N
otes on Chapter 11
pp 115 - 120 of your lab book
It is important to understand the simple spring system discussed in your lecture and in the Natural Oscillations lab. Many physical systems can be modeled by using either the simple spring system or by combinations of simple springs. The spring model is used in everything from inelastic collisions to vibrations in solid crystals. In our lab, we are going to discuss the very complicated behavior of air in a jar by making a simple spring model; by assuming that the complex interactions between the molecules in the jar can be simplified to a single simple spring. (The air is the spring. We will drop a mass into the jar; that is the "mass on the spring") If we do this our analysis is simple.
You already know how to measure the period of a spring. You also know how to get the frequency of oscillations from the period (f = 1/T). We are assuming that the frequency of the oscillations still obeys the equation:
pp 115 - 120 of your lab book
It is important to understand the simple spring system discussed in your lecture and in the Natural Oscillations lab. Many physical systems can be modeled by using either the simple spring system or by combinations of simple springs. The spring model is used in everything from inelastic collisions to vibrations in solid crystals. In our lab, we are going to discuss the very complicated behavior of air in a jar by making a simple spring model; by assuming that the complex interactions between the molecules in the jar can be simplified to a single simple spring. (The air is the spring. We will drop a mass into the jar; that is the "mass on the spring") If we do this our analysis is simple.
You already know how to measure the period of a spring. You also know how to get the frequency of oscillations from the period (f = 1/T). We are assuming that the frequency of the oscillations still obeys the equation:
The compressibility
of a fluid (how much you can compress a fluid per unit of pressure) can be
found by a quantity called the bulk modulus. Actually, compressibility =
1 / Bulk modulus. (When I say fluid, I mean the physics definition of fluid,
which includes gasses such as air. This quantity is related to the value
k in the equation above by the formula:
k = A
2B/V
where B =
Bulk modulus, A = cross sectional area, V = volume of the fluid. We will
discuss briefly how this was derived in class.
We will also find the ratio of heat capacities Cp/Cv , the heat capacity at constant pressure / the heat capacity at constant volume. I do not believe that this quantity is discussed in your lecture, in either the 151 or the 170 class. Refer to Appendix 11A if you wish to know about this quantity. Ordinarily this is left to a thermodynamics class (Physics 430!). With that in mind, I will not stress this at all, nor will I quiz you on this concept.
The ratio of heat capacities is given by the equation:
We will also find the ratio of heat capacities Cp/Cv , the heat capacity at constant pressure / the heat capacity at constant volume. I do not believe that this quantity is discussed in your lecture, in either the 151 or the 170 class. Refer to Appendix 11A if you wish to know about this quantity. Ordinarily this is left to a thermodynamics class (Physics 430!). With that in mind, I will not stress this at all, nor will I quiz you on this concept.
The ratio of heat capacities is given by the equation:
ratio of
heat capacity = Bulk modulus / Pressure