p38_051

# p38_051 - 51. (a) Before looking at our solution to part...

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51. (a) Before looking at our solution to part (a) (which uses momentum conservation), it might be ad- visable to look at our solution (and accompanying remarks) for part (b) (where a very diFerent approach is used). Since momentum is a vector, its conservation involves two equations (along the original direction of alpha particle motion, the x direction, as well as along the ±nal proton direction of motion, the y direction). The problem states that all speeds are much less than the speed of light, which allows us to use the classical formulas for kinetic energy and momentum ( K = 1 2 mv 2 and ~p = m~v , respectively). Along the x and y axes, momentum conservation gives (for the components of ~v oxy ): m α v α = m oxy v oxy ,x = v oxy ,x = m α m oxy v α 4 17 v α 0= m oxy v oxy ,y + m p v p = v oxy ,y = m p m oxy v p ≈− 1 17 v p . To complete these determinations, we need values (inferred from the kinetic energies given in the problem) for the initial speed of the alpha particle ( v α ) and the ±nal speed of the proton ( v p ). One
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