Answer:
50%
Explanation:
- Assuming no external forces acting during the collision, total momentum must be conserved.
- As one of the mass was initially at rest, the initial momentum can be written as follows:
[tex]p_{o} = m* v_{1o} (1)[/tex]
- If the collision is totally inelastic, both masses must move as one after the collision, so we can write the following equation:
- [tex]p_{f} = (m+m)* v_{f} = 2*m*v_{f}[/tex] (2)
- As po = pf, we can solve for vf in terms of v1o, as follows:
[tex]v_{f} =\frac{v_{1o}}{2}[/tex]
- The initial kinetic energy will be:
[tex]K_{1o} =\frac{1}{2} * m *v_{1o}^{2} (1)[/tex]
- The final kinetic energy of both masses will be as follows:
[tex]K_{f} =\frac{1}{2} * 2*m *(\frac{v_{1o}}{2}) ^{2} (2)[/tex]
- Rearranging in (2) we get:
[tex]K_{f} =\frac{1}{2} *m *v_{1o} ^{2} *\frac{1}{2} = \frac{K_{1o} }{2}[/tex]
- So, the fraction of the initial kinetic energy lost is just the half of the initial value.
