Procedure to solve impulse momentum problems

1

• Procedure to solve impulse momentum problems
• Step 1 Draw FBDs for each object of interest
• Step 2 Determine the net force along the
  direction of change in velocity
• Step 3 Write the impulse momentum equation along
  the direction in change of velocity ? mvX1
  ImpX12 mvX2
• Step 4 Add a kinematic equation if needed
• Step 5 Solve for unknown quantity(ies)

2

• Problem 13.134 The two blocks shown are released
• from rest at time t 0. Neglecting the masses of
  the
• pulleys and the effect of friction in the pulleys
  and
• between the blocks and the incline, determine (a)
  the
• velocity of block A at t 0.5 s, (b) the tension
  in the
• cable.

3

• Problem 13.134 The two blocks shown are released
• from rest at time t 0. Neglecting the masses of
  the
• pulleys and the effect of friction in the pulleys
  and
• between the blocks and the incline, determine (a)
  the
• velocity of block A at t 0.5 s, (b) the tension
  in the
• cable.

F
x
y
300
NA
10g
4

• Problem 13.134 The two blocks shown are released
• from rest at time t 0. Neglecting the masses of
  the
• pulleys and the effect of friction in the pulleys
  and
• between the blocks and the incline, determine (a)
  the
• velocity of block A at t 0.5 s, (b) the tension
  in the
• cable.
• For A mvX1 ImpX12 mvX2
• 10(0)

F
x
y
300
NA
10g
5

• Problem 13.134 The two blocks shown are released
• from rest at time t 0. Neglecting the masses of
  the
• pulleys and the effect of friction in the pulleys
  and
• between the blocks and the incline, determine (a)
  the
• velocity of block A at t 0.5 s, (b) the tension
  in the
• cable.
• For A mvX1 ImpX12 mvX2
• 10(0) (F 10gsin30)0.5

F
x
y
300
NA
10g
6

• Problem 13.134 The two blocks shown are released
• from rest at time t 0. Neglecting the masses of
  the
• pulleys and the effect of friction in the pulleys
  and
• between the blocks and the incline, determine (a)
  the
• velocity of block A at t 0.5 s, (b) the tension
  in the
• cable.
• For A mvX1 ImpX12 mvX2
• 10(0) (F 10gsin30)0.5 10vAX2

F
x
y
300
NA
10g
7

• Problem 13.134 The two blocks shown are released
• from rest at time t 0. Neglecting the masses of
  the
• pulleys and the effect of friction in the pulleys
  and
• between the blocks and the incline, determine (a)
  the
• velocity of block A at t 0.5 s, (b) the tension
  in the
• cable.
• For A mvX1 ImpX12 mvX2
• 10(0) (F 10gsin30)0.5 10vAX2

F
x
y
300
NA
10g
y
x
3F
300
NB
8g
8

• Problem 13.134 The two blocks shown are released
• from rest at time t 0. Neglecting the masses of
  the
• pulleys and the effect of friction in the pulleys
  and
• between the blocks and the incline, determine (a)
  the
• velocity of block A at t 0.5 s, (b) the tension
  in the
• cable.
• For A mvX1 ImpX12 mvX2
• 10(0) (F 10gsin30)0.5 10vAX2
• For B mvX1 ImpX12 mvX2
• 8(0)

F
x
y
300
NA
10g
y
x
3F
300
NB
8g
9

• Problem 13.134 The two blocks shown are released
• from rest at time t 0. Neglecting the masses of
  the
• pulleys and the effect of friction in the pulleys
  and
• between the blocks and the incline, determine (a)
  the
• velocity of block A at t 0.5 s, (b) the tension
  in the
• cable.
• For A mvX1 ImpX12 mvX2
• 10(0) (F 10gsin30)0.5 10vAX2
• For B mvX1 ImpX12 mvX2
• 8(0) (3F 8gsin30)0.5 8vBX2

F
x
y
300
NA
10g
y
x
3F
300
NB
8g
10

• Problem 13.134 The two blocks shown are released
• from rest at time t 0. Neglecting the masses of
  the
• pulleys and the effect of friction in the pulleys
  and
• between the blocks and the incline, determine (a)
  the
• velocity of block A at t 0.5 s, (b) the tension
  in the
• cable.
• For A mvX1 ImpX12 mvX2
• 10(0) (F 10gsin30)0.5 10vAX2
• For B mvX1 ImpX12 mvX2
• 8(0) (3F 8gsin30)0.5

