Lab Diving Canisters
 When objects are submerged in a fluid one of three outcomes is expected:   the object will float with a certain percentage of its volume above the surface of the fluid, the object will float in neutral equilibrium with all of its volume entirely submerged, or the object will sink and come to rest on the bottom of the container.   These outcomes are based on hydrostatic pressure and Archimedes' Principle.
Experimentation shows that a submerged, non-porous object will displace an amount of fluid equal to its volume. Thus if the volume of water in a graduated cylinder rises from 74.5 ml to 78.0 ml with the addition of an object that sinks to the bottom of the cylinder, then we know that the submerged object has a volume of V = 78.0 - 74.5 or 3.5 cm3. Note that we can change the unit from ml to cm3 since 1 ml of water occupies 1 cm3 of space.

Even if an object floats the buoyant force is still equal to the weight of the water that it displaces. It is just not necessary for the object to displace a volume of water equal to its entire volume. In fact, it turns out that the ratio of the relative volumes is equal to the ratio of the relative densities.

Which of our original three outcomes occur depends on the relative densities of the liquid and the submerged object.

If the density of the object is less than the density of the fluid, the object will rise, or float. If the density of the object is greater than the density of the fluid, the object will sink.

If the density of the object is exactly equal to the density of the fluid, then the object, when submerged, will be in neutral equilibrium. This is the desired result for scuba divers when they add weights to their belts so that they can swim at any desired depth without having to fight hydrostatic forces that are trying to force them to rise or sink. It is also the ultimate goal of our lab.

Refer to the following information for the next two questions.

Suppose a floating block of wood, having a volume of 50 cm3, displaces only 30 cm3 of water.
 What is the density of the wood comprising the block?

 How large is the buoyant force that the water exerts on the wood?

Equipment

• one dry film canister
• 20 dry pennies
• one triple beam balance
• 8-12 blocks
• hanger for canister
• plastic coffee can with water
• pipette
• towels

Procedure

Your first task is to use Archimedes' Principle to determine the volume of the film canister.

• Zero your triple beam balance.
• Mass the dry film canister with 20 dry pennies inside.
• Fill plastic coffee can with water.
• Carefully place your triple beam balance on top of the blocks high enough for the beaker to sit under the balance's pan. Secure the balance so that it does not slip. Zero the balance one more time.
• Gently suspend the wire hangers from the bottom of your triple beam balance. Ask for help if you are uncertain how to attach the wires. Rezero your balance.
• Submerge the bottom "wire basket" in the beaker of water and find its "tare mass."
• After making sure that the lid is snapped on securely, place your loaded film canister in the "wire basket" and completely submerge it into the water. Read the canister's "apparent mass."

 mass description (g)
 dry canister w/20 pennies
 "wet" tare mass of hanger
 submerged canister w/20 pennies

 Did the "mass" of the loaded film canister really change when it was submerged in the water? Explain.

 What is the buoyant force (in newtons) of the water on the loaded film canister?

 What is the volume (in cm3) of the canister?

Neutral Equilibrum

Your second task is to exactly match the density of the canister to that of water. You may remove and add pennies, and fine tune the mass by using the pipette to slowly add water to the inside of the film canister.

Once you are certain that your canister is ready, bring it up to the front of the room so it can timed in the large cylinder. Each group is allowed two trials to release their canister so that it neither breaks the surface or sinks to the bottom of the cylinder in less than 3 seconds. You are NOT allowed to change its mass between trials. Be careful of air bubbles!

 What total mass (film canister, pennies, and water) did your film canister need to accomplish this task?

 How many seconds did your canister remain submerged?

 Describe how the temperature of the water could affect your trial's outcome?

 What would happen to your canister if it were instead submerged in salt water? Would it still remain in neutral equilibrium, or would it float or sink? Explain.

Accelerated Canister

Your last task is to exactly calculate the mass of the canister needed to accelerate at the specified rate to the bottom of the glass cylinder.

Once you are certain that your canister is ready, bring it up to the front of the room so it can be timed falling through the cylinder. Remember to meaure your height once the film canister is totally submerged. It also must be released from rest. Each group is allowed two trials to release their canister. Be careful of air bubbles!

 What total mass (film canister, pennies, and water) does your film canister need to accomplish this task?

 How tall was the cylinder of water once your canister was submerged?

 How many seconds did your canister take to fall the length of the cylinder (trial 1)?

 How many seconds did your canister take to fall the length of the cylinder (trial 2)?

 What was your canister's average time?

 How many seconds should it have taken according to your designed acceleration?