Dependent motion multiple cords

1

• Dependent motion multiple cords
• Total length of cord
• L1 xA 2xD
• L2 (xB xD) (xC xD)
• 0 vA 2vD
• 0 (vB vD) (vC vD)
• 2vD vB vC
• 0 vA vB vC

Datum
x
xD
xA
D
A
xC
xB
C
B
2
Dependent motion

• Solution Procedure
• 1. Sketch with a datum line

3
Dependent motion

• Solution Procedure
• Sketch with a datum line
• Denote the positive direction

4
Dependent motion

• Solution Procedure
• Sketch with a datum line
• Denote the positive direction
• Denote the position of each object

5
Dependent motion

• Solution Procedure
• Sketch with a datum line
• Denote the positive direction
• Denote the position of each object
• Write an equation for the length of each cable

6
Dependent motion

• Solution Procedure
• Sketch with a datum line
• Denote the positive direction
• Denote the position of each object
• Write an equation for the length of each cable
• Apply the time derivatives

7
Dependent motion

• Solution Procedure
• Sketch with a datum line
• Denote the positive direction
• Denote the position of each object
• Write an equation for the length of each cable
• Apply the time derivatives
• Use the given data to solve for the unknowns

8

• 11-47 Block A moves down with a constant
• velocity of 2 ft/s. Determine (a) the velocity of
• block C, (b) the velocity of collar B relative to
  block
• A, (c) the relative velocity of portion D of the
  cable
• with respect to block A.

9

• 11-47 Block A moves down with a constant
• velocity of 2 ft/s. Determine (a) the velocity of
• block C, (b) the velocity of collar B relative to
  block
• A, (c) the relative velocity of portion D of the
  cable
• with respect to block A.
• Sketch with a datum line
• Denote the positive direction
• Denote the position of each object
• Write an equation for the length of each cable
• Apply the time derivatives
• Use the given data to solve for the unknowns

Datum Line
10

• 11-47 Block A moves down with a constant
• velocity of 2 ft/s. Determine (a) the velocity of
• block C, (b) the velocity of collar B relative to
  block
• A, (c) the relative velocity of portion D of the
  cable
• with respect to block A.
• Sketch with a datum line
• Denote the positive direction
• Denote the position of each object
• Write an equation for the length of each cable
• Apply the time derivatives
• Use the given data to solve for the unknowns

y
11

• 11-47 Block A moves down with a constant
• velocity of 2 ft/s. Determine (a) the velocity of
• block C, (b) the velocity of collar B relative to
  block
• A, (c) the relative velocity of portion D of the
  cable
• with respect to block A.
• Sketch with a datum line
• Denote the positive direction
• Denote the position of each object
• Write an equation for the length of each cable
• Apply the time derivatives
• Use the given data to solve for the unknowns

y
YD
YC
YB
YA
12

• 11-47 Block A moves down with a constant
• velocity of 2 ft/s. Determine (a) the velocity of
• block C, (b) the velocity of collar B relative to
  block
• A, (c) the relative velocity of portion D of the
  cable
• with respect to block A.
• Sketch with a datum line
• Denote the positive direction
• Denote the position of each object
• Write an equation for the length of each cable
• Apply the time derivatives
• Use the given data to solve for the unknowns
• L1 yA (yA-yB)

y
YD
YC
YB
YA
13

• 11-47 Block A moves down with a constant
• velocity of 2 ft/s. Determine (a) the velocity of
• block C, (b) the velocity of collar B relative to
  block
• A, (c) the relative velocity of portion D of the
  cable
• with respect to block A.
• Sketch with a datum line
• Denote the positive direction
• Denote the position of each object
• Write an equation for the length of each cable
• Apply the time derivatives
• Use the given data to solve for the unknowns
• L1 yA (yA-yB) L22yByC

