Question

You are shipwrecked and floating in the middle of the ocean on a raft. You have a treasure chest full of gold. Your raft is barely afloat, so you have two choices on how to position the treasure chest:

1) Keep the chest on top of the raft

2) Tie the treasure chest to the bottom of the raft, so that the chest is completely submerged.

A) Which choice would cause you to displace a greater mass of water? Or, would they both cause you to displace an equal mass of water?

B) Which choice would cause you to displace a greater volume of water? Or, would they both cause you to displace an equal volume of water?

C) Which choice would cause the raft to float higher in the water? Or would they both do so?

Please explain and show your work! Thank you!

Answer 1

Solution:

Buoyant force is the upthrust acting on the surface of boat and is equals to the weight of water displaced by the boat.

Now, if buoyant force equals the weight of the object, then that boat will float and if it is lesser than the weight of the boat it will sink.

The weight of water displaced can be obtained by multiplying the mass of water displaced with the acceleration due to gravity g.

The mass of water displaced is equals to the product of the volume of the boat lying below the surface of the water and the density of the water. Notice, the density is water will not change wherever you try to put the chest. Hence, the volume of the boat lying below the surface of the water will be the deciding factor here.

A)

If the chest is tied to the bottom of the raft, the volume of the boat will change will increase in-fact, hence more volume of the water will get displaced, thus, more mass of water will displace.

B)

If the chest is tied to the bottom of the raft, the volume of the boat will change will increase in-fact, hence more volume of the water will get displaced.

C)

From the discussions done in part A and B, the first choice of keeping chest The more load you add to a boat, the more it weighs, and the further it will have to sink for the upthrust to balance its weight. Because the pressure of water increases with depth: the further into the water the boat sinks, without actually submerging, the more upthrust is created. Hence, keeping the chest on the top of the raft would cause the raft to float higher.