F
x
y
300
NA
10g
y
x
3F
300
NB
8g
11

• Problem 13.134 The two blocks shown are released
• from rest at time t 0. Neglecting the masses of
  the
• pulleys and the effect of friction in the pulleys
  and
• between the blocks and the incline, determine (a)
  the
• velocity of block A at t 0.5 s, (b) the tension
  in the
• cable.
• For A mvX1 ImpX12 mvX2
• 10(0) (F 10gsin30)0.5 10vAX2
• For B mvX1 ImpX12 mvX2
• 8(0) (3F 8gsin30)0.5 8vBX2

-xA
-xB
F
x
y
300
NA
10g
y
x
3F
300
NB
8g
12

• Problem 13.134 The two blocks shown are released
• from rest at time t 0. Neglecting the masses of
  the
• pulleys and the effect of friction in the pulleys
  and
• between the blocks and the incline, determine (a)
  the
• velocity of block A at t 0.5 s, (b) the tension
  in the
• cable.
• For A mvX1 ImpX12 mvX2
• 10(0) (F 10gsin30)0.5 10vAX2
• For B mvX1 ImpX12 mvX2
• 8(0) (3F 8gsin30)0.5 8vBX2
• L - xA 3xB ? 0 - vAX - 3vBX

-xA
-xB
F
x
y
300
NA
10g
y
x
3F
300
NB
8g
13

• Problem 13.134 The two blocks shown are released
• from rest at time t 0. Neglecting the masses of
  the
• pulleys and the effect of friction in the pulleys
  and
• between the blocks and the incline, determine (a)
  the
• velocity of block A at t 0.5 s, (b) the tension
  in the
• cable.
• For A mvX1 ImpX12 mvX2
• - 3(10(0) (F 10gsin30)0.5 10vAX2)
• For B mvX1 ImpX12 mvX2
• 8(0) (3F 8gsin30)0.5 8vBX2
• L - xA 3xB ? 0 - vAX - 3vBX
• (22gsin30)0.5 - (98/3)vAX2

-xA
-xB
F
x
y
300
NA
10g
y
x
3F
300
NB
8g
14

• Problem 13.134 The two blocks shown are released
• from rest at time t 0. Neglecting the masses of
  the
• pulleys and the effect of friction in the pulleys
  and
• between the blocks and the incline, determine (a)
  the
• velocity of block A at t 0.5 s, (b) the tension
  in the
• cable.
• For A mvX1 ImpX12 mvX2
• 10(0) (F 10gsin30)0.5 10vAX2
• For B mvX1 ImpX12 mvX2
• 8(0) (3F 8gsin30)0.5 8vBX2
• L - xA 3xB ? 0 - vAX - 3vBX
• (22gsin30)0.5 - (98/3)vAX2
• vAX2 - 1.65 m/s

-xA
-xB
F
x
y
300
NA
10g
y
x
3F
300
NB
8g
15

• Problem 13.134 The two blocks shown are released
• from rest at time t 0. Neglecting the masses of
  the
• pulleys and the effect of friction in the pulleys
  and
• between the blocks and the incline, determine (a)
  the
• velocity of block A at t 0.5 s, (b) the tension
  in the
• cable.
• For A mvX1 ImpX12 mvX2
• 10(0) (F 10gsin30)0.5 10vAX2
• For B mvX1 ImpX12 mvX2
• 8(0) (3F 8gsin30)0.5 8vBX2
• L - xA 3xB ? 0 - vAX - 3vBX
• (22gsin30)0.5 - (98/3)vAX2
• vAX2 - 1.65 m/s
• (3F 8gsin30)0.5 8(.55)
• F 16.02 N

-xA
-xB
F
x
y
300
NA
10g
y
x
3F
300
NB
8g
16

• Internal forces are equal in magnitude but
  opposite in
• direction. Therefore the Impulses are equal in
  magnitude
• but opposite in sign.
• mAvA1 ImpA12 mAvA2
• mBvB1 ImpB12 mBvB2

17

• Internal forces are equal in magnitude but
  opposite in
• direction. Therefore the Impulses are equal in
  magnitude
• but opposite in sign.
• mAvA1 ImpA12 mAvA2
• mBvB1 ImpB12 mBvB2
• --------------------------------
• S(mv)1 0 S(mv)2

18

• Problem 13.146 The 30 lb suitcase A has been
  propped up against one end
• of an 80 lb carrier B and is prevented from
  sliding down by other luggage.
• When the luggage is unloaded and the last heavy
  trunk is removed from the
• carrier, the suitcase is free to slide down,
  causing the 80 lb carrier to move to
• the left with a velocity vB of magnitude 2.5
  ft/s. Neglecting friction, determine
• (a) the velocity vA/B of the suitcase relative to
  the carrier as it rolls on the floor
• of the carrier, (b) the velocity of the carrier
  after the suitcase hits the right
• side of the carrier without bouncing back, (c)
  the energy lost in the impact of
• the suitcase on the floor of the carrier.

