Power and Efficiency

1
Power and Efficiency

• Power dU/dt

2
Power and Efficiency

• Power dU/dt
• Power (F . dr)/dt but dr /dt v
• Power F . V

3
Power and Efficiency

• Power dU/dt
• Power (F . dr)/dt but dr /dt v
• Power F . V
• The metric unit is Nm/s or J/s or W
• The English unit is hp 550 ft lb/s

4
Power and Efficiency

• Power dU/dt
• Power (F . dr)/dt but dr /dt v
• Power F . V
• The metric unit is Nm/s or J/s or W
• The English unit is hp 550 ft lb/s
• Mechanical Efficiency h (power output)/(power
  input)

5

• Applications of Power
• Problem 13.48 A 70 kg sprinter starts from rest
  and
• accelerates uniformly for 5.4 s over a distance
  of 35 m.
• Neglecting air resistance, determine the average
  power
• developed by the sprinter.

6

• Applications of Power
• Problem 13.48 A 70 kg sprinter starts from rest
  and
• accelerates uniformly for 5.4 s over a distance
  of 35 m.
• Neglecting air resistance, determine the average
  power
• developed by the sprinter.
• uniform acceleration constant acceleration

7

• Applications of Power
• Problem 13.48 A 70 kg sprinter starts from rest
  and
• accelerates uniformly for 5.4 s over a distance
  of 35 m.
• Neglecting air resistance, determine the average
  power
• developed by the sprinter.
• uniform acceleration constant acceleration
• x x0 v0t (1/2)at2 ? 35 0 0(5.4)
  (1/2)a(5.4)2
• a 2.4 m/s2

8

• Applications of Power
• Problem 13.48 A 70 kg sprinter starts from rest
  and
• accelerates uniformly for 5.4 s over a distance
  of 35 m.
• Neglecting air resistance, determine the average
  power
• developed by the sprinter.
• uniform acceleration constant acceleration
• x x0 v0t (1/2)at2 ? 35 0 0(5.4)
  (1/2)a(5.4)2
• a 2.4 m/s2
• SFX maX ? F 70(2.4) ? F 168 N

F
y
N
70g
x
9

• Applications of Power
• Problem 13.48 A 70 kg sprinter starts from rest
  and
• accelerates uniformly for 5.4 s over a distance
  of 35 m.
• Neglecting air resistance, determine the average
  power
• developed by the sprinter.
• uniform acceleration constant acceleration
• x x0 v0t (1/2)at2 ? 35 0 0(5.4)
  (1/2)a(5.4)2
• a 2.4 m/s2
• SFX maX ? F 70(2.4) ? F 168 N
• U 168(35)

F
y
N
70g
x
10

• Applications of Power
• Problem 13.48 A 70 kg sprinter starts from rest
  and
• accelerates uniformly for 5.4 s over a distance
  of 35 m.
• Neglecting air resistance, determine the average
  power
• developed by the sprinter.
• uniform acceleration constant acceleration
• x x0 v0t (1/2)at2 ? 35 0 0(5.4)
  (1/2)a(5.4)2
• a 2.4 m/s2
• SFX maX ? F 70(2.4) ? F 168 N
• U 168(35)
• Average Power 168(35)/(5.4)
• Average Power 1090 W or 1.09 kW

F
y
N
70g
x
11

• Problem 13.50 It takes 16 s to raise a 2800 lb
• car and the supporting 650 lb hydraulic car lift
• platform to a height of 6.5 ft. Knowing that the
• overall conversion efficiency from electric to
• mechanical power for the system is 82 percent,
• determine (a) the average power delivered by
• the hydraulic pump to lift the system, (b) the
• average electric power required.