y
YD
YC
YB
YA
14

• 11-47 Block A moves down with a constant
• velocity of 2 ft/s. Determine (a) the velocity of
• block C, (b) the velocity of collar B relative to
  block
• A, (c) the relative velocity of portion D of the
  cable
• with respect to block A.
• Sketch with a datum line
• Denote the positive direction
• Denote the position of each object
• Write an equation for the length of each cable
• Apply the time derivatives
• Use the given data to solve for the unknowns
• L1 yA (yA-yB) L22yByC
  L3yB(yB-yD)

y
YD
YC
YB
YA
15

• 11-47 Block A moves down with a constant
• velocity of 2 ft/s. Determine (a) the velocity of
• block C, (b) the velocity of collar B relative to
  block
• A, (c) the relative velocity of portion D of the
  cable
• with respect to block A.
• Sketch with a datum line
• Denote the positive direction
• Denote the position of each object
• Write an equation for the length of each cable
• Apply the time derivatives
• Use the given data to solve for the unknowns
• L1 yA (yA-yB) L22yByC
  L3yB(yB-yD)
• d(L1 yA (yA-yB))/dt
• 02vA-vB

y
YD
YC
YB
YA
16

• 11-47 Block A moves down with a constant
• velocity of 2 ft/s. Determine (a) the velocity of
• block C, (b) the velocity of collar B relative to
  block
• A, (c) the relative velocity of portion D of the
  cable
• with respect to block A.
• Sketch with a datum line
• Denote the positive direction
• Denote the position of each object
• Write an equation for the length of each cable
• Apply the time derivatives
• Use the given data to solve for the unknowns
• L1 yA (yA-yB) L22yByC
  L3yB(yB-yD)
• d(L1 yA (yA-yB))/dt d(L22yByC)/dt
• 02vA-vB 02vBvC

y
YD
YC
YB
YA
17

• 11-47 Block A moves down with a constant
• velocity of 2 ft/s. Determine (a) the velocity of
• block C, (b) the velocity of collar B relative to
  block
• A, (c) the relative velocity of portion D of the
  cable
• with respect to block A.
• Sketch with a datum line
• Denote the positive direction
• Denote the position of each object
• Write an equation for the length of each cable
• Apply the time derivatives
• Use the given data to solve for the unknowns
• L1 yA (yA-yB) L22yByC
  L3yB(yB-yD)
• d(L1 yA (yA-yB))/dt d(L22yByC)/dt
  d(L3yB(yB-yD))/dt
• 02vA - vB
  02vBvC 02vB - vD

y
YD
YC
YB
YA
18

• 11-47 Block A moves down with a constant
• velocity of 2 ft/s. Determine (a) the velocity of
• block C, (b) the velocity of collar B relative to
  block
• A, (c) the relative velocity of portion D of the
  cable
• with respect to block A.
• Sketch with a datum line
• Denote the positive direction
• Denote the position of each object
• Write an equation for the length of each cable
• Apply the time derivatives
• Use the given data to solve for the unknowns
• L1 yA (yA-yB) L22yByC
  L3yB(yB-yD)
• d(L1 yA (yA-yB))/dt d(L22yByC)/dt
  d(L3yB(yB-yD))/dt
• 02vA - vB
  02vBvC 02vB vD
• Given vA2 ? vB2(2) 4

y
YD
YC
YB
YA
19

• 11-47 Block A moves down with a constant
• velocity of 2 ft/s. Determine (a) the velocity of
• block C, (b) the velocity of collar B relative to
  block
• A, (c) the relative velocity of portion D of the
  cable
• with respect to block A.
• Sketch with a datum line
• Denote the positive direction
• Denote the position of each object
• Write an equation for the length of each cable
• Apply the time derivatives
• Use the given data to solve for the unknowns
• L1 yA (yA-yB) L22yByC
  L3yB(yB-yD)
• d(L1 yA (yA-yB))/dt d(L22yByC)/dt
  d(L3yB(yB-yD))/dt
• 02vA - vB
  02vBvC 02vB vD
• Given vA2 ? vB2(2) 4 ? vC - 2(4) - 8 ft/s

