• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

Physics Spring Coursework

Extracts from this document...

Introduction

ÐÏࡱá>þÿ        þÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿýÿÿÿþÿÿÿþÿÿÿ        




 !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMþÿÿÿOþÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿRoot Entryÿÿÿÿÿÿÿÿ²Z¤


žÑ¤ÀO¹2ºP‘:m}ÈNCONTENTSÿÿÿÿ

–CompObjÿÿÿÿÿÿÿÿÿÿÿÿVSPELLINGÿÿÿÿÿÿÿÿÿÿÿÿHþÿÿÿ        





þÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ using logs.

The laws of logs:         1.        logax + logay = loga(xy)

                        2.        logax - logay = loga(x/y)

                        3.        logaxn = nlogax

lnx means logex, where e is the mathematical constant of approximate value 2.718.


































Experiment B

This experiment involved finding how the time period of oscillations varied with the mass added to a single spring (with spring constant k).

The laws of logs can be used to change the formula lnT= ln(pkqmr ) into a straight line graph, in the form y=mx+c.

Using Law 1, ln(pkqmr) =  ln(pkq) + ln(mr)

Using Law 3, ln(pkq) + ln(mr) = ln(pkq) + rln(m)

This gives the equation lnT =  rln(m)+ln(pkq)

Comparing this to y=mx+c, the gradient is r, and the y intercept is ln(pkq).

As lnT against lnm is a straight line, the original expression lnT= ln(pkqmr ) is in the correct form, and the values r and ln(pkq) can be found.

The gradient of my graph is 0.474±0.017, which is the value of r.

Using the point (-0.93, -0.23) (the point where the line of max gradient and min gradient cross) the y intercepts (ln(pkq)) of the lines can be found.

-0.23 - (0.491x-0.93) =cmax                cmax= 0.227
-0.23 - (0.457x-0.93) =cmin                cmin = 0.195

                        ln(pkq)= 0.21±0.02


















Experiment C

This experiment involved finding a relationship between the spring constant and time period of oscillations (with a constant mass). To do this different arrangements of springs (each with spring constant k)

...read more.

Middle




This proves that the oscillation is simple harmonic motion because the acceleration towards the rest point is negatively proportional the displacement from the rest point.

This means that         w2 =k/m
                        w = (k/m)0.5

And as                 T=2p/w
                        T=2p(k/m)-0.5                
                        T=2p(m/k)0.5        

Using  Physics  by Robert Hutchings, this can be confirmed as T = 2pk-0.5m0.5.  

This means:        p=2p
                q=-0.5
                r=0.5





Units

To find the units of p, k and q I will use the correct version of the formula (taken from  Physics  by Robert Hutchings.


T = 2pk-0.5m0.5

As the values of p and q are powers, they can have no units.

To find the units of p, I will work out the units on both sides of the equation then rearrange to find the units of p. P will be used to represent the units of p.

s =  P(Nm-1)-0.5(kg)0.5
s = P(kgm/N)0.5
s = P(kgm/kgms2)0.5
s = P(1/s2)0.5
s = P/s
s2 = P

This means that the units for p are s2.


















Bibliography:

www.hookeslaw.com/hookeslaw.htm
Physics 1 - Cambridge University Press
http://www.projectalevel.co.uk/maths/logs.htm
http://www.ndt-ed.org/EducationResources/Math/Math-e.htm
http://en.wikipedia.org/wiki/Simple_harmonic_motion
Evaluation

I feel like the experiment went well, although my results do not perfectly match the theory.

Actual Values for p,q and r:

p=2p
q=-0.5
r=0.5

My values for p, q and r:

p=5.55±0.52
q = -0.468±0.019
r = 0.474±0.017

This means that none of the values I found included the actual values in their error range.

...read more.