12

• Problem 13.50 It takes 16 s to raise a 2800 lb
• car and the supporting 650 lb hydraulic car lift
• platform to a height of 6.5 ft. Knowing that the
• overall conversion efficiency from electric to
• mechanical power for the system is 82 percent,
• determine (a) the average power delivered by
• the hydraulic pump to lift the system, (b) the
• average electric power required.
• Power Fv
• Average velocity 6.5/16 0.406 ft/s

13

• Problem 13.50 It takes 16 s to raise a 2800 lb
• car and the supporting 650 lb hydraulic car lift
• platform to a height of 6.5 ft. Knowing that the
• overall conversion efficiency from electric to
• mechanical power for the system is 82 percent,
• determine (a) the average power delivered by
• the hydraulic pump to lift the system, (b) the
• average electric power required.
• Power Fv
• Average velocity 6.5/16 0.406 ft/s

y
F
2800650
14

• Problem 13.50 It takes 16 s to raise a 2800 lb
• car and the supporting 650 lb hydraulic car lift
• platform to a height of 6.5 ft. Knowing that the
• overall conversion efficiency from electric to
• mechanical power for the system is 82 percent,
• determine (a) the average power delivered by
• the hydraulic pump to lift the system, (b) the
• average electric power required.
• Power Fv
• Average velocity 6.5/16 0.406 ft/s
• Piston force F 3450 lb
• Average Power 3450(0.406) 1400 ft lb/s

y
F
2800650
15

• Problem 13.50 It takes 16 s to raise a 2800 lb
• car and the supporting 650 lb hydraulic car lift
• platform to a height of 6.5 ft. Knowing that the
• overall conversion efficiency from electric to
• mechanical power for the system is 82 percent,
• determine (a) the average power delivered by
• the hydraulic pump to lift the system, (b) the
• average electric power required.
• Power Fv
• Average velocity 6.5/16 0.406 ft/s
• Piston force F 3450 lb
• Average Power 3450(0.406) 1400 ft lb/s
• Average Power 1400/550 2.55 hp

y
F
2800650
16

• Problem 13.50 It takes 16 s to raise a 2800 lb
• car and the supporting 650 lb hydraulic car lift
• platform to a height of 6.5 ft. Knowing that the
• overall conversion efficiency from electric to
• mechanical power for the system is 82 percent,
• determine (a) the average power delivered by
• the hydraulic pump to lift the system, (b) the
• average electric power required.
• Power Fv
• Average velocity 6.5/16 0.406 ft/s
• Piston force F 3450 lb
• Average Power 3450(0.406) 1400 ft lb/s
• Average Power 1400/550 2.55 hp
• h (power out)/(power in)

y
F
2800650
17

• Problem 13.50 It takes 16 s to raise a 2800 lb
• car and the supporting 650 lb hydraulic car lift
• platform to a height of 6.5 ft. Knowing that the
• overall conversion efficiency from electric to
• mechanical power for the system is 82 percent,
• determine (a) the average power delivered by
• the hydraulic pump to lift the system, (b) the
• average electric power required.
• Power Fv
• Average velocity 6.5/16 0.406 ft/s
• Piston force F 3450 lb
• Average Power 3450(0.406) 1400 ft lb/s
• Average Power 1400/550 2.55 hp
• h (power out)/(power in)
• .82 2.55/(power in)
• power in 3.11 hp

y
F
2800650
18
Potential energy (stored energy)

• Potential Energy is the energy stored in a
  mechanical
• system. Denoted by V with units of Nm or ft lb
• Potential Energy because a change in elevation
  Vg Wy
• where W is the weight and y the vertical distance
  from a
• datum Vg can either be positive or negative
  depending on
• the datum line

19
Potential energy (stored energy)

• Potential Energy is the energy stored in a
  mechanical
• system. Denoted by V with units of Nm or ft lb
• Potential Energy because a change in elevation
  Vg Wy
• where W is the weight and y the vertical distance
  from a
• datum Vg can either be positive or negative
  depending on
• the datum line
• Potential Energy of a spring Ve (1/2)kx2
• where is measured from the undeformed length of
  the
• spring. Note the Ve of the spring is always
  positive
• Regardless if the spring is in tension or
  compression

