One way that scientists measure the mass of an unknown particle is to bounce a f

Question

One way that scientists measure the mass of an unknown particle is to bounce a familiar particle, such as a proton or electron, off the unknown particle in a bubble chamber. The initial and rebound velocities of the familiar particle is measured from photographs of the bubbles it creates as it moves; the information is used to determine the mass of the unknown particle.

(a) If a known particle of mass m and initial speed v0 collides elastically, head-on with a stationary unknown particle and then rebounds with speed v, find the mass of the unknown particle in terms of m, v, and v0.
munknown =

(b) If the known particle is a proton and the unknown particle is a neutron, what will be the recoil speed of the proton and the final speed of the neutron?

Explanation / Answer

a)
speed of unknown particle after the collsion,

v_unknown = 2*m*vo/(m+m_unknown)

Apply conservation of momentum

m*vo = -m*v + m_unknown*v_unknown

m*vo = -m*v + m_unknown*(2*m*vo/(m+m_unknown))

m*(vo+v)*(m+m_unknown) = m_unknown*(2*m*vo)

m^2*(vo+v) = m_unknown*(2*m*vo - m*(vo+v))

m^2*(vo+v) = m_unknown*(2*m*vo - m*vo - m*v)

m^2*(vo+v) = m_unknown*(m*vo - m*v)

m^2*(vo+v) = m_unknown*m*(vo - v)

m*(vo+v) = m_unknown*(vo-v)

m_unknwon = m*(vo+v)/(vo-v) <<<<<<<------Answer

b) As the proton and netron have same masses velocities are interchanged.

vp,f = 0

vn,f = vo

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