y
YD
YC
YB
YA
20

• 11-47 Block A moves down with a constant
• velocity of 2 ft/s. Determine (a) the velocity of
• block C, (b) the velocity of collar B relative to
  block
• A, (c) the relative velocity of portion D of the
  cable
• with respect to block A.
• Sketch with a datum line
• Denote the positive direction
• Denote the position of each object
• Write an equation for the length of each cable
• Apply the time derivatives
• Use the given data to solve for the unknowns
• L1 yA (yA-yB) L22yByC
  L3yB(yB-yD)
• d(L1 yA (yA-yB))/dt d(L22yByC)/dt
  d(L3yB(yB-yD))/dt
• 02vA - vB
  02vBvC 02vB vD
• Given vA2 ? vB2(2) 4 ? vC - 2(4) - 8 ft/s
• vB/A vB vA 4 2 2 ft/s

y
YD
YC
YB
YA
21

• 11-47 Block A moves down with a constant
• velocity of 2 ft/s. Determine (a) the velocity of
• block C, (b) the velocity of collar B relative to
  block
• A, (c) the relative velocity of portion D of the
  cable
• with respect to block A.
• Sketch with a datum line
• Denote the positive direction
• Denote the position of each object
• Write an equation for the length of each cable
• Apply the time derivatives
• Use the given data to solve for the unknowns
• L1 yA (yA-yB) L22yByC
  L3yB(yB-yD)
• d(L1 yA (yA-yB))/dt d(L22yByC)/dt
  d(L3yB(yB-yD))/dt
• 02vA - vB
  02vBvC 02vB vD
• Given vA2 ? vB2(2) 4 ? vC - 2(4) - 8 ft/s
• vB/A vB vA 4 2 2 ft/s
• vD/A vD vA 2(4) 2 6 ft/s

y
YD
YC
YB
YA
22

• 11-47 Block A moves down with a constant
• velocity of 2 ft/s. Determine (a) the velocity of
• block C, (b) the velocity of collar B relative to
  block
• A, (c) the relative velocity of portion D of the
  cable
• with respect to block A.
• Sketch with a datum line
• Denote the positive direction
• Denote the position of each object
• Write an equation for the length of each cable
• Apply the time derivatives
• Use the given data to solve for the unknowns
• L1 yA (yA-yB) L22yByC
  L3yB(yB-yD) L4 yD yC
• d(L1 yA (yA-yB))/dt d(L22yByC)/dt
  d(L3yB(yB-yD))/dt
• 02vA - vB
  02vBvC 02vB vD
• Given vA2 ? vB2(2) 4 ? vC - 2(4) - 8 ft/s
• vB/A vB vA 4 2 2 ft/s
• vD/A vD vA 2(4) 2 6 ft/s

y
YD
YC
YB
YA
23

• 11-47 Block A moves down with a constant
• velocity of 2 ft/s. Determine (a) the velocity of
• block C, (b) the velocity of collar B relative to
  block
• A, (c) the relative velocity of portion D of the
  cable
• with respect to block A.
• Sketch with a datum line
• Denote the positive direction
• Denote the position of each object
• Write an equation for the length of each cable
• Apply the time derivatives
• Use the given data to solve for the unknowns
• L1 yA (yA-yB) L22yByC
  L3yB(yB-yD) L4 yD yC
• d(L1 yA (yA-yB))/dt d(L22yByC)/dt
  d(L3yB(yB-yD))/dt d(L4 yD yC)/dt
• 02vA - vB
  02vBvC 02vB vD
• Given vA2 ? vB2(2) 4 ? vC - 2(4) - 8 ft/s
• vB/A vB vA 4 2 2 ft/s
• vD/A vD vA 2(4) 2 6 ft/s