20
Conservation of Energy

• The total mechanical energy of a particle is the
  sum of the
• Kinetic Energy and Potential Energy
• In a frictionless system the total mechanical
  energy is
• constant
• T1 V1 T2 V2
• Note the problem only depends on the distribution
  of
• energy at each end of the path
• Find the kinetic energy at each end of the path
• Find the potential energy at each end of the path

21

• Applications of Conservation of Energy
• Problem 13.56 A 3kg block can slide without
• friction in a slot and is attached as shown to 3
• springs of equal length and spring constants k1
• 1 kN/m, k2 2 kN/m, and k3 4 kN/m. The
• springs are initially unstretched when the block
• is pushed to the left 45 mm and released.
• Determine (a) the maximum velocity of the
• block, (b) the velocity of the block when it is
  18
• mm from its initial position.

22

• Applications of Conservation of Energy
• Problem 13.56 A 3kg block can slide without
• friction in a slot and is attached as shown to 3
• springs of equal length and spring constants k1
• 1 kN/m, k2 2 kN/m, and k3 4 kN/m. The
• springs are initially unstretched when the block
• is pushed to the left 45 mm and released.
• Determine (a) the maximum velocity of the
• block, (b) the velocity of the block when it is
  18
• mm from its initial position.

1
2
0.045 m
23

• Applications of Conservation of Energy
• Problem 13.56 A 3kg block can slide without
• friction in a slot and is attached as shown to 3
• springs of equal length and spring constants k1
• 1 kN/m, k2 2 kN/m, and k3 4 kN/m. The
• springs are initially unstretched when the block
• is pushed to the left 45 mm and released.
• Determine (a) the maximum velocity of the
• block, (b) the velocity of the block when it is
  18
• mm from its initial position.
• At 1 T1 0 since it starts from rest
• Ve1 (1/2)(1000 2000 4000)(0.045)2
• Ve1 7.09 Nm

1
2
0.045 m
24

• Applications of Conservation of Energy
• Problem 13.56 A 3kg block can slide without
• friction in a slot and is attached as shown to 3
• springs of equal length and spring constants k1
• 1 kN/m, k2 2 kN/m, and k3 4 kN/m. The
• springs are initially unstretched when the block
• is pushed to the left 45 mm and released.
• Determine (a) the maximum velocity of the
• block, (b) the velocity of the block when it is
  18
• mm from its initial position.
• At 1 T1 0 since it starts from rest
• Ve1 (1/2)(1000 2000 4000)(0.045)2
• Ve1 7.09 Nm
• At 2 T2 (1/2)3v22
• Ve2 0 since the springs are unstretched

1
2
0.045 m
25

• Applications of Conservation of Energy
• Problem 13.56 A 3kg block can slide without
• friction in a slot and is attached as shown to 3
• springs of equal length and spring constants k1
• 1 kN/m, k2 2 kN/m, and k3 4 kN/m. The
• springs are initially unstretched when the block
• is pushed to the left 45 mm and released.
• Determine (a) the maximum velocity of the
• block, (b) the velocity of the block when it is
  18
• mm from its initial position.
• At 1 T1 0 since it starts from rest
• Ve1 (1/2)(1000 2000 4000)(0.045)2
• Ve1 7.09 Nm
• At 2 T2 (1/2)3v22
• Ve2 0 since the springs are unstretched
• T1 V1 T2 V2
• 0 7.09 1.5v22 0 ? v2 2.17 m/s

1
2
0.045 m
26

• Applications of Conservation of Energy
• Problem 13.56 A 3kg block can slide without
• friction in a slot and is attached as shown to 3
• springs of equal length and spring constants k1
• 1 kN/m, k2 2 kN/m, and k3 4 kN/m. The
• springs are initially unstretched when the block
• is pushed to the left 45 mm and released.
• Determine (a) the maximum velocity of the
• block, (b) the velocity of the block when it is
  18
• mm from its initial position.
• At 1 T1 0 since it starts from rest
• Ve1 (1/2)(1000 2000 4000)(0.045)2
• Ve1 7.09 Nm
• At 2 T2 (1/2)3v22
• Ve2 0 since the springs are unstretched
• T1 V1 T2 V2
• 0 7.09 1.5v22 0 ? v2 2.17 m/s
• Ve2 (1/2)(1000 2000 4000)(0.027)2
• Ve2 2.55 Nm

