Physics 1310 Manual--Design Measure and Analysis
Kevin T. Kilty, Copyright, 1996, All Rights Reserved.
Chapter 1-Concepts in measurement
I suggest adding exercizes in calculating mean, median, and standard deviation.
The purpose of the chapter is to familiarize students with the idea of noise and error, and emphasize early that encountering error in a lab is expected.
Chapter 2--Uniformly accelerated motion
There is incorrect subscripting in the eqaution on page 13. It should read v = vo + at.
Only the component of gravity tangent to track is effective in accelerating the cart.
Remind students about the digital timers wrapping around to zero again if they try to count too far.
One ought to add provision for leveling the track. The cart itself is useful here. Level the track until the cart has no tendency to drift. Then give the track a slope by setting one end on a slab of known height.
Chapter 3--Analysis of force
Remind students that the strings leading from force scale and restraint to the force ring must be orthogonal for a proper decomposition of forces. Students tend to align them in any convenient way, and sometimes the results are quite erroneous as a result.
Chapter 4--Using spreadsheet to do calculus
The ne-sided differences on bottom of page 24 are incorrect. Replace 3f(xo+2*dx) with 3f(xo) and f(xo) with f(xo+2*dx) in the first formula. Replace f(xo) with f(xo-2*dx) and 3f(xo-2*dx) with 3f(xo) in the second formula.
Note that numerical derivatives of the student's knee are actually at the CM of the lower leg 2/3 up from ankle.
I need to add some introduction to delta function here. The concept of distributions like the delta function and its kin are incredibly useful. Yet, it is rarely taught in any mathematics course, and most physicists and engineers learn it by experience. We may as well begin to introduce it earlier in college courses.
There is no definition of jerk in the manual. Jerk is a kinematic quantity that equals d3z/dt3.
Students need appropriate diskette files which are not included with the manual. Find them through HTTP download at "www.kilty.com/physicsI.htm"
Chapter 5--Efficiency and mechanical advantage
AMA is mg/T, the weight being raised or held divided by the force on the string or rope required to accomplish this. Unfortunately in an extremely compound block and tackle, it might be possible to keep a small weight suspended without any applied tension at all. The problem here of course is that friction is helping one to restrain the weight's motion. In such a case AMA becomes nearly infinite.
There are a couple of ways to deal with this situation. First, in a compound system with a large IMA, use a large suspended weight. Another way around the problem is to avoid measurements on a completely static system. Measure tension while raising and then lowering the weight slowly, and take an average of the two readings. This causes the accumulated friction to work against your efforts and raises the value of tension to a realistic level. Obviously we wish to move weight up or down with a block and tackle system, not merely restrain it.
Chapter 6--Statics in three parts
The main problem with this lab is the need to measure a very small horizontal tension on the hanging chain. The force scales cannot do the job. I suggest using a low friction pulley and a small weight to do it. Horizontal thrust must be measured accurately in order to compare the leading coefficient in the fit of parabola.
Chapter 7--scattering and collision
Stacey and I, in the course of hurrying this book along, managed to loose two very important figures -- 2 and 3, I think, which define the meaning of terms in the formulae. Look for the figures at "http://www.kilty.com/physicsI.htm" if they are not in your manual.
Typical scattering results are that of 62 scattered shots, 16 will be scattered into the back quadrants and 46 into the forward quadrants. 16/46 is very close to the 41% expected ratio.
There is an error on page 47 where the symbol "f" should be a greek phi.
Chapter 8--Coriolis force
Students have a hell of a time using the strobe to measure wheel rotation rate. Just be prepared to practice quite a bit before everyone has confidence in the values they are obtaining. This is how experimentation often works in practice. I have no better suggestion at the present time, though, except that the class could build a sensor from a magnet attached to a spoke, and a magnetic reed switch and battery on the axle that provides TTL (5VDC) pulses to a counter. The reed switch will have to use a de-bounce circuit.
Lab needs some example of calculating rotation and precession rates.
Typical derived constants from a successful lab are:
Moment of inertia down axle = 0.326 kgm2
gravitational torque=7.74 kgm2/s2
rotation rate = 370 rpm
expected precession = 0.61 rad/s
observed = 2*pi/6.5 rad/s
Please do not let this example of results bias the students own measurements. Everything will depend on how fast they spin the bicycle wheel.
The electric motor with eccentric shaft not is available. I had built the thing, but then destroyed it using parts of it for other experiments.
Build components of the Fram tachometer from fine piano wire cut to various lengths and clamped into the frame of the tachometer like cantilevers. You may give each component a lower natural frequency by loading the wire with a small fishing sinker or even a BB.
Do not stretch the springs available in the LCCC lab to a tension of 20N. This destroys the spring. 5-8N is sufficient.
The dispersion experiment is not quantitative unless students can record using a digital scope. The connection of input signal to the potentiometer shown on page 76 is wrong. Connection should be made to the two outside two terminals of potentiometer.
Students need about 50 feet of TIG wire to hear dispersion well. Any less will not allow the dispersion to develop.
Appendix I --
I have an SVD routine in 'C' language which students may find by HTTP download at "www.kilty.com/physicsI.htm"