Suppose you are on a ship at sea. Because of rolling waves, the table in your ca
ID: 1502500 • Letter: S
Question
Suppose you are on a ship at sea. Because of rolling waves, the table in your cabin is performing simple harmonic motion in the vertical direction, with amplitude 10cm and frequency 1 Hz. This being an old-fashioned cargo ship, there is a bottle of rum (mass 2 kg) on the table.
(a)[9 pts] Assuming the bottle remains in contact with the table throughout, find the maximum and minimum values of the normal force exerted on it by the table over an oscillation cycle.
(b)[5 pts] How large would the amplitude of the oscillations have to become for the bottle to lose contact with the table, assuming the frequency remains constant? (Hint: what is the value of the normal force at the point the bottle loses contact with the table?)
(c)[2 pts] Would the bottle be the only thing in the cabin to “fly up” at that point? (Assume there are other things in the cabin and they are not all bolted to the floor.) Explain.
Explanation / Answer
a) maximum value of acceleration = A * w2
= 0.1 * (2 * 3.14 * 1)2
= 3.9438 m/sec2
=> maximum values of the normal force = (2 * 9.8) + (2 * 3.9438 )
= 27.487 N
=> minimum values of the normal force = (2 * 9.8) - (2 * 3.9438 )
= 11.712 N
b) For, bottle to lose contact with the table value of maximum acceleration = 9.8 m/sec2
=> 9.8 = A * (2 * 3.14 * 1)2
=> A = 24.848 cm -------------------> amplitude of the oscillations
c) No, bottle would not be the only thing in the cabin to “fly up” at that point . All other things in the cabin would
“fly up” at that point . Because maximum acceleration due to waves becomes equal to 9.8 m/sec2 , so all other things would have a normal force of zero at that point .
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