A Spanish galleon is about to be boarded by bloodthirsty pirates in the shallows of a Caribbean island. To save a box of treasure on board, the captain orders his crew to secretly toss the box overboard, planning to come back for it later. The rectangular box is waterproof and measures 40.0 cm by 25.0 cm by 30.0 cm. It is made of wood and has mostly gold pieces inside, resulting in an average box density three times that of seawater.
Sinking below the surface, the box moves at constant vertical velocity of 1.15 m/s for 12.0 m before hitting the bottom. (a) Draw the free-body diagram for the box, (b) determine the magnitudes of the forces on the box, and (c) calculate the work done by each force and the net work done on the box. (d) Calculate the change in the box’s gravitational potential energy. (e) What is the change in the box’s total energy ?

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  1. Since the box is moving through sea water at a constant speed, the net force on it must be zero.
    The forces are:
    i) W= mg its weight downwards
    ii) Fb - buoyant force upwards
    iii) Ff - frictional force offered by water acting upwards.
    now W = mg = V*Db*g (Db-density of box)
    and Fb = V*Dw*g (Dw - density of water)

    Since Db = 3*Dw, W = 3*Fb
    So Ff = W - Fb
    = W - W/3 = 2W/3
    From these equations, find magnitudes of the three force viz. W, Fb and Ff by calculating volume V and taking sea water density Dw = 1024 Kg/m^3
    Once you know the forces, calculate the work done as force x Distance moved

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