19

• Problem 13.146 The 30 lb suitcase A has been
  propped up against one end
• of an 80 lb carrier B and is prevented from
  sliding down by other luggage.
• When the luggage is unloaded and the last heavy
  trunk is removed from the
• carrier, the suitcase is free to slide down,
  causing the 80 lb carrier to move to
• the left with a velocity vB of magnitude 2.5
  ft/s. Neglecting friction, determine
• (a) the velocity vA/B of the suitcase relative to
  the carrier as it rolls on the floor
• of the carrier, (b) the velocity of the carrier
  after the suitcase hits the right
• side of the carrier without bouncing back, (c)
  the energy lost in the impact of
• the suitcase on the floor of the carrier.
• S(mv)1 S(mv)2
• (30/g)0 (80/g)0

20

• Problem 13.146 The 30 lb suitcase A has been
  propped up against one end
• of an 80 lb carrier B and is prevented from
  sliding down by other luggage.
• When the luggage is unloaded and the last heavy
  trunk is removed from the
• carrier, the suitcase is free to slide down,
  causing the 80 lb carrier to move to
• the left with a velocity vB of magnitude 2.5
  ft/s. Neglecting friction, determine
• (a) the velocity vA/B of the suitcase relative to
  the carrier as it rolls on the floor
• of the carrier, (b) the velocity of the carrier
  after the suitcase hits the right
• side of the carrier without bouncing back, (c)
  the energy lost in the impact of
• the suitcase on the floor of the carrier.
• S(mv)1 S(mv)2
• (30/g)0 (80/g)0 (30/g)vA2 (80/g)(- 2.5)

21

• Problem 13.146 The 30 lb suitcase A has been
  propped up against one end
• of an 80 lb carrier B and is prevented from
  sliding down by other luggage.
• When the luggage is unloaded and the last heavy
  trunk is removed from the
• carrier, the suitcase is free to slide down,
  causing the 80 lb carrier to move to
• the left with a velocity vB of magnitude 2.5
  ft/s. Neglecting friction, determine
• (a) the velocity vA/B of the suitcase relative to
  the carrier as it rolls on the floor
• of the carrier, (b) the velocity of the carrier
  after the suitcase hits the right
• side of the carrier without bouncing back, (c)
  the energy lost in the impact of
• the suitcase on the floor of the carrier.
• S(mv)1 S(mv)2
• (30/g)0 (80/g)0 (30/g)vA2 (80/g)(- 2.5)
• vA 6.67 ft/s

22

• Problem 13.146 The 30 lb suitcase A has been
  propped up against one end
• of an 80 lb carrier B and is prevented from
  sliding down by other luggage.
• When the luggage is unloaded and the last heavy
  trunk is removed from the
• carrier, the suitcase is free to slide down,
  causing the 80 lb carrier to move to
• the left with a velocity vB of magnitude 2.5
  ft/s. Neglecting friction, determine
• (a) the velocity vA/B of the suitcase relative to
  the carrier as it rolls on the floor
• of the carrier, (b) the velocity of the carrier
  after the suitcase hits the right
• side of the carrier without bouncing back, (c)
  the energy lost in the impact of
• the suitcase on the floor of the carrier.
• S(mv)1 S(mv)2
• (30/g)0 (80/g)0 (30/g)vA2 (80/g)(- 2.5)
• vA 6.67 ft/s
• vA/B vA vB

23

• Problem 13.146 The 30 lb suitcase A has been
  propped up against one end
• of an 80 lb carrier B and is prevented from
  sliding down by other luggage.
• When the luggage is unloaded and the last heavy
  trunk is removed from the
• carrier, the suitcase is free to slide down,
  causing the 80 lb carrier to move to
• the left with a velocity vB of magnitude 2.5
  ft/s. Neglecting friction, determine
• (a) the velocity vA/B of the suitcase relative to
  the carrier as it rolls on the floor
• of the carrier, (b) the velocity of the carrier
  after the suitcase hits the right
• side of the carrier without bouncing back, (c)
  the energy lost in the impact of
• the suitcase on the floor of the carrier.
• S(mv)1 S(mv)2
• (30/g)0 (80/g)0 (30/g)vA2 (80/g)(- 2.5)
• vA 6.67 ft/s
• vA/B vA vB ? vA/B 6.67 ( - 2.5) 9.17
  ft/s

