How do I show the fractional change in Kinetic Energy in a completely inelastic collision?

20,117

What you need to do is use the conservation of momentum to get the velocity of the combined system: $$ m_1v_{1,i}+m_2v_{2,i}=\left(m_1+m_2\right)v_f $$ This conservation law shows that the final velocity of the two blocks will still be proportional to the initial velocity of the one block (i.e, $v_f\propto v_i$). Getting this into the fractional change equation is straight-forward from here.

Now, the negative sign here indicates that energy is lost in the collision. This should make sense since (a) inelastic collisions expect the non-conservation of KE and (b) you can't gain energy here without some source. Thus, the only option is the final state must have lesser kinetic energy than the initial state.

Share:
20,117

Related videos on Youtube

ToltarTheGreat
Author by

ToltarTheGreat

I am a Java/Web Developer who just is trying to make a difference in the world one line of code at a time. I hope I can help the community make a difference as well.

Updated on August 01, 2022

Comments

  • ToltarTheGreat
    ToltarTheGreat over 1 year

    Given the formula

    $$\frac{{\Delta}(KE)}{KE_i}=\frac{(KE_f-KE_i)}{KE_i}=\frac{-M}{(m+M)}$$

    Now I know these that the conservation of momentum is always applicable. Also I understand that

    $$KE=\frac{1}{2}mv^2$$ and $$p=mv$$ When trying to solve it I get $$\frac{m_2(v_2)^2}{m_1(v_1)^2}-1$$

    Is their anything I am doing wrong? If so, what do I need to do to go about this equation? Also, what is the significance of this the negative value in M?

    Disclaimer: I am not looking for the complete answer, I am looking to find out how to solve it so I can be sure to know how to do this in future situations. Please edit this post as you see fit for the sake of the quality of the content in this site to help others understand the same problem as well. I thank you all in advance for your contribution.