Suppose you are on a ship at sea. Because of rolling waves, the table in your ca

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 10 cm and
frequency 1Hz. 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) a max = kA/m = w^2*A = 4*pi^2*f^2*A = 4*3.14^2*1^2*0.1 = 3.943840 m/s/s
N max = mg + ma = 2(9.8+3.943840) = 27.48768 N
N min = m(g - a) = 11.71232 N
b) N min = 0 [ for leaving contact]
so a = g = 9.8 m/s/s = 4*3.14^2*A
A = 0.248488 m
c) N min is independent of mass, so every thing will flyk up

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