y
YD
YC
YB
YA
24

• 11-47 Block A moves down with a constant
• velocity of 2 ft/s. Determine (a) the velocity of
• block C, (b) the velocity of collar B relative to
  block
• A, (c) the relative velocity of portion D of the
  cable
• with respect to block A.
• Sketch with a datum line
• Denote the positive direction
• Denote the position of each object
• Write an equation for the length of each cable
• Apply the time derivatives
• Use the given data to solve for the unknowns
• L1 yA (yA-yB) L22yByC
  L3yB(yB-yD) L4 yD yC
• d(L1 yA (yA-yB))/dt d(L22yByC)/dt
  d(L3yB(yB-yD))/dt d(L4 yD yC)/dt
• 02vA - vB
  02vBvC 02vB vD
  0 vD vC
• Given vA2 ? vB2(2) 4 ? vC - 2(4) - 8 ft/s
• vB/A vB vA 4 2 2 ft/s
• vD/A vD vA 2(4) 2 6 ft/s

y
YD
YC
YB
YA
25

• 11-47 Block A moves down with a constant
• velocity of 2 ft/s. Determine (a) the velocity of
• block C, (b) the velocity of collar B relative to
  block
• A, (c) the relative velocity of portion D of the
  cable
• with respect to block A.
• Sketch with a datum line
• Denote the positive direction
• Denote the position of each object
• Write an equation for the length of each cable
• Apply the time derivatives
• Use the given data to solve for the unknowns
• L1 yA (yA-yB) L22yByC
  L3yB(yB-yD) L4 yD yC
• d(L1 yA (yA-yB))/dt d(L22yByC)/dt
  d(L3yB(yB-yD))/dt d(L4 yD yC)/dt
• 02vA - vB
  02vBvC 02vB vD
  0 vD vC
• Given vA2 ? vB2(2) 4 ? vC - 2(4) - 8 ft/s
  vD -(-8) 8 ft/s
• vB/A vB vA 4 2 2 ft/s
• vD/A vD vA 2(4) 2 6 ft/s

y
YD
YC
YB
YA
26

• 11-47 Block A moves down with a constant
• velocity of 2 ft/s. Determine (a) the velocity of
• block C, (b) the velocity of collar B relative to
  block
• A, (c) the relative velocity of portion D of the
  cable
• with respect to block A.
• Sketch with a datum line
• Denote the positive direction
• Denote the position of each object
• Write an equation for the length of each cable
• Apply the time derivatives
• Use the given data to solve for the unknowns
• L1 yA (yA-yB) L22yByC
  L3yB(yB-yD) L4 yD yC
• d(L1 yA (yA-yB))/dt d(L22yByC)/dt
  d(L3yB(yB-yD))/dt d(L4 yD yC)/dt
• 02vA - vB
  02vBvC 02vB vD
  0 vD vC
• Given vA2 ? vB2(2) 4 ? vC - 2(4) - 8 ft/s
  vD -(-8) 8 ft/s
• vB/A vB vA 4 2 2 ft/s
• vD/A vD vA 2(4) 2 6 ft/s
  vD/A 8 2 6
  ft/s

y
YD
YC
YB
YA
27

• 11-57 Slider block B moves to the left
• with a constant velocity of 2 in/s. At t0,
• slider block A is moving to the right with
• a constant acceleration and a velocity
• of 4 in/s. Knowing that at t2s slider
• block C has moved 1.5 in. to the right,
• determine (a) the velocity of slider
• block C at t0, (b) the accelerations of
• A and C.

28

• 11-57 Slider block B moves to the left with a
• constant velocity of 2 in/s. At t0, slider
• block A is moving to the right with a
• constant acceleration and a velocity of 4
• in/s. Knowing that at t2s slider block C has
• moved 1.5 in. to the right, determine (a) the
• velocity of slider block C at t0, (b) the
• accelerations of A and C.
• Sketch with a datum line
• Denote the positive direction
• Denote the position of each object
• Write an equation for the length of each cable
• Apply the time derivatives
• Use the given data to solve for the unknowns

29
X

• 11-57 Slider block B moves to the left with a
• constant velocity of 2 in/s. At t0, slider
• block A is moving to the right with a
• constant acceleration and a velocity of 4
• in/s. Knowing that at t2s slider block C has
• moved 1.5 in. to the right, determine (a) the
• velocity of slider block C at t0, (b) the
• accelerations of A and C.
• Sketch with a datum line
• Denote the positive direction
• Denote the position of each object
• Write an equation for the length of each cable
• Apply the time derivatives
• Use the given data to solve for the unknowns