1
2
0.045 m
1
2
0.018 m
27

• Problem 13.65 Blocks A and B weigh 8 lb and 3 lb
• respectively, and are connected by a cord and
• pulley system and released from rest in the
• position shown with the spring undeformed.
• Knowing that the constant of the spring is 20
  lb/ft,
• determine (a) the velocity of the block B after
  it has
• moved 6 in, (b) the maximum velocity of block B,
• (c) the maximum displacement of block B. Ignore
• friction and the masses of the pulleys and
  spring.

28
-xB

• Problem 13.65 Blocks A and B weigh 8 lb and 3 lb
• respectively, and are connected by a cord and
• pulley system and released from rest in the
• position shown with the spring undeformed.
• Knowing that the constant of the spring is 20
  lb/ft,
• determine (a) the velocity of the block B after
  it has
• moved 6 in, (b) the maximum velocity of block B,
• (c) the maximum displacement of block B. Ignore
• friction and the masses of the pulleys and
  spring.
• L -2xA yB ? 0 -2DxA DyB and 0 -2vA
  vB

-yB
1
2
DxA
1
DyB
2
29
-xB

• Problem 13.65 Blocks A and B weigh 8 lb and 3 lb
• respectively, and are connected by a cord and
• pulley system and released from rest in the
• position shown with the spring undeformed.
• Knowing that the constant of the spring is 20
  lb/ft,
• determine (a) the velocity of the block B after
  it has
• moved 6 in, (b) the maximum velocity of block B,
• (c) the maximum displacement of block B. Ignore
• friction and the masses of the pulleys and
  spring.
• L -2xA yB ? 0 -2DxA DyB and 0 -2vA vB
• T1 0 since it starts from rest

-yB
1
2
DxA
1
DyB
2
30
-xB

• Problem 13.65 Blocks A and B weigh 8 lb and 3 lb
• respectively, and are connected by a cord and
• pulley system and released from rest in the
• position shown with the spring undeformed.
• Knowing that the constant of the spring is 20
  lb/ft,
• determine (a) the velocity of the block B after
  it has
• moved 6 in, (b) the maximum velocity of block B,
• (c) the maximum displacement of block B. Ignore
• friction and the masses of the pulleys and
  spring.
• L -2xA yB ? 0 -2DxA DyB and 0 -2vA vB
• T1 0 since it starts from rest
• T2 (1/2)(8/g)vA22 (1/2)(3/g)vB22 (5/2g)vB22

-yB
1
2
DxA
1
DyB
2
31
-xB

• Problem 13.65 Blocks A and B weigh 8 lb and 3 lb
• respectively, and are connected by a cord and
• pulley system and released from rest in the
• position shown with the spring undeformed.
• Knowing that the constant of the spring is 20
  lb/ft,
• determine (a) the velocity of the block B after
  it has
• moved 6 in, (b) the maximum velocity of block B,
• (c) the maximum displacement of block B. Ignore
• friction and the masses of the pulleys and
  spring.
• L -2xA yB ? 0 -2DxA DyB and 0 -2vA vB
• T1 0 since it starts from rest
• T2 (1/2)(8/g)vA22 (1/2)(3/g)vB22 (5/2g)vB22
• Ve1 0 since spring is undeformed
• Vg1 0 since datum line is at 1

