Question

Question:A boat develops a leak and, after its passengers are rescued, eventually sinks to the bottom of a lake. When the boat is at the bottom, what is the force of the lake bottom on the boat? (a) greater than the weight of the boat (b) Equal to the weight of the boat (c) less than the weight of the boat (d) Equal to the weight of the displaced water (e) Equal to the buoyant force on the boat

Short answer

The force of the lake bottom on the boat is less than the weight of the boat; hence option (c) is correct.

Step-by-step solution

Step 1: Archimedes’ principle

When an object is partially or fully submerged in a fluid, the fluid exerts on the object an upward force called the buoyant force. According to Archimedes’s principle, the magnitude of the buoyant force is equal to the weight of the fluid displaced by the object:

B =${\rho }_{Fluid}g{V}_{disp}$

Where V_dispthe volume of fluid is displaced and${\rho }_{Fluid}$ is the density of the fluid.

Find when the boat is at the bottom, what is the force of the lake bottom on the boat

We use the above concept and first let’s draw the free body diagram of boat at the lake bottom.

From figure and by using Archimedes’s principle we can write the equations as;

W =N+F_B

N =W-F_B

Force by the lake bottom on the boat is W - F_B, which is less then to the weight of the boat.

Hence option (c), the force of the lake bottom on the boat is less than the weight of the boat is correct.