30
X

• 11-57 Slider block B moves to the left with a
• constant velocity of 2 in/s. At t0, slider
• block A is moving to the right with a
• constant acceleration and a velocity of 4
• in/s. Knowing that at t2s slider block C has
• moved 1.5 in. to the right, determine (a) the
• velocity of slider block C at t0, (b) the
• accelerations of A and C.
• Sketch with a datum line
• Denote the positive direction
• Denote the position of each object
• Write an equation for the length of each cable
• Apply the time derivatives
• Use the given data to solve for the unknowns

XC
XB
XA
31
X

• 11-57 Slider block B moves to the left with a
• constant velocity of 2 in/s. At t0, slider
• block A is moving to the right with a
• constant acceleration and a velocity of 4
• in/s. Knowing that at t2s slider block C has
• moved 1.5 in. to the right, determine (a) the
• velocity of slider block C at t0, (b) the
• accelerations of A and C.
• Sketch with a datum line
• Denote the positive direction
• Denote the position of each object
• Write an equation for the length of each cable
• Apply the time derivatives
• Use the given data to solve for the unknowns
• L -3xA 4xC 2xB

XC
XB
XA
32
X

• 11-57 Slider block B moves to the left with a
• constant velocity of 2 in/s. At t0, slider
• block A is moving to the right with a
• constant acceleration and a velocity of 4
• in/s. Knowing that at t2s slider block C has
• moved 1.5 in. to the right, determine (a) the
• velocity of slider block C at t0, (b) the
• accelerations of A and C.
• Sketch with a datum line
• Denote the positive direction
• Denote the position of each object
• Write an equation for the length of each cable
• Apply the time derivatives
• Use the given data to solve for the unknowns
• L -3xA 4xC 2xB
• d(L -3xA 4xC 2xB)/dt
• 0 -3vA 4vC 2vB

XC
XB
XA
33
X

• 11-57 Slider block B moves to the left with a
• constant velocity of 2 in/s. At t0, slider
• block A is moving to the right with a
• constant acceleration and a velocity of 4
• in/s. Knowing that at t2s slider block C has
• moved 1.5 in. to the right, determine (a) the
• velocity of slider block C at t0, (b) the
• accelerations of A and C.
• Sketch with a datum line
• Denote the positive direction
• Denote the position of each object
• Write an equation for the length of each cable
• Apply the time derivatives
• Use the given data to solve for the unknowns
• L -3xA 4xC 2xB
• d(L -3xA 4xC 2xB)/dt
• 0 -3vA 4vC 2vB 0 -3aA 4aC
  2aB

XC
XB
XA
34
X

• 11-57 Slider block B moves to the left with a
• constant velocity of 2 in/s. At t0, slider
• block A is moving to the right with a
• constant acceleration and a velocity of 4
• in/s. Knowing that at t2s slider block C has
• moved 1.5 in. to the right, determine (a) the
• velocity of slider block C at t0, (b) the
• accelerations of A and C.
• Sketch with a datum line
  Given vB - 2, aB 0
• Denote the positive direction
• Denote the position of each object
• Write an equation for the length of each cable
• Apply the time derivatives
• Use the given data to solve for the unknowns
• L -3xA 4xC 2xB
• d(L -3xA 4xC 2xB)/dt
• 0 -3vA 4vC 2vB 0 -3aA 4aC
  2aB

XC
XB
XA
35
X

• 11-57 Slider block B moves to the left with a
• constant velocity of 2 in/s. At t0, slider
• block A is moving to the right with a
• constant acceleration and a velocity of 4
• in/s. Knowing that at t2s slider block C has
• moved 1.5 in. to the right, determine (a) the
• velocity of slider block C at t0, (b) the
• accelerations of A and C.
• Sketch with a datum line
  Given vB - 2, aB 0
• Denote the positive direction
  t 0, aA k, vA 4
• Denote the position of each object
• Write an equation for the length of each cable
• Apply the time derivatives
• Use the given data to solve for the unknowns
• L -3xA 4xC 2xB
• d(L -3xA 4xC 2xB)/dt
• 0 -3vA 4vC 2vB 0 -3aA 4aC
  2aB

