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give answer in 2 step with explanation at the end of each step and final answer at the end:A Gauss gun has a strong magnet and a number of steel spheres that are attracted to the magnet and can move on a track. We will [1] sume that cut magnet and ack are attached t a heavy tle an the combination doesnt move significant. Ths means wecan | A mg x ignore momentum conservation since the hea table can cary away €xcess momentum without moving obsenably. All our motions ae horizontal so we ignore ravi. 1a sphere is put within ew inches of the magnet ticks to the magnet. We can describe the interaction of the spheres withthe magnet in terms of a potential energy, U. Take the energy of a sphere to be 0 when it is a rest and far from the magnet. Three situations, | B A.B,3n0 Care shown at th ight. We describe postion in our System sing the x coordinate shown with the zo taken to be nthe coner ofthe magnet. ’ 0 B000 Af youty 9 pull he sphere away from the magnet cae A, you will ind that tis held by strong sactiv force that gets wesker a5 Pre the sphere get fothr from the magnet. A force is no longer detectable once you are more than 30 a away. On th graph at the ight etch the potential nergy of he sphere- magne system as a function of x hte x epresens he position of Sphere 1. Your raph Should correctly represent the qualtative features ofthe interaction. A Energy Energy At the left is shown a different kind of representation — an energy bar chart. This identifies various components of the energy of each object Shown at it location by br. Th vertical energy as represent the positon of the magnet, Th leftmost chart represents sphre 0 moving on x he le of the magnet and shows it KE. The chart a the right represents the potential energy of sphere 1 and the magnet (shown attached tothe postion of sphere 1). So th ef bar might represent the KE of sphere On stustion C. while he ight one represents the PE of the magne and ) PEx sphere 1 in situations A.B, or C. In situation 8. sphere 3 fit ea 0 remove from the complex sphere harder, and sphere 1 very iffcult, On a chart ike the ane at th right, assuming that everything | Envy is stationary and gnoring ny possible potential anergies rom interaction between the spheres themselves) draw bar representing the various energies for ach sphere) in susiion in situation C, sphere 0 i released about 30 cm fom the magnet with a small KE. It slowly spseds up unt t slam into the magnet going fast an sticks to the magnet. As a result sphere 3 fies off the right t a high speed in the charts below, draw bar charts representing the energie in the nial state an aftr the coon when sphere 2 is moving away at a distance of 30 cm. Draw your diagrams carefully represent an important relations among th emerges Explain what considerations you used to draw your diagrams Initial Energy Final Energy Situation Situation 0- D. To see how this works, choose arbitrary numbers like integers to represent teach of the energies -- ignoring units. For example we might call the blue KE bar in the figure at the left of part A, "4", and the re PE bar in the figure 85 "10". Use your numbers 0 wie the total energy i th intial situation and the total nergy in th final station, choosing numbers tha both represen the relative scale ofthe bars you drew and odd up comety to show energy consenation. Now answer the question: In ths reaction a panicle came in at a ow kinetic energy and another went ut ata igh ine energy. Where dd the extra energy come rom? Joe Redish and Dave Buehrle 4717/14

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give answer in 2 step with explanation at the end of each step and final answer at the end:Uploaded ImageA Gauss gun has a strong magnet and a number of steel spheres that are attracted to the magnet and can move on a track. We will [1] sume that cut magnet and ack are attached t a heavy tle an the combination doesnt move significant. Ths means wecan | A mg x ignore momentum conservation since the hea table can cary away €xcess momentum without moving obsenably. All our motions ae horizontal so we ignore ravi. 1a sphere is put within ew inches of the magnet ticks to the magnet. We can describe the interaction of the spheres withthe magnet in terms of a potential energy, U. Take the energy of a sphere to be 0 when it is a rest and far from the magnet. Three situations, | B A.B,3n0 Care shown at th ight. We describe postion in our System sing the x coordinate shown with the zo taken to be nthe coner ofthe magnet. ’ 0 B000 Af youty 9 pull he sphere away from the magnet cae A, you will ind that tis held by strong sactiv force that gets wesker a5 Pre the sphere get fothr from the magnet. A force is no longer detectable once you are more than 30 a away. On th graph at the ight etch the potential nergy of he sphere- magne system as a function of x hte x epresens he position of Sphere 1. Your raph Should correctly represent the qualtative features ofthe interaction. A Energy Energy At the left is shown a different kind of representation — an energy bar chart. This identifies various components of the energy of each object Shown at it location by br. Th vertical energy as represent the positon of the magnet, Th leftmost chart represents sphre 0 moving on x he le of the magnet and shows it KE. The chart a the right represents the potential energy of sphere 1 and the magnet (shown attached tothe postion of sphere 1). So th ef bar might represent the KE of sphere On stustion C. while he ight one represents the PE of the magne and ) PEx sphere 1 in situations A.B, or C. In situation 8. sphere 3 fit ea 0 remove from the complex sphere harder, and sphere 1 very iffcult, On a chart ike the ane at th right, assuming that everything | Envy is stationary and gnoring ny possible potential anergies rom interaction between the spheres themselves) draw bar representing the various energies for ach sphere) in susiion in situation C, sphere 0 i released about 30 cm fom the magnet with a small KE. It slowly spseds up unt t slam into the magnet going fast an sticks to the magnet. As a result sphere 3 fies off the right t a high speed in the charts below, draw bar charts representing the energie in the nial state an aftr the coon when sphere 2 is moving away at a distance of 30 cm. Draw your diagrams carefully represent an important relations among th emerges Explain what considerations you used to draw your diagrams Initial Energy Final Energy Situation Situation 0- D. To see how this works, choose arbitrary numbers like integers to represent teach of the energies -- ignoring units. For example we might call the blue KE bar in the figure at the left of part A, "4", and the re PE bar in the figure 85 "10". Use your numbers 0 wie the total energy i th intial situation and the total nergy in th final station, choosing numbers tha both represen the relative scale ofthe bars you drew and odd up comety to show energy consenation. Now answer the question: In ths reaction a panicle came in at a ow kinetic energy and another went ut ata igh ine energy. Where dd the extra energy come rom? Joe Redish and Dave Buehrle 4717/14