-yB
1
2
DxA
1
DyB
2
32
-xB

• Problem 13.65 Blocks A and B weigh 8 lb and 3 lb
• respectively, and are connected by a cord and
• pulley system and released from rest in the
• position shown with the spring undeformed.
• Knowing that the constant of the spring is 20
  lb/ft,
• determine (a) the velocity of the block B after
  it has
• moved 6 in, (b) the maximum velocity of block B,
• (c) the maximum displacement of block B. Ignore
• friction and the masses of the pulleys and
  spring.
• L -2xA yB ? 0 -2DxA DyB and 0 -2vA vB
• T1 0 since it starts from rest
• T2 (1/2)(8/g)vA22 (1/2)(3/g)vB22 (5/2g)vB22
• Ve1 0 since spring is undeformed
• Vg1 0 since datum line is at 1
• Ve2 (1/2)20DxA2

-yB
1
2
DxA
1
DyB
2
33
-xB

• Problem 13.65 Blocks A and B weigh 8 lb and 3 lb
• respectively, and are connected by a cord and
• pulley system and released from rest in the
• position shown with the spring undeformed.
• Knowing that the constant of the spring is 20
  lb/ft,
• determine (a) the velocity of the block B after
  it has
• moved 6 in, (b) the maximum velocity of block B,
• (c) the maximum displacement of block B. Ignore
• friction and the masses of the pulleys and
  spring.
• L -2xA yB ? 0 -2DxA DyB and 0 -2vA vB
• T1 0 since it starts from rest
• T2 (1/2)(8/g)vA22 (1/2)(3/g)vB22 (5/2g)vB22
• Ve1 0 since spring is undeformed
• Vg1 0 since datum line is at 1
• Ve2 (1/2)20DxA2 Vg2 3 DyB

-yB
1
2
DxA
1
DyB
2
34
-xB

• Problem 13.65 Blocks A and B weigh 8 lb and 3 lb
• respectively, and are connected by a cord and
• pulley system and released from rest in the
• position shown with the spring undeformed.
• Knowing that the constant of the spring is 20
  lb/ft,
• determine (a) the velocity of the block B after
  it has
• moved 6 in, (b) the maximum velocity of block B,
• (c) the maximum displacement of block B. Ignore
• friction and the masses of the pulleys and
  spring.
• L -2xA yB ? 0 -2DxA DyB and 0 -2vA vB
• T1 0 since it starts from rest
• T2 (1/2)(8/g)vA22 (1/2)(3/g)vB22 (5/2g)vB22
• Ve1 0 since spring is undeformed
• Vg1 0 since datum line is at 1
• Ve2 (1/2)20DxA2 Vg2 3 DyB
• V2 (5/2)DyB2 3 DyB

-yB
1
2
DxA
1
DyB
2
35
-xB

• Problem 13.65 Blocks A and B weigh 8 lb and 3 lb
• respectively, and are connected by a cord and
• pulley system and released from rest in the
• position shown with the spring undeformed.
• Knowing that the constant of the spring is 20
  lb/ft,
• determine (a) the velocity of the block B after
  it has
• moved 6 in, (b) the maximum velocity of block B,
• (c) the maximum displacement of block B. Ignore
• friction and the masses of the pulleys and
  spring.
• L -2xA yB ? 0 -2DxA DyB and 0 -2vA vB
• T1 0 since it starts from rest
• T2 (1/2)(8/g)vA22 (1/2)(3/g)vB22 (5/2g)vB22
• Ve1 0 since spring is undeformed
• Vg1 0 since datum line is at 1
• Ve2 (1/2)20DxA2 Vg2 3 DyB
• V2 (5/2)DyB2 3 DyB
• 0 0 (5/2g)vB22 (5/2)DyB2 3 DyB