XC
XB
XA
36
X

• 11-57 Slider block B moves to the left with a
• constant velocity of 2 in/s. At t0, slider
• block A is moving to the right with a
• constant acceleration and a velocity of 4
• in/s. Knowing that at t2s slider block C has
• moved 1.5 in. to the right, determine (a) the
• velocity of slider block C at t0, (b) the
• accelerations of A and C.
• Sketch with a datum line
  Given vB - 2, aB 0
• Denote the positive direction
  t 0, aA k, vA 4
• Denote the position of each object
  t 2, delta xC 1.5
• Write an equation for the length of each cable
• Apply the time derivatives
• Use the given data to solve for the unknowns
• L -3xA 4xC 2xB
• d(L -3xA 4xC 2xB)/dt
• 0 -3vA 4vC 2vB 0 -3aA 4aC
  2aB

XC
XB
XA
37
X

• 11-57 Slider block B moves to the left with a
• constant velocity of 2 in/s. At t0, slider
• block A is moving to the right with a
• constant acceleration and a velocity of 4
• in/s. Knowing that at t2s slider block C has
• moved 1.5 in. to the right, determine (a) the
• velocity of slider block C at t0, (b) the
• accelerations of A and C.
• Sketch with a datum line
  Given vB - 2, aB 0
• Denote the positive direction
  t 0, aA k, vA 4
• Denote the position of each object
  t 2, delta xC 1.5
• Write an equation for the length of each cable
• Apply the time derivatives
• Use the given data to solve for the unknowns
• L -3xA 4xC 2xB
• d(L -3xA 4xC 2xB)/dt
• 0 -3vA 4vC 2vB 0 -3aA 4aC
  2aB
• aC (2aB 3aA)/4

XC
XB
XA
38
X

• 11-57 Slider block B moves to the left with a
• constant velocity of 2 in/s. At t0, slider
• block A is moving to the right with a
• constant acceleration and a velocity of 4
• in/s. Knowing that at t2s slider block C has
• moved 1.5 in. to the right, determine (a) the
• velocity of slider block C at t0, (b) the
• accelerations of A and C.
• Sketch with a datum line
  Given vB - 2, aB 0
• Denote the positive direction
  t 0, aA k, vA 4
• Denote the position of each object
  t 2, delta xC 1.5
• Write an equation for the length of each cable
• Apply the time derivatives
• Use the given data to solve for the unknowns
• L -3xA 4xC 2xB
• d(L -3xA 4xC 2xB)/dt
• 0 -3vA 4vC 2vB 0 -3aA 4aC
  2aB
• aC (2aB 3aA)/4 (2(0) 3k)/4 3k/4

XC
XB
XA
39
X

• 11-57 Slider block B moves to the left with a
• constant velocity of 2 in/s. At t0, slider
• block A is moving to the right with a
• constant acceleration and a velocity of 4
• in/s. Knowing that at t2s slider block C has
• moved 1.5 in. to the right, determine (a) the
• velocity of slider block C at t0, (b) the
• accelerations of A and C.
• Sketch with a datum line
  Given vB - 2, aB 0
• Denote the positive direction
  t 0, aA k, vA 4
• Denote the position of each object
  t 2, delta xC 1.5
• Write an equation for the length of each cable
• Apply the time derivatives
• Use the given data to solve for the unknowns
• L -3xA 4xC 2xB
• d(L -3xA 4xC 2xB)/dt
• 0 -3vA 4vC 2vB 0 -3aA 4aC
  2aB
• aC (2aB 3aA)/4 (2(0) 3k)/4 3k/4
• at t 0, vC0 (2vB0 3vA0)/4

