Question

A proton of mass m is at rest when it is suddenly struck head-on by an alpha particle (which consists of 2 protons and 2 neutrons) moving at speed v. If the collision is perfectly elastic, what speed will the alpha particle have after the collision? (Assume the neutron's mass is equal to the proton's mass.) a) zero b) 2v/3 c) 3v/5 d) 5v/3

Answer 1

Answer:

The answer is c). The alpha particle will have a speed of 3/5 v.

Explanation:

In a perfectly elastic collision the momentum and the kinetic energy are maintained.

The equation to describe the velocity of the particles is:

$VA_f=(\frac{m_A-m_B}{m_A+m_B})VA_i+(\frac{2m_B}{m_A+m_B})VB_i$

From the problem you have:

$VA_i=v\\VB_i=0$

Then you solve the equation using the information in the problem. In this case, A is the alpha particle and B is the proton.

$VA_f=(\frac{4m-m}{4m+m})v\\VA_f=\frac{3m}{5m}v\\VA_f=\frac{3}{5}v$