Question

A 20 kg treasure chest is raised by a rope at constant speed from the bottom of a lake (density

3 −3 3 1000kg/m ). The volume of the chest is 12×10 m .

1. a) Determine the tension in the rope while the chest is being raised and is still completely submerged. Note that this involves Newton’s second law and the solution should include the usual ingredients used in applying Newton’s second law, i.e. a free body diagram, etc,. . .

2. b) The chest eventually begins to emerge from the water and is held at rest with half of its volume still submerged. Determine the tension in the rope at this point.

Answer 1

(a) Volume and density of the chest is not clear in this problem. I am considering the volume as 12 x 10^-3 m³ and the density as 1000 Kg/m³.

The buoyant force (F_b) acting upward will be equal to the weight replaced by the chest. It is equal to

The weight of the chest is W and it is equal to

Let us consider that the tension on the rope will be T. As the chest is moving upward at constant speed, the net acceleration will be zero according to Newton´s 2nd law. Therefore, net force will be zero. Hence

(b) If the chest is submerged with half of its volume still inside water, the buoyancy force will be half. Hence, F_b = 117.6/2 = 58.8 N. Therefore, the tension in the rope will be