Question

A "Mechanics" challenge

Answer 1

Let's suppose a colllision between a neutron which is moving with a velocity V1, and a nucleus at rest. The unit of measure of the masses is the nucleon mass, so the neutron has mass equal to 1, whereas the mass of the nucleus is A, where A is the mass number of that nucleus.

1) find the velocity of the center of mass of the system neutron-nucleus
2) show that with respect to the center of mass, the total momentum of the system nucleus-neutron is the null vector
@IrishBoy123 @Empty @Astrophysics

Answer 2

hint:
the velocity of the center of mass of a system composed by N particles, whose mass are m_i and velocities are v_i, is given by the subsequent fromula:
\[\Large {{\mathbf{v}}_{CM}} = \frac{{\sum\limits_1^N {{m_i}{{\mathbf{v}}_i}} }}{{\sum\limits_1^N {{m_i}} }}\]

Answer 3

*first* bit:


\(\huge \vec v_{cm}=\frac {∑^N_i \ m_i \vec v_i}{∑^N_1 \ m_i}\)

conservation of momentum:
\(\large \vec v_1 = \vec v_2 + A \vec v_f \)


\(\huge \vec v_{cm}=\frac { \vec v_2 + A \vec v_f }{A + 1} = \frac {\vec v_1 }{A + 1}\)

if that's totally off beam, pls advise.