24

• Problem 13.146 The 30 lb suitcase A has been
  propped up against one end
• of an 80 lb carrier B and is prevented from
  sliding down by other luggage.
• When the luggage is unloaded and the last heavy
  trunk is removed from the
• carrier, the suitcase is free to slide down,
  causing the 80 lb carrier to move to
• the left with a velocity vB of magnitude 2.5
  ft/s. Neglecting friction, determine
• (a) the velocity vA/B of the suitcase relative to
  the carrier as it rolls on the floor
• of the carrier, (b) the velocity of the carrier
  after the suitcase hits the right
• side of the carrier without bouncing back, (c)
  the energy lost in the impact of
• the suitcase on the floor of the carrier.
• S(mv)1 S(mv)2
• (30/g)0 (80/g)0 (30/g)vA2 (80/g)(- 2.5)
• vA 6.67 ft/s
• vA/B vA vB ? vA/B 6.67 ( - 2.5) 9.17
  ft/s
• S(mv)2 S(mv)3
• (30/g)6.67 (80/g)(- 2.5)

25

• Problem 13.146 The 30 lb suitcase A has been
  propped up against one end
• of an 80 lb carrier B and is prevented from
  sliding down by other luggage.
• When the luggage is unloaded and the last heavy
  trunk is removed from the
• carrier, the suitcase is free to slide down,
  causing the 80 lb carrier to move to
• the left with a velocity vB of magnitude 2.5
  ft/s. Neglecting friction, determine
• (a) the velocity vA/B of the suitcase relative to
  the carrier as it rolls on the floor
• of the carrier, (b) the velocity of the carrier
  after the suitcase hits the right
• side of the carrier without bouncing back, (c)
  the energy lost in the impact of
• the suitcase on the floor of the carrier.
• S(mv)1 S(mv)2
• (30/g)0 (80/g)0 (30/g)vA2 (80/g)(- 2.5)
• vA 6.67 ft/s
• vA/B vA vB ? vA/B 6.67 ( - 2.5) 9.17
  ft/s
• S(mv)2 S(mv)3
• (30/g)6.67 (80/g)(- 2.5) (30/g 80/g)vB3

26

• Problem 13.146 The 30 lb suitcase A has been
  propped up against one end
• of an 80 lb carrier B and is prevented from
  sliding down by other luggage.
• When the luggage is unloaded and the last heavy
  trunk is removed from the
• carrier, the suitcase is free to slide down,
  causing the 80 lb carrier to move to
• the left with a velocity vB of magnitude 2.5
  ft/s. Neglecting friction, determine
• (a) the velocity vA/B of the suitcase relative to
  the carrier as it rolls on the floor
• of the carrier, (b) the velocity of the carrier
  after the suitcase hits the right
• side of the carrier without bouncing back, (c)
  the energy lost in the impact of
• the suitcase on the floor of the carrier.
• S(mv)1 S(mv)2
• (30/g)0 (80/g)0 (30/g)vA2 (80/g)(- 2.5)
• vA 6.67 ft/s
• vA/B vA vB ? vA/B 6.67 ( - 2.5) 9.17
  ft/s
• S(mv)2 S(mv)3
• (30/g)6.67 (80/g)(- 2.5) (30/g 80/g)vB3
• vB3 0

27

• Problem 13.146 The 30 lb suitcase A has been
  propped up against one end
• of an 80 lb carrier B and is prevented from
  sliding down by other luggage.
• When the luggage is unloaded and the last heavy
  trunk is removed from the
• carrier, the suitcase is free to slide down,
  causing the 80 lb carrier to move to
• the left with a velocity vB of magnitude 2.5
  ft/s. Neglecting friction, determine
• (a) the velocity vA/B of the suitcase relative to
  the carrier as it rolls on the floor
• of the carrier, (b) the velocity of the carrier
  after the suitcase hits the right
• side of the carrier without bouncing back, (c)
  the energy lost in the impact of
• the suitcase on the floor of the carrier.
• S(mv)1 S(mv)2 ? (30/g)0 (80/g)0 (30/g)vA2
  (80/g)(- 2.5)
• vA 6.67 ft/s vA/B vA vB ? vA/B 6.67
  ( - 2.5) 9.16 ft/s
• S(mv)2 S(mv)3 ? (30/g)6.67 (80/g)(- 2.5)
  (30/g 80/g)vB3
• vB3 0
• Kinetic Energy after impact (1/2)(30/g)6.672

