course Phy 201
Rubber band measurementsYou have data that allows you to determine the length of the thin rubber bands and the length of the thick rubber band, for each setup.
Report the span of your hand on the 'ruler' you used to measure the rubber band system, as well as your height in inches. Report as two numbers separated by commas:
&&&& (report your numbers starting on the next line)
26.5, 57
Report you raw data below (this will be the quantities you actually measured in class; note that you didn't measure the lengths of the rubber bands but the positions of their ends, so your raw data will not include the lengths). :
&&&& Your raw data from class should be reported starting in the next line:
Trial 1 the thick rubber band was 12cm long and the thin was also 12 cm long, the Second trial the thick rubber band was 13cm and the thin was 15 cm long, the Third trial the thick rubber band was 14cm and the thin rubber band was 22cm.
* In the first setup you had a single 'thin' rubber band opposing the single 'thicker' rubber band. You observed this system for three different degrees of stretch.
Beginning in the line below, report the lengths of the 'thin' rubber band and the length of the 'thick' rubber band, as determined from your raw data. Each line should be reported as two numbers, separated by a comma:
&&&& (lengths of 'thin' then 'thick' bands, first trial (least stretch)):12,12
&&&& (lengths of 'thin' then 'thick' bands, second trial (medium stretch)):15,13
&&&& (lengths of 'thin' then 'thick' bands, third trial (greatest stretch observed)):22,15
Now sketch a graph of y vs. x, where y = length of 'thin' rubber band and x = length of 'thick' band. Your graph will consist of three points.
&&&& What is the slope between the first and second point on your graph (give the slope in the line below, then starting in a new line explain how you calculated the slope)?
Slope is Rise/Run. Which would be 15-12=3, and 13-12=1 so rise 3/run 1=slope of 3
&&&& What is the slope of the graph between the second and third point on your graph (give the slope in the line below, then starting in a new line explain how you calculated the slope)?Slope is Rise/Run. Which would be 22-15=7 and 15-13=2, so rise is 7/ run is 2 slope is 3.5
&&&& Do you believe that the difference in the slopes is due mainly to unavoidable errors in measurement, or to the actual behavior of the rubber bands? Support your answer with the best arguments you can. Yes because you had to remember the numbers you did not have someone helping you so I was rounding to the closest whole number. So I could remember what to write on my paper.
* In the second setup you had three 'thin' rubber bands, all stretched between the same two paper clips, opposing the single 'thicker' rubber band. You observed this system for three different degrees of stretch.
Beginning in the line below, report the lengths of the 'thin' rubber bands and the length of the 'thick' rubber band, as determined from your raw data. Each line should be reported as two numbers, separated by a comma:
&&&& (lengths of 'thin' then 'thick' bands, first trial (least stretch)):11,12.5
&&&& (lengths of 'thin' then 'thick' bands, second trial (medium stretch)):13,16
&&&& (lengths of 'thin' then 'thick' bands, third trial (greatest stretch observed)): 14,18
Now sketch a graph of y vs. x, where y = common length of 'thin' rubber bands and x = length of 'thick' band. Your graph will consist of three points.
&&&& What is the slope between the first and second point on your graph (give the slope in the line below, then starting in a new line explain how you calculated the slope)?
Slope= Rise/Run; 13-11=2, 16-12.5=3.5, so the rise is 2 and the run is 3.5 so 2/3.5=.57
&&&& What is the slope between the second and third point on your graph (give the slope in the line below, then starting in a new line explain how you calculated the slope)?
Slope=Rise/Run; 14-13=1, 18-16=2 so the rise is .5
&&&& Do you believe that the difference in the slopes is due mainly to unavoidable errors in measurement, or to the actual behavior of the rubber bands? Support your answer with the best arguments you can. Yes, because one again I had to hold the rubber bands still get four numbers and also hold the ruler so it was easier to just to round such as the half or a whole number.
