Difference between revisions of "Finding the Space Between Lead Shots"

From New IAC Wiki
Jump to navigation Jump to search
 
 
(24 intermediate revisions by the same user not shown)
Line 1: Line 1:
 +
[http://wiki.iac.isu.edu/index.php/PhotoFission_with_Polarized_Photons_from_HRRL Go Back]
 +
 +
 
==Plan 1==
 
==Plan 1==
 
By Mass
 
By Mass
 
+
[[Image:lead shot labeled.jpg|thumb|Lead Shot|400 px]]
 
1 - Empty box, m <sub>1</sub>
 
1 - Empty box, m <sub>1</sub>
  
Line 13: Line 16:
 
m <sub>Pb</sub> = m <sub>2</sub> - m <sub>1</sub>
 
m <sub>Pb</sub> = m <sub>2</sub> - m <sub>1</sub>
  
V <sub>Pb</sub> = m <sub>2</sub> - m <sub>1</sub> / ρ <sub>Pb</sub>
+
V <sub>Pb</sub> = (m <sub>2</sub> - m <sub>1</sub>) / ρ <sub>Pb</sub>
  
  
 
m <sub>H <sub>2</sub> 0</sub> = m <sub>3</sub> - m <sub>2</sub>
 
m <sub>H <sub>2</sub> 0</sub> = m <sub>3</sub> - m <sub>2</sub>
  
V <sub>H <sub>2</sub> 0</sub> = m <sub>3</sub> - m <sub>2</sub> / ρ <sub>Pb</sub>
+
V <sub>H <sub>2</sub> 0</sub> = (m <sub>3</sub> - m <sub>2</sub>) / ρ <sub>Pb</sub> = V <sub>SP</sub> (The space between the lead)
 +
 
 +
ratio = V <sub>Pb</sub> / V <sub>tot</sub>
 +
 
 +
 
 +
==Plan 2==
 +
By Volume
 +
 
 +
1 - V <sub>H <sub>2</sub> 0 1</sub> = V <sub>tot</sub>
 +
 
 +
2 - V <sub>H <sub>2</sub> 0 2</sub> = V <sub>SP</sub>
 +
 
 +
 
 +
V <sub>Pb</sub> = V <sub>tot</sub> - V <sub>SP</sub>
 +
 
 +
R = V <sub>Pb</sub> / V <sub>tot</sub> = (V <sub>tot</sub> - V <sub>SP</sub>) / V <sub>tot</sub> => 1 -  (V <sub>SP</sub> / V <sub>tot</sub>)
 +
 
 +
==Experiment==
 +
 
 +
===Plan 1===
 +
We had 2 scales to measure the weight. Let's call them scale #1 and scale #2, measurement on them were called weight #1 and Weight respectively.
 +
{| border="1" cellpadding="20" cellspacing="0"
 +
|-
 +
|Mesurements
 +
|Discriptions
 +
|masses
 +
|weight #1 (£)
 +
|weight #2 (£)
 +
|Weight AVE (£)
 +
|Weight AVE (g)
 +
|-
 +
|1 ||Box || m <sub>1</sub> ||3 ||4 ||3.5 || 1587.6
 +
|-
 +
|2  ||Box+Pb ||m <sub>2</sub> ||102 ||103  ||102.5 ||46493.2
 +
|-
 +
|3 ||Box+Pb+<math>H_{2}</math>O ||m<sub>3</sub>||105 || 111||108 ||48988.0
 +
|-
 +
|4 ||Box+<math>H_{2}</math>O ||m<sub>4</sub>||15 ||18 ||16.5  ||7484.3
 +
|-
 +
|}
 +
 
 +
Calculations
 +
 
 +
V<sub>Pb</sub> = (m<sub>2</sub> - m<sub>1</sub>)/ρ<sub>Pb</sub>=3959.2 <math>cm^3</math>
 +
 
 +
V<sub>Pb</sub> = (m<sub>4</sub> - m<sub>1</sub>)/ρ<sub>H2O</sub>=5896.8 <math>cm^3</math>
 +
 
 +
Ratio = V<sub>Pb</sub>/V<sub>tot</sub> =67%
 +
 
 +
=== Plan 2===
 +
 
 +
{| border="1" cellpadding="20" cellspacing="0"
 +
|-
 +
|Measurements
 +
|Descriptions
 +
|V<sub>H2O</sub> = V<sub>sp</sub> (<math>cm^3</math>)
 +
|V<sub>tot</sub> (<math>cm^3</math>)
 +
|Ratio
 +
|-
 +
|1 ||without shaking ||2600 || 6500 ||60%
 +
|-
 +
|2 ||without shaking ||840 ||2000 ||58%
 +
|-
 +
|2 ||with a lot of shaking ||210 ||510 ||64.7%
 +
|-
 +
|}
 +
 
 +
 
 +
Calculations
 +
 
 +
Ratio = 1 -  V<sub>sp</sub>/V<sub>tot</sub>
 +
 
 +
== Conclusion==
 +
 
 +
We believe the plan 2 is more precise. The reason is in the plan 1 the scales we had are not precise and there are error propagation when use mass to calculate volume. However, in plan 2 we directly measured the volume.
 +
 
 +
Experiment  also shows that shaking will increase the packing ratio significantly.
 +
 
 +
[http://wiki.iac.isu.edu/index.php/PhotoFission_with_Polarized_Photons_from_HRRL Go Back]

Latest revision as of 06:26, 5 February 2009

Go Back


Plan 1

By Mass

Lead Shot

1 - Empty box, m 1

2 - Box filled with Lead, m 2

3 - Box filled with Lead and H 2 0, m 3

4 - Box filled with H 2 0, m 4


m Pb = m 2 - m 1

V Pb = (m 2 - m 1) / ρ Pb


m H 2 0 = m 3 - m 2

V H 2 0 = (m 3 - m 2) / ρ Pb = V SP (The space between the lead)

ratio = V Pb / V tot


Plan 2

By Volume

1 - V H 2 0 1 = V tot

2 - V H 2 0 2 = V SP


V Pb = V tot - V SP

R = V Pb / V tot = (V tot - V SP) / V tot => 1 - (V SP / V tot)

Experiment

Plan 1

We had 2 scales to measure the weight. Let's call them scale #1 and scale #2, measurement on them were called weight #1 and Weight respectively.

Mesurements Discriptions masses weight #1 (£) weight #2 (£) Weight AVE (£) Weight AVE (g)
1 Box m 1 3 4 3.5 1587.6
2 Box+Pb m 2 102 103 102.5 46493.2
3 Box+Pb+[math]H_{2}[/math]O m3 105 111 108 48988.0
4 Box+[math]H_{2}[/math]O m4 15 18 16.5 7484.3

Calculations

VPb = (m2 - m1)/ρPb=3959.2 [math]cm^3[/math]

VPb = (m4 - m1)/ρH2O=5896.8 [math]cm^3[/math]

Ratio = VPb/Vtot =67%

Plan 2

Measurements Descriptions VH2O = Vsp ([math]cm^3[/math]) Vtot ([math]cm^3[/math]) Ratio
1 without shaking 2600 6500 60%
2 without shaking 840 2000 58%
2 with a lot of shaking 210 510 64.7%


Calculations

Ratio = 1 - Vsp/Vtot

Conclusion

We believe the plan 2 is more precise. The reason is in the plan 1 the scales we had are not precise and there are error propagation when use mass to calculate volume. However, in plan 2 we directly measured the volume.

Experiment also shows that shaking will increase the packing ratio significantly.

Go Back