Problem 11 186 A C B In the

Problem 11. 186 A C B In the position shown, collar B moves to the left with a velocity of 150 mm/s. Determine (a) the velocity of collar A, (b) the velocity of portion C of the cable, (c) the relative velocity of portion C of the cable with respect to collar B.

Problem 11. 186 Solving Problems on Your Own In the position shown, collar B moves to the left with a velocity of 150 mm/s. Determine (a) the velocity of collar A, C (b) the velocity of portion C of the cable, (c) the relative velocity of portion B C of the cable with respect to collar B. 1. Dependent motion of two or more particles: A 1 a. Draw a sketch of the system: Select a coordinate system, indicating clearly a positive sense for each of the coordinate axes. The displacements, velocities, and accelerations have positive values in the direction of the coordinate axes. 1 b. Write the equation describing the constraint: When particles are connected with a cable, its length which remains constant is the constraint.

Problem 11. 186 Solving Problems on Your Own A C B In the position shown, collar B moves to the left with a velocity of 150 mm/s. Determine (a) the velocity of collar A, (b) the velocity of portion C of the cable, (c) the relative velocity of portion C of the cable with respect to collar B. 1 c. Differentiate the equation describing the constraint: This gives the corresponding relations among velocities and accelerations of the various particles.

Problem 11. 186 Solution Draw a sketch of the system. x. A Write the equation describing the constraint. A C B x. B (a) x. C The total length of the cable: constant = 2 x. A + x. B + (x. B - x. A) v. B = 150 mm/s Differentiate the equation describing the constraint. 0 = v. A + 2 v. B = 150 mm/s v. A = - 2 v. B v. A = -300 mm/s v. A = 300 mm/s

x. A A (b) The length of the cable from the right end to an arbitrary point on portion C of the cable: C B x. B Problem 11. 186 Solution x. C v. B = 150 mm/s (c) Relative velocity of portion C: v. C = v. B + v. C/B 600 = 150 + v. C/B = 450 mm/s constant = 2 x. A + x. C 0 = 2 v. A + v. C = - 2 v. A v. C = 600 mm/s