Question to think about (and answer as best you can): You you think that during the measurement process, the rubber bands were being held apart by force, power, energy or something else, or perhaps by all three? Answer beginning in the line below, and support your answers with your best reasoning. Don't worry about being wrong, but do give it some thought. &&&&
I would say force and energy because the force between the paper clip and the rubber band it is stretching the rubber band so there is some force because it is stretching. The reason I say energy is because it takes something for it to move which would only make since for energy to be involved because it goes to rest to stretch which involved some sort of energy to move it just didn’t happen on it own.
Acceleration of Toy Cars in Two Opposite Directions
You also measured the motion of a couple of toy cars, moving in two opposite directions. You were asked to obtain information that will tell you the acceleration of each car in each direction.
&&&& Give your raw data in starting in the line below. Be sure to include all information necessary to interpret your data. We done three different trials on north to south and then three trials from south to north. The pendulum was 20cm long in each trial and we had the same person do each trail so they would know how much force was behind it and how to count the pendulum.
Pick 'north' or 'south' for your positive direction. State your choice: &&&&
South is my positive direction
For the first trial in which the car moved in the northerly direction, explain how you reason out the acceleration. Show how you reason out your results, starting with the raw data, based on the definitions of rate of change, average velocity and average acceleration. You may assume that the acceleration is uniform, so that the v vs. t graph is in fact trapezoidal. Give you explanation starting in the line below:
&&&& For the first trial with the car going in the northerly direction went 58 cm in 2 full oscillations.
You have to reason out the acceleration using the definitions, the graph, etc..
Repeat for the first trial in the southerly direction:
&&&& For the First trial with the car going in the southerly direction went 83 cm in 3 full oscillations.
Find the acceleration for the next trial; however you may abbreviate your calculations and don't need to repeat the verbal explanations:
&&&&
65cm, 2.5 oscillations
60cm, 2.3 oscillations
You have to reason out the acceleration using the definitions, the graph, etc..
What might be the initial event and the final event in each of the following situations, and what quantities are given for each?
A drag racer completes a 1/4 mile time trial in 12 seconds. &&&&Vo-0seconds, Vf 12seconds
What is the name of the quantity which represents the 1/4 mile?
A muon created in the upper atmosphere spends 12 milliseconds in the atmosphere before disintegrating. &&&&Vo-0 milliseconds, Vf 12 milliseconds
After receiving a handoff at his own 10-yard line, with the game clock reading 3:42, a fullback gains 30 yards before being tackled with the game clock reading 3:37. &&&&Vo 3:42, Vf 3:37
These are not the initial and final velocities.
A mosquito hatched at 9:00 a.m. is eaten by a bat at 3:42 p.m. of the same day, and a point 40 feet north of where it hatched. &&&& Vo-9:00 a.m., Vf-3:42 p.m.
* Exercise 1: You have already analyzed your information for the race cars you observed in class. Now do the following:
Write down on your paper the symbols v0, vf, a, `dt, `ds.
From your raw data you can determine `ds and `dt.
The initial and final events can be described as 'car leaves end of finger' and 'car comes to rest'. So you also know the value of which of the five quantities? &&&&Vf, ‘ds,’dt
On your paper circle the symbols for the three quantities you know.
Now write down all four equations, and circle the symbols for the three quantities you know (i.e., circle vf, `ds and `dt in all four equations).
Write down the one equation which includes all three symbols, and circle these symbols in the equation. Which equation did you write down, and which symbol was not circled? &&&&Equation 1 has all three Vf ‘ds and ‘dt
Solve this equation for the non-circled variable and describe the steps necessary to do so. If your algebra is rusty you might find this challenging, but make your best attempt. We will be discussing this much more fully in our next class, but you at least need to get the wheels turning, and your instructor needs to know what you can and cannot do with the algebra. &&&&
I will be solving for Vo.
