A ball with a mass of # 6 kg# is rolling at #16 m/s# and elastically collides with a resting ball with a mass of # 1 kg#. What are the post-collision velocities of the balls?

1 Answer
Apr 10, 2018

Answer:

These momentum problems are the first in physics where you're responsible for managing a (relatively) large number of variables.

Explanation:

Recall,

#nu_A - nu_B = nu_B' - nu_A'#

Which is derived starting from,

#m_A(nu_A-nu_A') = m_b(nu_B' - nu_B)# #(1)#

#m_A(nu_A^2 - nu_A^('2)) = m_B(nu_B^('2) - nu_B^2)# #(2)#

(a restatement of the law of conservation of momentum and energy, respectively).

Then, by factoring out (2), and dividing the expansion by (1).

From here, since ball B is at rest, it's easy. Consider,

#nu_A = nu_B' - nu_A'#

#=> nu_B' = nu_A +nu_A'#

Now, consider the conformity with the law of conservation of momentum, and substituting this variable in,

#nu_A = nu_A' + nu_A + nu_A'#

#nu_A' = (0"m")/"s"#,

and by extension,

#nu_A = nu_B' = (16"m")/"s"#

From this calculation, we can understand that:

In perfectly elastic collisions, all of the energy or momentum is transferred perfectly from one body to the other, if one is at rest.