Physics 12 Lab #1

Simple Measurement

Theory

Density = Mass / Volume
Volume of a cylinder = height of cylinder x area of base
Area of a circle = pi x radius2
Period of a pendulum = 2 x pi x SQRT(length of pendulum/acceleration due to gravity)
Acceleration due to gravity = 9.8 m/s2
Error of quantities added or subtracted = sum of the errors on each quantity
Relative error of quantities multiplied or divided = sum of relative errors on each quantity
Relative error of quantity raised to a power = the power times the relative error of the quantity
Relative error = error divided by quantity

Procedure

It is crucial to get reading errors for each measurement.  If you are keen you will do repeated measurements where feasible to get a more accurate error. You should always give final results in MKS units. The order in which you perform sections 1, 2 and 3 is unimportant, so feel free to proceed to another section if the equipment you need is unavailable. Section 4 must follow 3 and section 5 must follow 1 and 2.

Part #1 Cylinder Dimensions/Volume

Compare two methods of determining the volume of the cylinder.
  1. Use the calipers to find the height and diameter of the cylinder and calculate the volume via the known formula.  If you do not remember it, look it up in a book or on the internet.
  2. Use the graduated cylinder to measure the volume via the displacement method.
  3. Discuss the precision of the two methods by comparing their calculated errors.
Part #2 Cylinder Mass

Compare the precision of two balances in determining the mass of the cylinder.
  1. Use the two pan balance to mass the cylinder three times.
  2. Use the triple beam balance to mass the cylinder times.
  3. Compare the precision of the two balances.
Part #3 Timing Error

Using the digital timers develop techniques to minimize reaction and other timing errors. Reaction time is the difference in time between receiving a stimulus and your brain sending a message to your body to act. It can be as large as half a second.
  1. Have one person start two stop watches at the same time by having one in each hand. The other partner should take one of the stop watches and watch the first partner to see if he or she clicks the watch stopped. When this occurs the second partner should try to stop his or her watch as quickly as possible. The difference between the two times will be the reaction time of the second partner. Measure each of your reaction times with error by taking multiple readings.
  2. Now repeat the process from above but have the first person count down rhythmically prior to clicking the stop button. Calculate and compare reaction times here to those above.
Part #4 The Pendulum Clock

You will measure the period of a pendulum bob and compare to the theoretical value. (A period of a pendulum is defined as the time from release unitl it comes back to the release point. It is independent of how high the pendulum swings.)
  1. Hang a mass from about 1 meter of string. Measure the period of the pendulum by timing one, five and ten oscillations. Figure out which gives the most precise result. Compare the result to the expected value.
  2. Now calculate the length of a pendulum of period one second. Build it and confirm your calculation.
Part #5 Calculating Density

Using the most precise results from part one and two calculate the density of your sample. Use the table of densities below to figure out from what material your cylinder is most likely composed.

Densities of Metals
Magnesium 1,700 kg/m3
Aluminum 2,700 kg/m3
Copper 8,700 kg/m3
Gold 19,300 kg/m3
Iron 7,800 kg/m3
Lead 11,300 kg/m3
Platinum 21,400 kg/m3

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