28

• Problem 13.146 The 30 lb suitcase A has been
  propped up against one end
• of an 80 lb carrier B and is prevented from
  sliding down by other luggage.
• When the luggage is unloaded and the last heavy
  trunk is removed from the
• carrier, the suitcase is free to slide down,
  causing the 80 lb carrier to move to
• the left with a velocity vB of magnitude 2.5
  ft/s. Neglecting friction, determine
• (a) the velocity vA/B of the suitcase relative to
  the carrier as it rolls on the floor
• of the carrier, (b) the velocity of the carrier
  after the suitcase hits the right
• side of the carrier without bouncing back, (c)
  the energy lost in the impact of
• the suitcase on the floor of the carrier.
• S(mv)1 S(mv)2 ? (30/g)0 (80/g)0 (30/g)vA2
  (80/g)(- 2.5)
• vA 6.67 ft/s vA/B vA vB ? vA/B 6.67
  ( - 2.5) 9.16 ft/s
• S(mv)2 S(mv)3 ? (30/g)6.67 (80/g)(- 2.5)
  (30/g 80/g)vB3
• vB3 0
• Kinetic Energy after impact (1/2)(30/g)6.672
  (1/2)(80/g)(-2.5)2

29

• Problem 13.146 The 30 lb suitcase A has been
  propped up against one end
• of an 80 lb carrier B and is prevented from
  sliding down by other luggage.
• When the luggage is unloaded and the last heavy
  trunk is removed from the
• carrier, the suitcase is free to slide down,
  causing the 80 lb carrier to move to
• the left with a velocity vB of magnitude 2.5
  ft/s. Neglecting friction, determine
• (a) the velocity vA/B of the suitcase relative to
  the carrier as it rolls on the floor
• of the carrier, (b) the velocity of the carrier
  after the suitcase hits the right
• side of the carrier without bouncing back, (c)
  the energy lost in the impact of
• the suitcase on the floor of the carrier.
• S(mv)1 S(mv)2 ? (30/g)0 (80/g)0 (30/g)vA2
  (80/g)(- 2.5)
• vA 6.67 ft/s vA/B vA vB ? vA/B 6.67
  ( - 2.5) 9.16 ft/s
• S(mv)2 S(mv)3 ? (30/g)6.67 (80/g)(- 2.5)
  (30/g 80/g)vB3
• vB3 0
• Kinetic Energy after impact (1/2)(30/g)6.672
  (1/2)(80/g)(-2.5)2 28.47 ft lb

30

• Problem 13.146 The 30 lb suitcase A has been
  propped up against one end
• of an 80 lb carrier B and is prevented from
  sliding down by other luggage.
• When the luggage is unloaded and the last heavy
  trunk is removed from the
• carrier, the suitcase is free to slide down,
  causing the 80 lb carrier to move to
• the left with a velocity vB of magnitude 2.5
  ft/s. Neglecting friction, determine
• (a) the velocity vA/B of the suitcase relative to
  the carrier as it rolls on the floor
• of the carrier, (b) the velocity of the carrier
  after the suitcase hits the right
• side of the carrier without bouncing back, (c)
  the energy lost in the impact of
• the suitcase on the floor of the carrier.
• S(mv)1 S(mv)2 ? (30/g)0 (80/g)0 (30/g)vA2
  (80/g)(- 2.5)
• vA 6.67 ft/s vA/B vA vB ? vA/B 6.67
  ( - 2.5) 9.16 ft/s
• S(mv)2 S(mv)3 ? (30/g)6.67 (80/g)(- 2.5)
  (30/g 80/g)vB3
• vB3 0
• Kinetic Energy after impact (1/2)(30/g)6.672
  (1/2)(80/g)(-2.5)2 28.47 ft lb
• Potential energy before impact 30(16 4)/12