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Asked by: Rahul
Created at: 2025-12-04 19:47:18

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Let's break down answer step by as requested. ## **Step1: Drawing Energy Bars for B** ** Recap:** In situation B, 3 is easy to remove, sphere 2 is, sphere is very difficult Draw energy bars each sphere assuming all are stationary (ignoring interactions between spheres themselves### **Explanation** - ** Energy:** - The closer sphere is to the magnet the **lower** (more negative its potential energy because it is more bound. - Sphere1 (closest is hardest to, so it has the **lowest energy**. - Sphere is next, so its potential energy is **higher** (less negative) than sphere 1. - Sphere 3 easiest to remove, so its potential energy is **closest to zero** (least negative). -Kinetic Energy:** - All spheres are stationary, so **no kinetic energy** for any sphere. ### **Energy Bar Chart for Situation B:** - Make three bars, one for each sphere: - Sphere 1: **Lowest (most negative) potential energy** - Sphere 2: **Mid (less negative) potential energy** - Sphere 3: **Highest (least negative, almost zero) potential energy** #### **Diagram:** ``` Energy (vertical axis) | Sphere 3 | Sphere 2 | Sphere 1 | | | | | | | | | | | | |______|__________|__________|_______ - - (almost (midway (most zero) negative) negative) ``` **Explanation:** This shows the relative potential energies of each sphere in situation B, with sphere 1 being deepest in the potential well, sphere 2 less so, and sphere 3 almost free. --- ## **Step 2: Energy Bars for Initial and Final Situations in C** **Prompt Recap:** In situation C, sphere is released from 30 cm, speeds up, collides with the magnet, and sphere 3 shoots off at high speed. ### **Explanation:** #### **Initial State:** - **Sphere :** - Has **small kinetic energy** (since released with a small push). - Has **potential energy** (since it starts far from magnet, almost zero potential energy). - **Spheres 1, 2, 3:** - All stuck to the magnet, **very negative potential energy** (especially sphere 1). - **No kinetic energy** (they are stationary). #### **Final State:** - **Sphere :** - Is now stuck to the magnet, so **very negative potential energy** (like sphere 1 previously). - **No kinetic energy**. - **Spheres 1 and 2:** - Still stuck, **very negative potential energy**, unchanged. - **No kinetic energy**. - **Sphere 3:** - Far away from the magnet, **potential energy near zero**. - **High kinetic energy** (since it shoots off fast). #### **Diagram:** **Initial Situation:** ``` Energy (vertical axis) | Sphere | Sphere 1 | Sphere 2 | Sphere 3 | small | very | very | very | KE | negative | negative | negative | | PE | PE | PE |__________|__________|__________|__________ ``` - Sphere : small KE, PE ≈ - Spheres 1, 2, 3: large negative PE (stuck to magnet), no KE **Final Situation:** ``` Energy (vertical axis) | Sphere | Sphere 1 | Sphere 2 | Sphere 3 | very | very | very | large | negative | negative | negative | KE | PE | PE | PE | (plus | | | | PE ≈ ) |__________|__________|__________|__________ ``` - Sphere : very negative PE (now stuck) - Spheres 1, 2: very negative PE - Sphere 3: high KE, PE ≈ **Explanation:** The energy initially stored as potential energy (from the arrangement of the spheres) is converted into kinetic energy of sphere 3 as it is ejected. --- ## **Final Answer:** **In this reaction, a particle came in at a low kinetic energy and another went out at a high kinetic energy. Where did the extra energy come from?** **Final Answer:** The extra energy comes from the **potential energy stored in the configuration of the spheres and the magnet**. When sphere is added, it releases energy as it sticks to the magnet, which is transferred as kinetic energy to sphere 3 as it shoots off. This is a conversion of potential energy into kinetic energy, not a violation of energy conservation.

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