Conclusion

Î>Î4


"PS"        $Š  088


"PS"        $Š  086


"PS"        $Š  08"
"PS"        $Š2
"PS"        $Š  08# 4^4°4

5


5|5~5ä5æ5þ5ü6þ6^7`7h7j7~7€7Š7Œ7ž7 7Š:¤:ú>ü>dA~ANGjG(J*J8J<JPW^WÄ’Ä’Ä’Ä’Z’8’’Z’’Z’’Z’’Z’Z’’Þ’Z6
"PS"        $Š  08$
"PS"        $Š-

"


"PS"        $Š8

"PS"        $Š  082


"PS"        $Š  08<
"PS"        $Š  08."ÿ^W`WbWR\V\È”bX

"        2


"PS"        $Š  084

"PS"        $Š  088


"PS"        $Š  08T


dë0œ8>b†š¤®¸ÂÖð


4ÿÿÿÿDefinition TermDefinition ListH1H2H3H4H5H6Address

Blockquote


Preformattedz-Bottom of Form
z-Top of FormŽdë¢p~†”œª¸ÎØèò

 0:JTdlzŽ¾DP‚


"


"


"ø|


" ¦"ø|


"



"ø|"


"



"ˆ¶"


"


"


"



"ð"


"



"àŒ"


"



"ð"


"ð        
"ø|


"ø|,


"ð$Š  08)P2‚J'
(Š@ ÅJ         Š• Oà  +%( Ùu.0 žÀ78 c
A@ (VJH í SP ²ë\.

"àŒ

$Š  08Ùu.


"àŒ

$Š  08Ùutt|†(~5R\V\^`bdfh
N–è `%Ö&¬(B/ 4^WV\jlnprtvxz|~”lë‘ž8HZxTimes New RomanArialSymbol


Arial Narrow
Courier New0

ÿÿÚSa‰

§
t€AX °¾ËÚéõ0@N[jy…“è!20;UW_rÁß~X†¿~¯¿Ï}$)-"""úÿÿÿ"@""þÿÿÿ

"-

"8

"3"""úÿÿÿ

"

"

"

"

"

"

"        

"

"

"

"

"


"

"


"

"

"

"

"

"

"

"

"

"

"

"

"

"!

""

"#

"$

"%

"&

"'

"(

")

"*

"

"

"

"

"

"+

",

"-

".

"

"/¤0


ÛaÀÈÐØ&‚ôü


$,4<DLT\dlt|„Œ”œ¤¬´¼$,4<DLT\dlt|„Œ”œSPCSPCSPC&http://www.hookeslaw.com/hookeslaw.htm-http://www.projectalevel.co.uk/maths/logs.htm8http://www.ndt-ed.org/EducationResources/Math/Math-e.htmSPCSPCSPCSPCSPCSPCSPCSPCSPCSPCSPCSPCSPCSPCSPCSPCSPCSPCSPCSPCSPCSPCSPCSPCSPC3http://en.wikipedia.org/wiki/Simple_harmonic_motionSPCSPCSPCSPCSPCSPCSPCSPCSPCSPCSPCSPCSPCSPCSPCSPCÿ)-

"

"

"¤øÃìÈXXôKMicrosoft XPS Document WriterœXÿš
4dXXA4ÿÿÿÿDINU"L


ÊÒör        SMTJMicrosoft XPS Document WriterInputBinFORMSOURCERESDLLUniresDLLInterleavingOFFImageTypeJPEGMedOrientationPORTRAITCollateOFFResolutionOption1PaperSizeLETTERColorMode24bpp
MXDW1winspoolMicrosoft XPS Document WriterXPSPort:Fÿÿ"\²"€‘"ÑV"$c"ð`        "ð`""A."@ÿÿ"\²"ðù"ÑV"$c"ð`        "ð`"."Spring CW.wps""Øp"Øp

("        )"787J7L76:P:Z>\>Ê@ä@.FHF–K˜K¦KªKbUpUÄ’Ä’Ä’Ä’Z’8’’Z’’Z’’Z’’Z’Z’’Þ’Z6


"PS"        $Š  08$
"PS"        $Š-

"


