Two tugboats pull a disabled container-ship loaded to 40,000 metric tons (40 mil
ID: 1585916 • Letter: T
Question
Two tugboats pull a disabled container-ship loaded to 40,000 metric tons (40 million kg). Each tug exerts a constant force of 1.80×106 N , one at an angle 12.0 west of north, and the other at an angle 12.0 east of north, as they pull the ship 0.880 km northward at constant 6 m/s.
A. What is the total work done to the ship by the two tugboat Forces? in mega joules
B. What is the container-ship's Kinetic Energy? in mega joules
C.Starting from rest, how far would the tugs have pulled the ship before achieving its 6 m/s velocity? Ignore water resistance for this estimate.
Explanation / Answer
Net force in north direction = 2 X 1.80 X 10^6N X cos12 = 3.52 Mega N
Distance tugged = 0.880 X 10^3 meter North
Work done by tugs = 3.52 X 10^6 N X 0.880 X 10^3m = 3097 X 10^6 J = 3097 Mega J
B. KE = 0.5 X 40 X 10^6 Kg X (6m/s)^2 = 720 Mega J
C. Force on ship = 3.52 X 10^6 N ( towards north)
Acceleration in north direction = 3.52 X 10^6 N/(40X10^6 Kg) = 0.088 m/s^2
Final velocity = 6 m/s Initial velocity = 0m/s
6^2 = 2 X 0.88 m/s^2 X S , where S is the distance moved
S = 20.4 m
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