# Warm-Up Exercise 2 - Answers

## Due 12:15 pm, Wed 29 Aug 2012

Physics 123, Fall 2012

An apple is held completely submerged just below the surface of water in a container. The apple is then moved to a deeper point in the water. Compared with the force needed to hold the apple just below the surface, is the force required now bigger or smaller than at first? Explain your answer. (Assume that the density of water is the same at all depths.)

The force required to hold the apple under water will be the same at both depths. The pressure on the bottom of the apple will be larger as the depth increases, but so will the pressure on the top of the apple. The net difference will be the same independent of the depth. So the force will also be the same. (Also: buoyant force is weight of displaced fluid, so as long as density is not changing the buoyant force won't change.)

A wooden block floats in water, and a steel object is attached to the bottom of the block by a string. If the block remains floating, which of the following statements are valid. (Choose all the correct statements.)
☐ The buoyant force on the steel object is equal to its weight.
☐ The buoyant force on the block is equal to its weight.
☐ The tension in the string is equal to the weight of the steel object.
☑ The tension in the string is less than the weight of the steel object.
☑ The buoyant force on the block is equal to the weight of the volume of the water it displaces.

Since the block is in equilibrium, the net force on the block must be zero: buoyant force (upwards) = weight (downwards) + tension (downwards). Similarly, for the steel object, buoyant force (upwards) + tension (upwards) = weight (downwards). 1 and 2 are false because they don't take into account the tension forces. 3 is false because it doesn't take into account the buoyant force. 4 is true, since tension in string = weight of steel object - buoyant force (eqn 2 above). 5 is just the application of Archimedes' principle to the part of the block that is submerged.