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Weighing Dinosaurs
Weighing Dinosaurs
Introduction:
How can a scientist determine the mass of a dinosaur when the last of these animals were alive over sixty five million years ago? Actually it is not difficult at all if we have accurate models of dinosaurs and some simple equipment.
Equipment Needed:
 Solid plastic models of dinosaurs
 Water bucket with side overflow spout
 Table Scale
 Hanging Scale
 Cups
 Dishwashing soap
 String
 Calculator
Theory:
If we know 1) the scaling factor between the dinosaur model and an actual dinosaur, 2) the volume of the dinosaur model, and 3) the density of a dinosaur then we can calculate the mass of an actual dinosaur. Dividing known dimensions of dinosaurs by the same dimension of our model will give us the scaling factor. Measuring how much water is displaced when we submerge our dinosaur in water will give us the mass of the displaced water that we need for our calculations. Finally even though we can not directly measure the density of dinosaurs since they are extinct, we can still compare these extinct vertebrates to present vertebrates and conclude that the density of a dinosaur is at or close to 1.0 g / cm^{3}.
Density is a measurement of how much mass is contained per unit volume (D = M / V). Most metals have high densities while foam materials used for packing boxes for shipment have very low density. A solid high density object will sink when placed in the water while a low density object will float. One gram per centimeter cube is the density of water.
Because the mass of a dinosaur is the same as the mass of the water that it displaces, we can calculate the mass of an actual dinosaur by measuring the mass of
water that a model dinosaur displaces and then use our scaling factor to determine the mass of an actual dinosaur.
Procedure:
MASS OF THE WATER DISPLACED BY THE DINOSAUR MODEL: the Water Runoff Method
 Place your water bucket on a steady table with a cup under the overflow spout to catch the water.
 Add a couple drops of dishwater soap to the bucket and then fill the bucket with water until it starts to overflow. The dishwater soap is critical for lowering the surface tension of the water and this is necessary to produce precise measurements of the water being displaced. As an extra bonus the soap also cleans our dinosaur models while they are taking their baths.
 Replace the partial filled cup with an empty cup and set this empty cup on the scale. Set the mode of the scale to grams.
 It is not necessary to wait until the water completely stops dripping out of the spout. Instead simply click the tare button to zero out the scale before slowly submerging your dinosaur in the water. Once the water flow slows down to where it is again barely dripping record the mass of the water in the cup.
MASS OF THE WATER DISPLACED BY THE DINOSAUR MODEL: Archimedes' Principle
 Tie a string around the middle of your dinosaur then tie the other end of your string in a loop so that you can hang your dinosaur by the hanging scale.
 Tare your scale to zero while there is no tension on the string then lift your scale so that the plastic model hangs in the air. Record the mass of the plastic model.
 Submerge your model in the bucket of water. Allow the model to rest on the bottom of the bucket and tare your scale to zero. Lift your scale so that the model is off the bottom but still submerged. Record the mass of the submerged model.
 Subtract the mass of the submerged model from the mass of the plastic model. Record this as the mass of the displaced water.
CALCULATING THE MASS OF AN ACTUAL DINOSAUR
 Multiply the mass of the displaced water by your scaling factor cubed and then enter this answer in the column marked Mass of Reptile Dinosaur. If a dinosaur had a respiratory system like that of a reptile then this is the mass of the full size dinosaur.
 Some dinosaurs may have had a birdlike respiratory system. To account for this multiply your last answer by 0.70 and enter the result in the last column.
Repeat this procedure for each of your dinosaurs.
Science Educator's Demonstration using Archimedes' Principle:
Example  Scaling Factor  Mass of Plastic Model (kg) 
Mass of Submerged Model (kg) 
Mass of Displaced Water (kg) 
Mass of Elephant (kg) 

African Elephant 
30  0.275  0.070  0.205  5,500 
Student Worksheet using Archimedes' Principle:
Name of Dinosaur  Scaling Factor  Mass of Plastic Model (kg) 
Mass of Submerged Model (kg) 
Mass of Displaced Water (kg) 
Mass of Reptile Dinosaur (kg) 
Mass of Bird Dinosaur (kg) 

TRex  .  .  .  .  .  . 
Triceratops  .  .  .  .  .  . 
Brachiosaurus  .  .  .  .  .  . 
Helpful Equations:
Scaling Factor equals length of actual dinosaur divided by the length of the model.
S.F. = L_{d} / L_{m}
Volume of dinosaur equals volume of dinosaur model times the scaling factor cubed.
V_{d} = V_{m} x (S.F.)^{3}
Volume is equal to the mass divided by density.
V = M / D
(M_{d} / D_{d}) = (M_{w} / D_{w}) x (S.F.)^{3}
Density of a dinosaur is extremely close to being equal to the density of water.
D_{d} = D_{w}
Therefore the mass of the dinosaur equals the mass of displaced water times the scaling factor cubed.
M_{d} = M_{w} x (S.F.)^{3}
High School and College Science Teachers and Instructors
You need this experiment: it is a great applied science and math experiment that students love. With a lot of time and effort you might be able to assemble a dinosaur kit that is nearly comparable to the one pictured above, or you could just purchase this complete experiment and save over 50%. In addition to the dinosaurs and other physical items shown, the complete classroom kit comes with laminated theory sheets for the students, student worksheets, a teacher’s manual, and a CD disk for easy printing of additional student worksheets. The experiment has been teacher reviewed and classroom tested numerous times, and it always comes out a favorite for both educators and students.
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Please properly cite DinosaurTheory.com if you use this material.