‘ds=(Vf+Vo)/2*’Dt
First I will divide by ‘Dt on both sides so I will get the following
‘ds/’Dt=(vf+vo)/2
Then I will multiply by each side by 2 to get the following
‘ds/Dt*2=Vf+Vo
Then I will subtract Vf to get Vo on a side by itself
‘Ds/Dt*2-Vf=Vo
Vo=“ds/’Dt*2-Vf
very good
Having solved the equation as best you can, substitute the values of the three known quantities vf, `ds and `dt into that equation. Then simplify your expression to get the value of the unknown quantity. Again, this will take some practice and you might have made some errors, but do your best, for the same reasons outlined above. &&&&
Vo=58/2*2-58
&#These quantities have units, which must be specified with the quantities. &#
* Exercise 2
A ball is released from rest on a ramp of length 4 meters, and is timed from the instant it is released to the instant it reaches the end of the ramp. It requires 2 seconds to reach the end of the ramp.
What are the events that define the beginning and the end of the interval? &&&& The length of the ramp, time it took 2 seconds to reach the end of ramp.
Write down on your paper the symbols v0, vf, a, `dt, `ds.
From the given information you know the values of three of the five quantities. What are the known quantities? &&&& ‘ds,Vf,_ave
On your paper circle the symbols for the three quantities you know.
Now write down all four equations, and circle the symbols for the three quantities you know.
Write down an equation which includes all three symbols, and circle these symbols in the equation. Which equation did you write down, and which symbol was not circled? &&&& Equation 2 a_ave=(vf-vo)/’dt
you know v0, `ds and `dt. You don't know vf or a_ave.
Solve this equation for the non-circled variable and describe the steps necessary to do so. If your algebra is rusty you might find this challenging, but as before make your best attempt. &&&&
I will be solving for Vo
a_ave=(vf-vo)/’Dt
I will multiply both sides by ‘dt
a_ave*’ dt =(vf-vo)
Then subtract vf from both sides
a_ave*’Dt-Vf=-Vo
We have to get the negative sign from both sides so you must multiply by a negative so I will get the following equation.
Vo=-a_ave*-Dt+Vf
your algebra is good
Having solved the equation as best you can, substitute the values of the three known quantities into that equation. Then simplify your expression to get the value of the unknown quantity. Again, do your best. &&&&
Vo=1s/m*-2+4
&#You need to specify the units of these quantities, and also think about what these units tell you about the meanings of the quantities, which help you identify errors. &#
* Exercise 3
A ball is dropped from rest and falls 2 meters to the floor, accelerating at 10 m/s^2 during its fall.
What are the events that define the beginning and the end of the interval? &&&&
Write down on your paper the symbols v0, vf, a, `dt, `ds.
From the given information you know the values of three of the five quantities. What are the known quantities? &&&& a=10m/s^2, ‘ds 2 meters, Vf
On your paper circle the symbols for the three quantities you know.
Now write down all four equations, and circle the symbols for the three quantities you know.
Write down the one equation which includes all three symbols, and circle these symbols in the equation. Which equation did you write down, and which symbol was not circled? &&&& Equation 4
There are two equations which each contain three of the five symbols. Write down the other equation and circle the three known symbols in the equation. Which equation did you write down, and which symbol was not circled? &&&&Vo
One of your equations has `dt as the 'uncircled' variable. You want to avoid that situation (though if you're ambitious you may give it a try). Solve the other equation for its non-circled variable (which should be vf) and describe the steps necessary to do so. If your algebra is rusty you might find this challenging, but as before make your best attempt. &&&&
Vf^2=Vo^2+2 a’*ds^2
Subtract 2 a
Vf^2-2a=Vo^2*ds^2
Divide by ‘ds^2
Vf^2-2a/’ds^2=Vo^2
good to here
We will get rid of the ^2
you do that by taking the square root, or the 1/2 power, of both sides
Vo=Vf-2a/’ds
this isn't correct
Having solved the equation as best you can, substitute the values of the three known quantities into that equation. Then simplify your expression to get the value of the unknown quantity. Again, do your best. &&&&
Vo=2-2(10m/s^2)/2
Overall your algebra is good and you're doing pretty well with the equations.
You need to use units.
&#See my notes and let me know if you have questions. &#