Question

During an ecology experiment, an aquarium half filled with water is placed on a scale. The scale reads 195 N.

a. A rock weighing 8 N is added to the aquarium. If the rock sinks to the bottom of the aquarium, what will the scale read?
b. The rock is removed from the aquarium, and the amount of water is adjusted until the scale again reads 195 N. A fish weighing 2 N is added to the aquarium. What is the scale reading with the fish in the aquarium?

Answer 1

a. A rock weighing 8 N is added to the aquarium. If the rock sinks to the bottom of the aquarium, what will the scale read?

F_g = 195 N + 8 N = 203 N

b. The rock is removed from the aquarium, and the amount of water is adjusted until the scale again reads 195 N. A fish weighing 2 N is added to the aquarium. What is the scale reading with the fish in the aquarium?

F_g = 195 N + 2 N = 197 N

In each case the buoyant force is equal to the weight of the water displaced.That is

F_gtotal = F_gaquarium + [(F_grock(fish) - F_buoyant) + F_{gwater displaced}]

         = F_gaquarium + F_grock(fish)

(or: By Pascal