PHYSICS 201 & 213 EXPERIMENT 12

ARCHIMEDES PRINCIPLE

Lab- 12 points, Questions at the end, 8 points.

INTRODUCTION

Archimedes Principle states: A body (m_o) wholly or partially submerged in a liquid will be buoyed up by a force (F_B) equal to the weight (W_f = m_f g) of the fluid displaced, or F_B = W_f = m_f g.

Density r: r = mass (m)/volume (V), hence m = rV!

The density of water, r_w = 1g/cm³ = 10³ kg/m³.

So an object's weight W_o equals its mass m_o times acceleration due to gravity g, or, W_o = m_og = r_o V_og

If an object floats, then the buoyant force F_B equals both the weight of the object and the weight of the fluid displaced.

If an object sinks, then the apparent weight, W_A , of the object after submersion equals the weight of the object minus the weight of the object's volume of water.

OBJECTIVES

Study Archimedes Principle and use it to find the densities of some liquids and solid objects.

APPARATUS

Vernier Caliper - cab 5B, POGMMD- G/3C, metal Cylinder - cab 5C, Wooden block- G/2C, String-next to fire extinguisher, south wall, Meter stick-countertop north wall, 500 ml beaker PS-5B, Vertical support rods-corner by cab 6, Force Probe -in red box in cab PS 5

REFERENCES

your text's chapter on Fluids

PROCEDURE

Part I. Determination of density by r = M/V.

l. Obtain and record mass of cylinder and wooden block using the POGMMD.

2. Using Vernier caliper, make and record on your data sheet the length (L), and diameters (D) of the cylinder. Using these values, and the volume of a cylinder formula, V_cyl = π/4 (LD²),
calculate the volume of the cylinder and record. Finally, calculate the density of the cylinder.

3. Using a metric ruler, make and record determinations of the length, width and height of the wooden block. Finally, calculate and record the density of the block . Show whatever quantities and equations you use to obtain this value.

Part II. Determination of densities using Archimedes Principle.

(This is the dreaded "verification of a principle" part of the lab.) You will determine the density using Archimedes Principle and compare it to the value above to (hopefully) "see" that it really works!

Note: Although our instruments are crude, your accuracy should be fairly good (meaning, your percent difference should be 15 % or less). If it is worse than that, either your lab techniques or your algebra is unacceptably awful.

l. Wooden block--very carefully and slowly lower the wooden block into a beaker of water. Now carefully remove it. The water line should be easily seen. Measure and record the depth to which the block sank in the water four different places on the block. Using the mean value of this depth along with the length and width measured in Part I, calculate the volume V_f of water displaced by the block. Now, using Archimedes Principle, calculate and record the density of the block. Next calculate and record the percent difference between this value and the one obtained in Part I.

2. Brass Cylinder--attach one end of a piece of string to the brass cylinder and the other to the Force Probe (after calibrating and zeroing). The force probe must have the switch in 10 N mode. Lower the brass cylinder into a beaker of water and measure the tension in the string using the force probe. Now the tension (T) in the string plus the buoyant force F_B must equal the weight of the brass cylinder M_bg. Or: F_B + T = M_bg. Use this and the fact that M_b= r_bV_b to find r_b. Show any calculations you make.

Record this value of r_b. Also find and record the percent difference between this value and the one found in Part I.

^* Part III. Determination of the density of an unkown fluid.

Note: The unknown liquid is vegetable oil in bottom shelf of cabinet PS-5.

Since you know both the weight and volume of the brass cylinder, you should be able to use this fact and a procedure similar to the above to find the density of an unknown fluid! The only trouble is, the force probes are not very good at absolute accuracy, but they are pretty good at comparative accuracy. (Is that a word?) What I mean is, when compared to its own readings, in the same trial, its results are consistent. But when compared to some other device, the POGMMD, for instance, or even its own readings in different trials, it is not. So, for this part of the lab, you must use the force probes value for the weight of the cylinder. The force probe must have the switch in 10N mode. Do this, then zero, then attach the brass cylinder to a string and attach the other end to the force probe (don't forget to zero ). Start loggerPro, let it run a few seconds to record the weight of the cylinder in air, then bring the beaker containing solution l up to submerge the cylinder to record its weight in the fluid. Now record the weight of the cylinder in air as the M_bg, and the force after submersion as T₁. The buoyancy force should now be within your grasp, and since it must equal the weight of the fluid displaced by the cylinder, You should be able to find, and record, r₁, the density of solution 1.

QUESTIONS (2 points each)

l. A balloon has an inflated volume of 12000 ft³. If the balloon and the harness attached to it weigh 500 lbs. what payload can be lifted by the balloon when filled with helium? (Density of air = .0807 lb/ft³ and the density of helium = .0111 lb/ft³ at sea level.)

2. For your block, to what depth would it sink if floated in an oil of specific gravity = 0.7? (specific gravity of a substance S_s = r_s/r_w). a) write equation and solve for unknown, b) substitute in values for your block.

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* if time permits.