-yB
1
2
DxA
1
DyB
2
36
-xB

• Problem 13.65 Blocks A and B weigh 8 lb and 3 lb
• respectively, and are connected by a cord and
• pulley system and released from rest in the
• position shown with the spring undeformed.
• Knowing that the constant of the spring is 20
  lb/ft,
• determine (a) the velocity of the block B after
  it has
• moved 6 in, (b) the maximum velocity of block B,
• (c) the maximum displacement of block B. Ignore
• friction and the masses of the pulleys and
  spring.
• L -2xA yB ? 0 -2DxA DyB and 0 -2vA vB
• T1 0 since it starts from rest
• T2 (1/2)(8/g)vA22 (1/2)(3/g)vB22 (5/2g)vB22
• Ve1 0 since spring is undeformed
• Vg1 0 since datum line is at 1
• Ve2 (1/2)20DxA2 Vg2 3 DyB
• V2 (5/2)DyB2 3 DyB
• 0 0 (5/2g)vB22 (5/2)DyB2 3 DyB
• vB2 ((2g/5)((5/2)DyB2 3 DyB))1/2
• DyB -.5 ? vB2 3.36 ft/s

-yB
1
2
DxA
1
DyB
2
37
-xB

• Problem 13.65 Blocks A and B weigh 8 lb and 3 lb
• respectively, and are connected by a cord and
• pulley system and released from rest in the
• position shown with the spring undeformed.
• Knowing that the constant of the spring is 20
  lb/ft,
• determine (a) the velocity of the block B after
  it has
• moved 6 in, (b) the maximum velocity of block B,
• (c) the maximum displacement of block B. Ignore
• friction and the masses of the pulleys and
  spring.
• L -2xA yB ? 0 -2DxA DyB and 0 -2vA vB
• T1 0 since it starts from rest
• T2 (1/2)(8/g)vA22 (1/2)(3/g)vB22 (5/2g)vB22
• Ve1 0 since spring is undeformed
• Vg1 0 since datum line is at 1
• Ve2 (1/2)20DyA2 Vg2 3 DyB
• V2 (5/2)DyB2 3 DyB
• 0 0 (5/2g)vB22 (5/2)DyB2 3 DyB
• vB2 ((2g/5)((5/2)DyB2 3 DyB))1/2
• DyB -.5 ? vB2 3.36 ft/s

-yB
1
2
DxA
1
DyB
2
38
-xB

• Knowing that the constant of the spring is 20
  lb/ft,
• determine (a) the velocity of the block B after
  it has
• moved 6 in, (b) the maximum velocity of block B,
• (c) the maximum displacement of block B. Ignore
• friction and the masses of the pulleys and
  spring.
• L -2xA yB ? 0 -2DxA DyB and 0 -2vA vB
• Ve1 0 since spring is undeformed
• Vg1 0 since datum line is at 1
• Ve2 (1/2)20DyA2 Vg2 3 DyB
• V2 (5/2)DyB2 3 DyB
• 0 0 (5/2g)vB22 (5/2)DyB2 3 DyB
• vB2 ((2g/5)((5/2)DyB2 3 DyB))1/2
• DyB -.5 ? vB2 3.36 ft/s
• dvB2/dDyB (1/2)((2g/5)((5/2)DyB2 3 DyB))-1/2
  (5DyB3)
• 0 5DyB 3 ? DyB .6 ft and vB2 3.40 ft/s

-yB
1
2
DxA
1
DyB
2
39
-xB

• Knowing that the constant of the spring is 20
  lb/ft,
• determine (a) the velocity of the block B after
  it has
• moved 6 in, (b) the maximum velocity of block B,
• (c) the maximum displacement of block B. Ignore
• friction and the masses of the pulleys and
  spring.
• L -2xA yB ? 0 -2DxA DyB and 0 -2vA vB
• Ve1 0 since spring is undeformed
• Vg1 0 since datum line is at 1
• Ve2 (1/2)20DyA2 Vg2 3 DyB
• V2 (5/2)DyB2 3 DyB
• 0 0 (5/2g)vB22 (5/2)DyB2 3 DyB
• vB2 ((2g/5)((5/2)DyB2 3 DyB))1/2
• DyB -.5 ? vB2 3.36 ft/s
• dvB2/dDyB (1/2)((2g/5)((5/2)DyB2 3 DyB))-1/2
  (5DyB3)
• 0 5DyB 3 ? DyB .6 ft and vB2 3.40 ft/s
• At maximum displacement velocity is 0 ? T2 0