31

• Problem 13.146 The 30 lb suitcase A has been
  propped up against one end
• of an 80 lb carrier B and is prevented from
  sliding down by other luggage.
• When the luggage is unloaded and the last heavy
  trunk is removed from the
• carrier, the suitcase is free to slide down,
  causing the 80 lb carrier to move to
• the left with a velocity vB of magnitude 2.5
  ft/s. Neglecting friction, determine
• (a) the velocity vA/B of the suitcase relative to
  the carrier as it rolls on the floor
• of the carrier, (b) the velocity of the carrier
  after the suitcase hits the right
• side of the carrier without bouncing back, (c)
  the energy lost in the impact of
• the suitcase on the floor of the carrier.
• S(mv)1 S(mv)2 ? (30/g)0 (80/g)0 (30/g)vA2
  (80/g)(- 2.5)
• vA 6.67 ft/s vA/B vA vB ? vA/B 6.67
  ( - 2.5) 9.16 ft/s
• S(mv)2 S(mv)3 ? (30/g)6.67 (80/g)(- 2.5)
  (30/g 80/g)vB3
• vB3 0
• Kinetic Energy after impact (1/2)(30/g)6.672
  (1/2)(80/g)(-2.5)2 28.47 ft lb
• Potential energy before impact 30(16 4)/12
  30 ft lb

32

• Problem 13.146 The 30 lb suitcase A has been
  propped up against one end
• of an 80 lb carrier B and is prevented from
  sliding down by other luggage.
• When the luggage is unloaded and the last heavy
  trunk is removed from the
• carrier, the suitcase is free to slide down,
  causing the 80 lb carrier to move to
• the left with a velocity vB of magnitude 2.5
  ft/s. Neglecting friction, determine
• (a) the velocity vA/B of the suitcase relative to
  the carrier as it rolls on the floor
• of the carrier, (b) the velocity of the carrier
  after the suitcase hits the right
• side of the carrier without bouncing back, (c)
  the energy lost in the impact of
• the suitcase on the floor of the carrier.
• S(mv)1 S(mv)2 ? (30/g)0 (80/g)0 (30/g)vA2
  (80/g)(- 2.5)
• vA 6.67 ft/s vA/B vA vB ? vA/B 6.67
  ( - 2.5) 9.16 ft/s
• S(mv)2 S(mv)3 ? (30/g)6.67 (80/g)(- 2.5)
  (30/g 80/g)vB3
• vB3 0
• Kinetic Energy after impact (1/2)(30/g)6.672
  (1/2)(80/g)(-2.5)2 28.47 ft lb
• Potential energy before impact 30(16 4)/12
  30 ft lb
• Energy lost 30 28.47 1.53 ft lb

33

• Procedure for conservation of linear momentum
• Step 1 determine the pre and post impulse
  velocities of each object

34

• Procedure for conservation of linear momentum
• Step 1 determine the pre and post impulse
  velocities of each object
• Step 2 write conservation of momentum equation
• S(mv)1 S(mv)2

35

• Procedure for conservation of linear momentum
• Step 1 determine the pre and post impulse
  velocities of each object
• Step 2 write conservation of momentum equation
• S(mv)1 S(mv)2
• Step3 add a kinematic relation if needed

36

• Procedure for conservation of linear momentum
• Step 1 determine the pre and post impulse
  velocities of each object
• Step 2 write conservation of momentum equation
• S(mv)1 S(mv)2
• Step3 add a kinematic relation if needed
• Step 4 Solve equations for unknowns

37

• Problem 13.147 A 112 Mg tugboat is moving at 2
• m/s with a slack towing cable attached to an 88
  Mg
• barge which is at rest. The cable is being
  unwound
• from a drum on the tugboat at a constant rate of
• 1.8 m/s and that rate is maintained after the
  cable
• becomes taut. Neglecting the resistance of the
• water, determine (a) the velocity of the tugboat
• after the cable becomes taut, (b) the impulse
• exerted on the barge as the cable becomes taut.

38

• Problem 13.147 A 112 Mg tugboat is moving at 2
• m/s with a slack towing cable attached to an 88
  Mg
• barge which is at rest. The cable is being
  unwound
• from a drum on the tugboat at a constant rate of
• 1.8 m/s and that rate is maintained after the
  cable
• becomes taut. Neglecting the resistance of the
• water, determine (a) the velocity of the tugboat
• after the cable becomes taut, (b) the impulse
• exerted on the barge as the cable becomes taut.
• Part (a) since the force in the cable is
  internal
• S(mv)1 S(mv)2
• 88000(0)

39

• Problem 13.147 A 112 Mg tugboat is moving at 2
• m/s with a slack towing cable attached to an 88
  Mg
• barge which is at rest. The cable is being
  unwound
• from a drum on the tugboat at a constant rate of
• 1.8 m/s and that rate is maintained after the
  cable
• becomes taut. Neglecting the resistance of the
• water, determine (a) the velocity of the tugboat
• after the cable becomes taut, (b) the impulse
• exerted on the barge as the cable becomes taut.
• Part (a) since the force in the cable is
  internal
• S(mv)1 S(mv)2
• 88000(0) 112000(2)

