#$&*
course Phy 241
If you start getting partial assignments, it's because I'm trying to get as much as possible submitted so I might cut out some questions in order to get the actual lab data submitted.
`q001: Lab investigation:You investigated the question of whether a fixed amount of energy imparted to a system has a consistent result.
The energy came from a rubber band chain.
The system was a rotating ramp with dominoes on its ends.
Give a description of the system and how it was used.
****
We had a 60 cm long strap balanced on a single die. On each end of the strap we rubberbanded one domino. One the first set of data we had a paperclip at the very end (30 cm from the middle) of the strap to which we attached the rubberband chain. On the second data set we had a paperclip at 15 cm from center, and then on the 3rd set we had the paperclip 1/4 of the way out (roughly 7.5 cm).
We attached the rubberband to the paperclip and deformed the rubberband by 8 cm before releasing. We got 7 trials for each data set.
#$&*
Give your data.
****
Arm length = 30 cm.
Degrees:
1680
1335
1170
1275
1140
1180
1040
Arm length = 15.
915
840
675
1095
980
840
1090
Arm length = approx. 7.5.
675
840
1175
990
945
1160
820
@&
Do you believe that the differences are significant?
If the rubber band's length decreases by the full 8 cm while in contact with the system, our first-level expectation would be that the energy imparted to the system was the same for all trials, and that there would not be a significant difference in coasting distances.
If the differences were significant, what factors do you think might explain at least some of the differences?
*@
`q002. Your ramp has mass 200 grams and length 60 cm. By itself its moment of inertia is 1/12 M L^2, where M is its mass and L its length. What is its moment of inertia?
****
1/12 (.2 kg)*(.6 m)^2 = .006 kg*m^2.
#$&*
Your dominoes each had mass about 16 grams. How far was the center of each domino from the axis of rotation (your best estimate, recalling that the dimensions of a domino are 5 cm long by 2.5 cm wide by about .8 or .9 cm thick) and what was the moment of inertia of each?
****
Approximately 28 cm each from the center.
I = m r^2.
I = (.016 kg)*(.28 m)^2 = .00125 kg*m^2.
#$&*
What therefore was the moment of inertia of your system?
****
.00725 kg m^2
#$&*
`q003. In the experiment your rubber band had some average tension as it snapped back from release. We want to find the work done on the system as it snapped back.
Using a reasonable rough estimate, how many dominoes do you think the rubber band would have supported at the stretched length of your chain?
****
Roughly 2.
#$&*
At .16 Newtons per supported domino, roughly how much force did the chain therefore exert at this length?
****
2 * .16 N = .32 N.
#$&*
What approximate average force did the chain therefore exert between release and losing contact with the rotating system?
****
Release = .32 N.
Losing contact = 0 N.
Ave force = .16 N.
#$&*
Through what distance do you think this average force was exerted?
****
Maybe 10 cm.
@&
Probably wouldn't have been over 8 cm.
*@
#$&*
How much work did the chain therefore do on the system?
****
Work = Ave Force*Displacement = .1 m * .16 N = .016 N*m.
#$&*
You have calculated the moment of inertia I for the system, and you have the definition KE = 1/2 I omega^2. If the work done by the chain on the system all went into kinetic energy, what then should omega have been at the instant the rubber band chain lost contact? Include units throughout your solution. You probably won't know how to interpret the units of your final solution, but don't worry about that.
****
KE 0 + Work = KE final. KE 0 = 0.
Work = KE final.
.016 N*m = 1/2 (.00725 kg*m^2)(omega)^2.
omega^2 = 11.034/s^2. omega = 3.32/s.
@&
I should have asked you to observe the coasting distances. Assuming a 10 second coast we get average velocities around 100 degrees / second, which imply initial velocities of 200 deg / sec, pretty close to 3 radians / second. The 10 seconds is of course a very ballpark figure, but you can understand how time observations would have allowed this comparison.
*@
#$&*
`q004. Suppose that another system gains 5 Joules of energy from an ideal (and hence conservative) rubber band chain, while losing 2 Joules of energy to friction. How many Joules of kinetic energy would you expect it to gain?
****
3 Joules.
#$&*
For this situation, identify each of the quantities `dW_noncons_ON, `dKE and `dW_cons_ON.
****
dW_noncons_ON = work done by nonconservative forces = -2 Joules (lost energy, negative work).
dKE = change in kinetic energy = what we're looking for.
dW_cons_ON = 5 Joules.
#$&*
Reconcile your conclusions with the equation `dW_noncons_ON = `dKE - `dW_cons_ON.
****
dKE = dW_noncons_ON + `dW_cons_ON = -2 + 5 = 3 Joules.
#$&*
Identify `dPE for this situation.
****
dPE = Negative change in work done by conservative forces. Work done by conservative forces = 5 Joules.
dPE = -5 Joules.
#$&*
Write the above equation in terms of `dW_noncons_ON, `dKE and `dPE
****
`dW_noncons_ON - dPE = dKE.
#$&*"
@&
Good, but there are a couple of questions I'd like you to answer. It shouldn't take you long.
&#Please see my notes and submit a copy of this document with revisions, comments and/or questions, and mark your insertions with &&&& (please mark each insertion at the beginning and at the end).
Be sure to include the entire document, including my notes. &#
*@