-yB
1
2
DxA
1
DyB
2
40
-xB

• Knowing that the constant of the spring is 20
  lb/ft,
• determine (a) the velocity of the block B after
  it has
• moved 6 in, (b) the maximum velocity of block B,
• (c) the maximum displacement of block B. Ignore
• friction and the masses of the pulleys and
  spring.
• L -2xA yB ? 0 -2DxA DyB and 0 -2vA vB
• Ve1 0 since spring is undeformed
• Vg1 0 since datum line is at 1
• Ve2 (1/2)20DyA2 Vg2 3 DyB
• V2 (5/2)DyB2 3 DyB
• 0 0 (5/2g)vB22 (5/2)DyB2 3 DyB
• vB2 ((2g/5)((5/2)DyB2 3 DyB))1/2
• DyB -.5 ? vB2 3.36 ft/s
• dvB2/dDyB (1/2)((2g/5)((5/2)DyB2 3 DyB))-1/2
  (5DyB3)
• 0 5DyB 3 ? DyB .6 ft and vB2 3.40 ft/s
• At maximum displacement velocity is 0 ? T2 0
• 0 0 0 (5/2)DyB2 3 DyB

-yB
1
2
DxA
1
DyB
2
41
-xB

• Knowing that the constant of the spring is 20
  lb/ft,
• determine (a) the velocity of the block B after
  it has
• moved 6 in, (b) the maximum velocity of block B,
• (c) the maximum displacement of block B. Ignore
• friction and the masses of the pulleys and
  spring.
• L -2xA yB ? 0 -2DxA DyB and 0 -2vA vB
• Ve1 0 since spring is undeformed
• Vg1 0 since datum line is at 1
• Ve2 (1/2)20DyA2 Vg2 3 DyB
• V2 (5/2)DyB2 3 DyB
• 0 0 (5/2g)vB22 (5/2)DyB2 3 DyB
• vB2 ((2g/5)((5/2)DyB2 3 DyB))1/2
• DyB -.5 ? vB2 3.36 ft/s
• dvB2/dDyB (1/2)((2g/5)((5/2)DyB2 3 DyB))-1/2
  (5DyB3)
• 0 5DyB 3 ? DyB .6 ft and vB2 3.40 ft/s
• At maximum displacement velocity is 0 ? T2 0
• 0 0 0 (5/2)DyB2 3 DyB
• DyB - 1.2 ft or -14.4 in

-yB
1
2
DxA
1
DyB
2
42
-xB

• Knowing that the constant of the spring is 20
  lb/ft,
• determine (a) the velocity of the block B after
  it has
• moved 6 in, (b) the maximum velocity of block B,
• (c) the maximum displacement of block B. Ignore
• friction and the masses of the pulleys and
  spring.
• L -2xA yB ? 0 -2DxA DyB and 0 -2vA vB
• Ve1 0 since spring is undeformed
• Vg1 0 since datum line is at 1
• Ve2 (1/2)20DyA2 Vg2 3 DyB
• V2 (5/2)DyB2 3 DyB
• 0 0 (5/2g)vB22 (5/2)DyB2 3 DyB
• vB2 ((2g/5)((5/2)DyB2 3 DyB))1/2
• DyB -.5 ? vB2 3.36 ft/s
• dvB2/dDyB (1/2)((2g/5)((5/2)DyB2 3 DyB))-1/2
  (5DyB3)
• 0 5DyB 3 ? DyB .6 ft and vB2 3.40 ft/s
• At maximum displacement velocity is 0 ? T2 0
• 0 0 0 (5/2)DyB2 3 DyB
• DyB - 1.2 ft or -14.4 in
• For part b Maximum velocity occurs when
  acceleration is 0 Alternative solution

-yB
1
2
DxA
1
DyB
2