40

• Problem 13.147 A 112 Mg tugboat is moving at 2
• m/s with a slack towing cable attached to an 88
  Mg
• barge which is at rest. The cable is being
  unwound
• from a drum on the tugboat at a constant rate of
• 1.8 m/s and that rate is maintained after the
  cable
• becomes taut. Neglecting the resistance of the
• water, determine (a) the velocity of the tugboat
• after the cable becomes taut, (b) the impulse
• exerted on the barge as the cable becomes taut.
• Part (a) since the force in the cable is
  internal
• S(mv)1 S(mv)2
• 88000(0) 112000(2) 88000vB2

41

• Problem 13.147 A 112 Mg tugboat is moving at 2
• m/s with a slack towing cable attached to an 88
  Mg
• barge which is at rest. The cable is being
  unwound
• from a drum on the tugboat at a constant rate of
• 1.8 m/s and that rate is maintained after the
  cable
• becomes taut. Neglecting the resistance of the
• water, determine (a) the velocity of the tugboat
• after the cable becomes taut, (b) the impulse
• exerted on the barge as the cable becomes taut.
• Part (a) since the force in the cable is
  internal
• S(mv)1 S(mv)2
• 88000(0) 112000(2) 88000vB2 112000vT2

42

• Problem 13.147 A 112 Mg tugboat is moving at 2
• m/s with a slack towing cable attached to an 88
  Mg
• barge which is at rest. The cable is being
  unwound
• from a drum on the tugboat at a constant rate of
• 1.8 m/s and that rate is maintained after the
  cable
• becomes taut. Neglecting the resistance of the
• water, determine (a) the velocity of the tugboat
• after the cable becomes taut, (b) the impulse
• exerted on the barge as the cable becomes taut.
• Part (a) since the force in the cable is
  internal
• S(mv)1 S(mv)2
• 88000(0) 112000(2) 88000vB2 112000vT2
• 28 11vB2 14vT2

43

• Problem 13.147 A 112 Mg tugboat is moving at 2
• m/s with a slack towing cable attached to an 88
  Mg
• barge which is at rest. The cable is being
  unwound
• from a drum on the tugboat at a constant rate of
• 1.8 m/s and that rate is maintained after the
  cable
• becomes taut. Neglecting the resistance of the
• water, determine (a) the velocity of the tugboat
• after the cable becomes taut, (b) the impulse
• exerted on the barge as the cable becomes taut.
• Part (a) since the force in the cable is
  internal
• S(mv)1 S(mv)2
• 88000(0) 112000(2) 88000vB2 112000vT2
• 28 11vB2 14vT2
• V(B/T)2 vB2 - vT2

44

• Problem 13.147 A 112 Mg tugboat is moving at 2
• m/s with a slack towing cable attached to an 88
  Mg
• barge which is at rest. The cable is being
  unwound
• from a drum on the tugboat at a constant rate of
• 1.8 m/s and that rate is maintained after the
  cable
• becomes taut. Neglecting the resistance of the
• water, determine (a) the velocity of the tugboat
• after the cable becomes taut, (b) the impulse
• exerted on the barge as the cable becomes taut.
• Part (a) since the force in the cable is
  internal
• S(mv)1 S(mv)2
• 88000(0) 112000(2) 88000vB2 112000vT2
• 28 11vB2 14vT2
• V(B/T)2 vB2 - vT2
• -1.8 vB2 - vT2

45

• Problem 13.147 A 112 Mg tugboat is moving at 2
• m/s with a slack towing cable attached to an 88
  Mg
• barge which is at rest. The cable is being
  unwound
• from a drum on the tugboat at a constant rate of
• 1.8 m/s and that rate is maintained after the
  cable
• becomes taut. Neglecting the resistance of the
• water, determine (a) the velocity of the tugboat
• after the cable becomes taut, (b) the impulse
• exerted on the barge as the cable becomes taut.
• Part (a) since the force in the cable is
  internal
• S(mv)1 S(mv)2
• 88000(0) 112000(2) 88000vB2 112000vT2
• 28 11vB2 14vT2
• V(B/T)2 vB2 - vT2
• -1.8 vB2 - vT2
• 2 equations 2 unknowns vB2 , vT2
• vT2 1.912 m/s vB2 0.112 m/s