XC
XB
XA
40
X

• 11-57 Slider block B moves to the left with a
• constant velocity of 2 in/s. At t0, slider
• block A is moving to the right with a
• constant acceleration and a velocity of 4
• in/s. Knowing that at t2s slider block C has
• moved 1.5 in. to the right, determine (a) the
• velocity of slider block C at t0, (b) the
• accelerations of A and C.
• Sketch with a datum line
  Given vB - 2, aB 0
• Denote the positive direction
  t 0, aA k, vA 4
• Denote the position of each object
  t 2, delta xC 1.5
• Write an equation for the length of each cable
• Apply the time derivatives
• Use the given data to solve for the unknowns
• L -3xA 4xC 2xB
• d(L -3xA 4xC 2xB)/dt
• 0 -3vA 4vC 2vB 0 -3aA 4aC
  2aB
• aC (2aB 3aA)/4 (2(0) 3k)/4 3k/4
• at t 0, vC0 (2vB0 3vA0)/4 (2(-2)
  3(4))/4 2 in/s

XC
XB
XA
41
X

• 11-57 Slider block B moves to the left with a
• constant velocity of 2 in/s. At t0, slider
• block A is moving to the right with a
• constant acceleration and a velocity of 4
• in/s. Knowing that at t2s slider block C has
• moved 1.5 in. to the right, determine (a) the
• velocity of slider block C at t0, (b) the
• accelerations of A and C.
• Sketch with a datum line
  Given vB - 2, aB 0
• Denote the positive direction
  t 0, aA k, vA 4
• Denote the position of each object
  t 2, delta xC 1.5
• Write an equation for the length of each cable
• Apply the time derivatives
• Use the given data to solve for the unknowns
• L -3xA 4xC 2xB
• d(L -3xA 4xC 2xB)/dt
• 0 -3vA 4vC 2vB 0 -3aA 4aC
  2aB
• aC (2aB 3aA)/4 (2(0) 3k)/4 3k/4
• at t 0, vC0 (2vB0 3vA0)/4 (2(-2)
  3(4))/4 2 in/s

XC
XB
XA
42
X

• 11-57 Slider block B moves to the left with a
• constant velocity of 2 in/s. At t0, slider
• block A is moving to the right with a
• constant acceleration and a velocity of 4
• in/s. Knowing that at t2s slider block C has
• moved 1.5 in. to the right, determine (a) the
• velocity of slider block C at t0, (b) the
• accelerations of A and C.
• Sketch with a datum line
  Given vB - 2, aB 0
• Denote the positive direction
  t 0, aA k, vA 4
• Denote the position of each object
  t 2, delta xC 1.5
• Write an equation for the length of each cable
• Apply the time derivatives
• Use the given data to solve for the unknowns
• L -3xA 4xC 2xB
• d(L -3xA 4xC 2xB)/dt
• 0 -3vA 4vC 2vB 0 -3aA 4aC
  2aB
• aC (2aB 3aA)/4 (2(0) 3k)/4 3k/4
• at t 0, vC0 (2vB0 3vA0)/4 (2(-2)
  3(4))/4 2 in/s

XC
XB
XA
43
X

• 11-57 Slider block B moves to the left with a
• constant velocity of 2 in/s. At t0, slider
• block A is moving to the right with a
• constant acceleration and a velocity of 4
• in/s. Knowing that at t2s slider block C has
• moved 1.5 in. to the right, determine (a) the
• velocity of slider block C at t0, (b) the
• accelerations of A and C.
• Sketch with a datum line
  Given vB - 2, aB 0
• Denote the positive direction
  t 0, aA k, vA 4
• Denote the position of each object
  t 2, delta xC 1.5
• Write an equation for the length of each cable
• Apply the time derivatives
• Use the given data to solve for the unknowns
• L -3xA 4xC 2xB
• d(L -3xA 4xC 2xB)/dt
• 0 -3vA 4vC 2vB 0 -3aA 4aC
  2aB
• aC (2aB 3aA)/4 (2(0) 3k)/4 3k/4
• at t 0, vC0 (2vB0 3vA0)/4 (2(-2)
  3(4))/4 2 in/s

XC
XB
XA