfaces is 0.20, determine the value of horizontal force P to cause motion to impend to the right. Assume that the strut is a uniform rod weighing 300 lb.