46

• Problem 13.147 A 112 Mg tugboat is moving at 2
• m/s with a slack towing cable attached to an 88
  Mg
• barge which is at rest. The cable is being
  unwound
• from a drum on the tugboat at a constant rate of
• 1.8 m/s and that rate is maintained after the
  cable
• becomes taut. Neglecting the resistance of the
• water, determine (a) the velocity of the tugboat
• after the cable becomes taut, (b) the impulse
• exerted on the barge as the cable becomes taut.
• Part (a) since the force in the cable is
  internal
• S(mv)1 S(mv)2
• 88000(0) 112000(2) 88000vB2 112000vT2
• 28 11vB2 14vT2
• V(B/T)2 vB2 - vT2
• -1.8 vB2 - vT2
• 2 equations 2 unknowns vB2 , vT2
• vT2 1.912 m/s vB2 0.112 m/s
• Part (b)
• mBvB1 ImpB12 mBvB2

x
F
47

• Problem 13.147 A 112 Mg tugboat is moving at 2
• m/s with a slack towing cable attached to an 88
  Mg
• barge which is at rest. The cable is being
  unwound
• from a drum on the tugboat at a constant rate of
• 1.8 m/s and that rate is maintained after the
  cable
• becomes taut. Neglecting the resistance of the
• water, determine (a) the velocity of the tugboat
• after the cable becomes taut, (b) the impulse
• exerted on the barge as the cable becomes taut.
• Part (a) since the force in the cable is
  internal
• S(mv)1 S(mv)2
• 88000(0) 112000(2) 88000vB2 112000vT2
• 28 11vB2 14vT2
• V(B/T)2 vB2 - vT2
• -1.8 vB2 - vT2
• 2 equations 2 unknowns vB2 , vT2
• vT2 1.912 m/s vB2 0.112 m/s
• Part (b)
• mBvB1 ImpB12 mBvB2

x
F
48

• Problem 13.147 A 112 Mg tugboat is moving at 2
• m/s with a slack towing cable attached to an 88
  Mg
• barge which is at rest. The cable is being
  unwound
• from a drum on the tugboat at a constant rate of
• 1.8 m/s and that rate is maintained after the
  cable
• becomes taut. Neglecting the resistance of the
• water, determine (a) the velocity of the tugboat
• after the cable becomes taut, (b) the impulse
• exerted on the barge as the cable becomes taut.
• Part (a) since the force in the cable is
  internal
• S(mv)1 S(mv)2
• 88000(0) 112000(2) 88000vB2 112000vT2
• 28 11vB2 14vT2
• V(B/T)2 vB2 - vT2
• -1.8 vB2 - vT2
• 2 equations 2 unknowns vB2 , vT2
• vT2 1.912 m/s vB2 0.112 m/s
• Part (b)
• mBvB1 ImpB12 mBvB2

x
F
49

• Problem 13.147 A 112 Mg tugboat is moving at 2
• m/s with a slack towing cable attached to an 88
  Mg
• barge which is at rest. The cable is being
  unwound
• from a drum on the tugboat at a constant rate of
• 1.8 m/s and that rate is maintained after the
  cable
• becomes taut. Neglecting the resistance of the
• water, determine (a) the velocity of the tugboat
• after the cable becomes taut, (b) the impulse
• exerted on the barge as the cable becomes taut.
• Part (a) since the force in the cable is
  internal
• S(mv)1 S(mv)2
• 88000(0) 112000(2) 88000vB2 112000vT2
• 28 11vB2 14vT2
• V(B/T)2 vB2 - vT2
• -1.8 vB2 - vT2
• 2 equations 2 unknowns vB2 , vT2
• vT2 1.912 m/s vB2 0.112 m/s
• Part (b)
• mBvB1 ImpB12 mBvB2

x
F
50

• Problem 13.147 A 112 Mg tugboat is moving at 2
• m/s with a slack towing cable attached to an 88
  Mg
• barge which is at rest. The cable is being
  unwound
• from a drum on the tugboat at a constant rate of
• 1.8 m/s and that rate is maintained after the
  cable
• becomes taut. Neglecting the resistance of the
• water, determine (a) the velocity of the tugboat
• after the cable becomes taut, (b) the impulse
• exerted on the barge as the cable becomes taut.
• Part (a) since the force in the cable is
  internal
• S(mv)1 S(mv)2
• 88000(0) 112000(2) 88000vB2 112000vT2
• 28 11vB2 14vT2
• V(B/T)2 vB2 - vT2
• -1.8 vB2 - vT2
• 2 equations 2 unknowns vB2 , vT2
• vT2 1.912 m/s vB2 0.112 m/s
• Part (b)
• mBvB1 ImpB12 mBvB2

x
F