"PS"        $Š8

"PS"        $Š  082


"PS"        $Š  08<
"PS"        $Š  08."ÿø
ÿÿÿÿSTSHSTSHh¢SYIDSYID

„SGP SGP „INK INK "„BTEPPLC &„@BTECPLC f„hFONTFONT΄¨TOKNPLC v…pSTRSPLC æŒ:PRNTWNPR gFRAMFRAM‡‘ˆTITLTITL’DOP DOP +’"þÿ

ÿÿÿÿ²Z¤


žÑ¤ÀO¹2ºQuill96 Story Group Classÿÿÿÿô9²q‹Ô
y‹Ô‹Ôly‹Ôo‹ÔàykAhykAheykAhkAh²ykAh·kAh{ykAh}kAh,ykAh2kAh4ykAh8kAh9ykAh;kAhLykAhQkAhTykAhXkAhYykAh\kAheykAhkkAhnykAhtkAhvykAhykAh€ykAh……kAh!ykAh#…kAh@ykAhBkAhPykAhSkAhwykAhzkAhäykAhçkAhT

ykAhW

kAh!
ykAh$
kAhA
ykAhE
kAh«
ykAh°
kAhô
ykAhù
kAh


ykAh


kAh


ykAh"


kAh3


ykAh5


kAha


ykAhd


kAhÎ


ykAhÑ


kAhykAh
kAh>ykAhAkAh7ykAh:kAh–ykAh™kAh

ykAh


kAhykAhkAhœykAh kAh¨ykAh¬kAhÿykAhkAhTykAhYkAhLykAhNkAh[ykAh]kAhjykAhmkAh4ykAh7kAh@ykAhCkAhaykAhdkAhtykAhwkAhŠykAhkAhÆykAhòkAhoykAhrkAhô ykAhü kAhC*ykAhK*{kAhý,ykAh-

...read more.

This student written piece of work is one of many that can be found in our AS and A Level Fields & Forces section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related AS and A Level Fields & Forces essays

  1. Marked by a teacher

    Experiment to determine gravity from a spring using digital techniques

    3 star(s)

    * The mass is displaced 5cm and allowed to oscillate, while the the "start" button is pressed. After at least 11 oscillations, the "stop" button is pressed to end recording. * The "smart tool" icon was selected, and "smart tool" was used to find the times for the 1st and 11th peaks.

  2. Peer reviewed

    Determination of the acceleration due to gravity (g)

    4 star(s)

    From the method of using a ticker timer, I got a tape after experiment and I stick every five-dot- tape on the graph paper, then I drew the line of best fit through the mid-point of the tape. The line of best fit is drawn by velocity against time, hence,

  1. Experiment to determine gravity from a spring using analogue techniques

    * This was repeated for each spring. Again, the second spring could not take as much mass as the first without hitting the table. Instead, the masses placed on it increased in 0.005kg increments but only up to 0.06kg. It was not deemed necessary to repeat the experiment for each

  2. The experiment involves the determination, of the effective mass of a spring (ms) and ...

    Average xT. 200 40 26.1 25.6 25.85 500 25 25.4 25.2 25.3 100 50 23.3 23.7 25.3 600 25 26.9 27.0 26.95 These were the trial readings taken before the experiment, they were taken to help in the decision of the size of the limits.

  1. Investigating the relationship of projectile range and projectile motion using a ski jump.

    It will create a vertical acceleration if it bends resulting in an increase in the horizontal component. In theory, we have assumed that the air through which the projectile moves has no effect on its motion, a reasonable assumption at low speeds.

  2. Measuring The Constant g; The Acceleration Due To Gravity

    For each height increment, repeat this 5 times in order to obtain an average estimate for the drop time. 4) Calculate g for each repeat using the formula, and hence calculate an average value for g from all of the repeats from every increment, to obtain a final overall estimate.

  1. Experiment to calculate spring constant of 2 springs

    * The trolley was pulled 0.2m away from the force sensor, and the "tare" button of the force sensor was pressed, setting it to 0. In data studio, this was recorded as the 0 distance, and this value of 0 force was recorded by pressing the "start" button on the datastudio interface, in order for it to start recording data.

  2. Lab Report - In this lab report, it will describe the weight of the ...

    it at 70� � 0.5 having an average time of 1.32 � 0.01 seconds (Table 3) Table 3: The measurements of the pendulum's period with different length of strings. Length of String � 0.05 cm Angle � 0.5� Bob (The mass of the bob stayed consisted throughout the trial.)

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work