A 120-ton tugboat is moving at 6 ft/s with a slack towing cable attached to a 100-ton barge that is at rest. The cable is being unwound from a drum on the tugboat at a constant rate of 5.4 ft/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.
(a)
Velocity of the tugboat after the cable becomes taut
Answer to Problem 13.145P
The velocity of the tugboat after the cable becomes taut is equal to
Explanation of Solution
Given information:
Weight of tugboat is
Weight of barge is
The velocity of tugboat is
Cable is being unwound at a constant rate of
“A force acting on a particle during a very short time interval but large enough to produce a definite change in momentum is called an impulsive force.”
Impulse momentum principle for impulsive motion is defined as,
Calculation:
Mass
Mass
Assume
Apply Impulse momentum principle
Apply impulse momentum principle
The relative velocity
According to above equations
Solve
Conclusion:
The velocity of the tugboat after the cable becomes taut is equal to
(b)
Impulse exerted on the barge as the cable becomes taut
Answer to Problem 13.145P
The impulse
Explanation of Solution
Given information:
Weight of tugboat is
Weight of barge is
The velocity of tugboat is
Cable is being unwound at a constant rate of
“A force acting on a particle during a very short time interval but large enough to produce a definite change in momentum is called an impulsive force.”
Impulse momentum principle for impulsive motion is defined as
Calculation:
According to sub part A
Velocity
Mass
The velocity
The impulse
Conclusion:
The impulse
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Chapter 13 Solutions
Vector Mechanics For Engineers
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