Elastic Collisions

Key Questions

  • What are some examples of elastic collisions?

    billiard balls
    Newton's cradle
    curling rocks
    shuffleboard pucks
    bowling ball and pins

    Always take time to think because in real-life situations, most collisions are a combination of elastic and inelastic.

    Amory W. · · Aug 24 2014
  • Question #15adf

    #m_1, m_2# be the two bodies
    #u_1, v_1# be initial and final velocities of #m_1#
    #u_2,v_2# be initial and final velocities of #m_2#

    let the initial velocity of #m_2# = o. So, #u_2# = 0.

    As the collision is elastic, Kinetic Energy and Momentum are conserved.

    Initial Momentum is #m_1u_1#
    Final Momentum is #m_1v_1+m_2v_2#

    So, #m_1u_1 = m_1v_1+m_2v_2#
    #rArr# #m_1u_1-m_1v_1=m_2v_2#
    #rArr# #m_1(u_1-v_1)=m_2v_2# #-># