Question

A toy boat made of steel is floating in a beaker having water. The beaker is placed on a spring balance. The boat tilts and sinks into water.

Answer 1

The reading on the spring balance will decrease.

Answer 2

When the boat floats, it displaces a volume of water whose weight is equal to the weight of the boat. By Newton's third law, the boat exerts a downward force equal to its weight on the water. The spring balance reading is the weight of the beaker + weight of water + weight of the boat.

When the boat sinks, it is fully submerged. The buoyant force on the fully submerged boat is $F_B = \rho_{water} V_{boat} g$. Since the boat sinks, its weight $W_{boat}$ is greater than $F_B$. The boat rests on the bottom of the beaker, and the bottom exerts a normal force $N$ upwards on the boat. For the boat to be in equilibrium, $W_{boat} = F_B + N$, so $N = W_{boat} - F_B$. By Newton's third law, the boat exerts a downward force $N$ on the bottom of the beaker.

The new spring balance reading is the weight of the beaker + weight of water + $N$. New reading = $W_{beaker} + W_{water} + (W_{boat} - F_B)$. The change in reading is $(W_{beaker} + W_{water} + W_{boat} - F_B) - (W_{beaker} + W_{water} + W_{boat}) = -F_B$. Since $F_B$ is positive, the reading decreases by an amount equal to the buoyant force on the fully submerged boat.