INTRODUCTION In the 3 rd century BC, Archimedes was asked by a king to figure out the purity of the gold in the king s crown. While Archimedes knew he could find the weight of the crown using a balance, he had no direct or easy way of measuring the exact volume of the crown. While pondering this problem as he sat in his bathtub, he realized that he felt lighter when immersed in the water than when he was outside the tub. Archimedes got so excited that he rushed out, naked, into the street shouting "Eureka!" (I have found it!). So what exactly did Archimedes learn from this event? He realized that any object he placed under water lost weight while in the water. Larger the volume of the object, greater was this apparent loss in weight. This gave him a way to measure the volume of the crown and it led to Archimedes principle. Archimedes Principle can be stated as follows: An immersed object is buoyed up by a force equal to the weight of the fluid it displaces. This can be mathematically expressed as F buoyant = m fluid displaced g = Weight fluid displaced The density of any object is its mass divided by its volume. Since the density of water is 1 g/cm 3, the mass (in grams) of a certain amount of water, is numerically the same as its volume. Therefore, it is an advantage to use water rather than any other liquid. The mass of fluid displaced (and therefore the buoyant force) will depend on the density of the liquid in which the object is displaced. Here are some points to keep in mind when doing this lab. 1. volume fluid displaced = volume submerged object 2. mass fluid displaced = volume fluid displaced density fluid 3. Buoyant force = mass fluid displaced g = volume fluid displaced density fluid g If you step into a bathtub, you will notice that the level of the water at the side of the tub rises. Your body (the part that is under water) displaces some of the water, thus causing the level to rise. If you submerge your entire body under water, you will displace a volume of water equal to your own volume since your body is mostly incompressible. In the lab we will find the volume of smaller objects by immersing them in water and measuring the amount of water these objects displace. From this and the mass, the density can be calculated. 1
Figure 1 The weight of any object is due to the gravitational pull of the earth on the object. The object in figure 1 displaces a certain amount of water. This displaced water has a certain amount of weight due to the earth s gravitational pull on it. The buoyant force on the object is due to the difference in fluid pressure on the top and bottom surfaces of the object. This buoyant force always acts in the upward direction. If the buoyant force is greater than the weight of the object, the object will float. If the buoyant force is less than the weight of the object, the object will sink. PROCEDURE Part A: Finding Volume from Mass of Displaced Water 1. Use two cups, one bigger than the other. Fill the smaller cup completely with water and carefully set it inside the bigger cup, making sure there is no spillage into the bigger cup. 2. Find the mass of one of the odd shaped objects that you are given and record this value in data table 1 on the worksheet. 3. Carefully place this object in the smaller cup. The water displaced by this object will flow into the bigger cup. Remove the smaller cup with the mass inside it. 4. Find the mass of the bigger cup plus the water in it. Find the mass of the water alone and record this value in data table 1 on the worksheet. 5. From this mass, find the volume of water displaced and record this on the worksheet. 6. From this mass, and the density of water (D water = 1 g/cm 3 ), determine the volume of water displaced. Record this value in data table 1. 7. Repeat steps 1-5 for the other five objects and complete data table 1 on the worksheet. 2
8. Calculate the density of each object from the mass and volume data. CHECKPOINT 1: HAVE YOUR TA CHECK YOUR WORK BEFORE PROCEEDING Part B: Floating vs. Sinking Objects denser than water will sink, while objects less dense than water will float. You are given 4 similar shaped cylindrical objects. 1. Measure and record the mass of one of the cylinders in data table 2 on the worksheet. 2. Measure the diameter (d) and the height (h) of the cylinder and record them in data table 2. 3. Using the formula V cylinder = πd 2 h, calculate the volume of the cylinder and record this in data 4 table 2. 4. Set the cylinder in the tub of water provided. Note if it sinks or floats and record this information in data table 2. 5. Repeat steps 1 through 4 for the other three cylinders and record the data in data table 2 on the worksheet. The PVC pipe that is open at both ends is like two cylinders; an outer one made of PVC pipe and an inner cylinder of air. So you will need to subtract out the cylinder of air to get the volume of the PVC section of the cylinder. CHECKPOINT 2: HAVE YOUR TA CHECK YOUR WORK BEFORE PROCEEDING Part C: Finding the Buoyant Force 1. Use a rubber band to attach the given object to the spring scale. Measure the weight of this object in air and record this value in data table 3 on the worksheet. 2. Submerge the object in water, (make sure that no part of the spring scale is in the water), and record the new weight in data table 3. 3
3. Find the apparent loss of weight in water of the object and the buoyant force. 4. Using the buoyant force and the density of water, determine the amount of water displaced by the object. From this determine the volume of water displaced. 5. Calculate the density of the object using the values of the mass and the volume of the object. CHECKPOINT 3: HAVE YOUR TA CHECK YOUR WORK BEFORE PROCEEDING 4
LIQUIDS - WORKSHEET Part A: Finding Volume from Mass of Displaced Water TABLE 1 Object Mass of object (g) Mass of water displaced (g) Volume of water displaced (cm 3 ) Density of object (g/cm 3 ) CHECKPOINT 1 5
Part B: Floating vs. Sinking TABLE 2 Cylinder Mass (grams) Diameter (cm) Height (cm) Volume (cm 3 ) Density (g/cm 3 ) SINK or FLOAT? PVC Pipe (open) Inside: Outside: Inside: Outside: TOTAL: PVC Pipe (closed) Wood Metal CHECKPOINT 2 Table 3 Part C: Finding the Buoyant Force Object Weight in Air (N=kgm/s 2 ) Weight in Water (N=kgm/s 2 ) Difference in weight = Buoyant Force (N=kgm/s 2 ) Volume of water displaced (m 3 ) Density of object (kg/m 3 ) CHECKPOINT 3 6