How Is the Mass of the Target Nucleus Calculated in an Elastic Collision?

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SUMMARY

The mass of the target nucleus in an elastic collision involving a proton can be calculated using conservation of momentum. In this scenario, a proton with a mass of 1 u and an initial speed of 2.40×106 m/s rebounds at 75% of its initial speed, while the target nucleus moves at 3.50×105 m/s. The correct calculation reveals that the mass of the target nucleus is approximately 1.71 u, but the final proton velocity must be considered negative to account for direction, leading to the correct mass determination.

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A proton (mass 1 u) is shot toward an unknown target nucleus at a speed of 2.40×10^6 m/s. The proton rebounds with its speed reduced by 25% while the target nucleus acquires a speed of 3.50×10^5 m/s.

What is the mass, in atomic mass units, of the target nucleus?




I tried:
Mp*Vip+Mn*Vin=Mp*Vfp+Mn*Vfn

where Mp= Mass proton=1
Vip= intial proton velocity=2.4E6
Mn= Mass nucleus=unknown
Vin=Initial Velocity of nucleus=0
Vfp= Final velocity proton=.75(2.4E6)
Vfn=final velocity nucleus= 3.5E5


i get 1.71u but its wrong
 
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The final proton velocity has a minus sign
 
borgwal said:
The final proton velocity has a minus sign

Thank you very much got the answer
 

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