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course phy 201
Experiment 7. Measuring MassesUsing a balance constructed from pieces of shelf standard, balanced on a knife edge and with a brass damping cylinder partially submerged in water, we investigate the rotational displacement of the balance from equilibrium in response to the addition of small weights. We then use the balance with the mass set to precisely measure the masses of various objects. See video clip on CD EPS01.
You have been supplied with a mass set and a crude but effective and precise balance. With this balance you can with reasonable accuracy determine the mass of an object by placing it on one side of the balance and adding masses from the mass set to achieve a balance. The balance is very sensitive to small changes in mass, capable of detecting changes on the order of .01 grams.
The mass set consists of masses of .1 gram, .2 gram, .3 grams, .5 gram, 1 gram, 2 grams, 3 grams, 5 grams, 10 grams, 20 grams, 30 grams, 50 grams and 100 grams. Using various combinations of these masses you can obtain any mass from .1 gram to over 200 grams, in increments of .1 gram. Each mass is accurate to within +-.5%.
Note that 1 gram is, within very narrow limits of precision, the mass of a 1 cm cube of liquid water at 20 degrees Celsius.
Place the balance beam on the stand, balanced on the edge of the dulled blade, with the damping cylinder partially immersed in water.
Be sure that the beam is resting as precisely as possible at the vertex of the angle formed at the notch near its center, as demonstrated on the video clip.
Place a cup of water beneath the damping cylinder, with the water depth adjusted so that the cylinder will be about halfway immersed when the beam is horizontal.
As shown on the video clip, adjust the position of the washer on the beam until the damping cylinder is about halfway immersed in the water and the beam is horizontal. Mark the position of the washer or accurately measure it from the nearest end of the beam so that in case it moves, it will be easy to reposition. Use a small amount of thin tape to help hold the washer in its place.
Place a ruler or other measuring device (the pendulum stand might be convenient for this purpose) at the position of the damping cylinder, and note the position of the top of the beam relative to this measuring device.
Add enough water to the cup to increase the water level by approximately 1 cm.
What happens to the position of the beam?
Can you explain why the position of the beam changes, why it changes in the direction it does (i.e., up or down), and why the change is equal to, greater than or less than the change in the water level (as the case may be)?
Now we will observe what happens to the position of the beam when various masses are added to the balance at the position of the damping cylinder, and also when the same masses are added at a position opposite to the position of the damping cylinder.
Place the .1 gram mass on the beam, at the position of the damping cylinder. By how much does the reading on the measuring device change? By how much would you expect the reading to change for a .2 gram mass?
Record the mass added and the position of the beam, as determined by the measuring device.
Record also the position of the beam in the absence of the added weight.
Remove the .1 gram mass, note the reading on the measuring device, and add the .2 gram mass.
How much displacement corresponds to the addition of the .2 gram mass?
Record the mass added and the position of the beam, as determined by the measuring device.
Repeat twice more, first with the .3 gram and then with the .5 gram mass.
Now, place the .1, .2, .3 and .5 grams masses, in turn, on the opposite side of the balance at the same distance from the balancing point as the damping cylinder. For each mass, record the reading on the measuring device.
The position of the beam in the absence of any added mass will be called the equilibrium position of the system. We will construct a graph to determine the displacement of the beam as a function of the mass added at the position of the cylinder.
You have recorded the position of the beam at equilibrium and with the addition of 4 masses at the position of the damping cylinder and 4 masses at the position opposite that of the damping cylinder. Place these data in a table.
For each line of your table, calculate the displacement of the beam from its equilibrium position. The displacement will be either positive or negative, depending on whether the reading on the measuring device is greater or less than the reading at equilibrium.
Sketch a graph of y = beam displacement from equilibrium vs. x = added mass.
If the graph appears to be linear, sketch the straight line corresponding to the behavior of the system. If the graph does not appear linear, sketch a smooth curve to fit the data as closely as possible without attempting to go through any point except the origin (i.e., don't go out of your way to actually 'hit' any point; come as close as possible on the average to the points you have graphed without making nonsensical wobbles to accomodate experimental errors which have nothing to do with the behavior of the actual system).
Using your graph, estimate the beam displacement corresponding to the addition of .15 gram, .25 gram, .4 gram and .7 gram at the position of the cylinder, and opposite to the position of the cylinder.
Place these masses on the beam at the appropriate points and record beam positions. Compare with your predictions.
Now you will use the balance to accurately determine the masses of various objects.
Hang the 'balance pans' at opposite ends of the beam, at equal distances from the balancing point.
To check the symmetry of your pan placements, take two of the largest washers supplied with the lab kit and place one at the center of each pan. See if the equilibrium position of the system changes, and if so how much. Then exchange the washers between the pans and again note any change in the equilibrium position of the system. How do your results determine whether the pans were positioned symmetrically about the balancing point?
If necessary, adjust the positions of the pans until you can verify symmetry by the preceding procedure.
With the pans unloaded, record the position of the beam with respect to the measuring device. This will be the equilibrium position for the balance pans.
Measure the masses of various objects.
Place a pencil or pen in one pan, and in the other place a combination of masses from the mass set to bring the system back as near as possible to its equilibrium position. Add all masses in such a way that the balance pans continue to hang symmetrically about a vertical line.
Note the total of the masses added from the mass set. If the balance pans have been placed at equal distances from the equilibrium position, and if they have been kept symmetric about a vertical line, then the total of these masses will be equal to the mass of the pencil or pen.
Repeat this procedure to measure as accurately as possible the mass of each washer supplied with the lab kit (if there are more than 3 of a given type of washer, randomly select 3 washers of that type). Record these masses for future reference.
Determine the mass of your friction car, and record this mass for future reference.
Determine the masses of four randomly selected paper clips and record these masses for future reference.
Answer the following questions:
Why is it essential that the balancing pans be placed at equal distances from the balancing point?
How much would the result of weighing a 40 gram object be affected if one pan was positioned 29 cm from the balancing point, and the other 28 cm from this point?
If when determining the mass of a small washer, the beam position could be brought to within .1 cm of its original position by a balancing mass of 1.21 grams, then what might be the mass of the washer?
Why does the beam not balance at its equilibrium position when unequal masses are added at the two ends?
Why does the beam not balance at its equilibrium position when equal masses are added at unequal distances from the balancing point?
There is more force exerted at farther distances from the balancing point
The one that is farther away will go down it exerts more force
1.21 grams
one will have more force exerted on it which will make gravity pull one end down
More force is exerted when one is at a further distance so it is equal to putting two items of different masses on it"