Friction

Find the least value of P required to cause the system of blocks shown in Fig. P-511 to have impending motion to the left. The coefficient of friction under each block is 0.20.

Solution 511

HideClick here to show or hide the solution From the FBD of 10 kN block on the inclined plane Sum up forces normal to the incline

Amount of friction

Sum up forces parallel to the incline

From the FBD of 30 kN block on the horizontal plane Sum up vertical forces

Amount of friction

Sum up horizontal forces

To minimize P, differentiate then equate to zero

Thus,

answer

In Fig. P-512, the homogeneous block weighs 300 kg and the coefficient of friction is 0.45. If h = 50 cm, determine the force P to cause motion to impend.

Solution 513

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answer

The blocks shown in Fig. P-509 are connected by flexible, inextensible cords passing over frictionless pulleys. At A the coefficients of friction are μs = 0.30 and μk = 0.20 while at B they are μs = 0.40 and μk = 0.30. Compute the magnitude and direction of the friction force acting on each block.

Solution 509

HideClick here to show or hide the solution Neglecting friction

2TA is greater than TB, thus, the system will move to the left if contact surfaces are frictionless. Considering friction The angle of static friction at A, φA = arctan 0.30 = 16.70°, is not enough to hold the block from sliding the incline of angle θ = arctan (3/4) = 36.87° from horizontal. If TB is insufficient to hold 2TA statically the system will move to the left, otherwise, the system is stationary.

Assume the blocks are stationary (use μs)

TB < 2TA. TB is insufficient to hold the system in static equilibrium, thus, the blocks are moving to the left. Blocks are moving to the left (Use μk) answer answer - See more at: http://www.mathalino.com/reviewer/engineering-mechanics/problem-509friction#sthash.QN21wSFE.dpuf

Block A in Fig. P-515 weighs 120 lb, block B weighs 200 lb, and the cord is parallel to the incline. If the coefficient of friction for all surfaces in contact is 0.25, determine the angle θ of the incline of which motion of B impends.

Solution 515

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answer - See more at: http://www.mathalino.com/reviewer/engineering-mechanics/problem-515friction#sthash.VO0pod3F.dpuf What weight W is necessary to start the system of blocks shown in Fig. P-510 moving to the right? The coefficient of friction is 0.10 and the pulleys are assumed to be frictionless.

Solution 510

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Locate the centroid of the shaded area in Fig. P-723.

Solution 723

HideClick here to show or hide the solution For rectangular area

For quarter circle

For the triangle

For the shaded region

answer

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Refer again to Fig. P-714. To what value should the 6-in. width of the flange be changed so that the centroid of the area is 2.5 in. above the base?

Solution 721

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answer

Locate the centroid of the shaded area in Fig. P-722 created by cutting a semicircle of diameter r from a quarter circle of radius r.

Solution 722

HideClick here to show or hide the solution For the quarter circle

For the semicircle

For the shaded area

answer

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Locate the centroid of the bent wire shown in Fig. P-717. The wire is homogeneous and of uniform crosssection.

Solution 717

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By symmetry answer

answer - See more at: http://www.mathalino.com/reviewer/engineering-mechanics/717-symmetricall-arcs-andline-centroid-composite-line#sthash.zGRdrXrJ.dpuf The centroid of the sahded area in Fig. P-720 is required to lie on the y-axis. Determine the distance b that will fulfill this requirement.

Solution 720

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The centroid will lie on the y-axis, thus,

Hence,

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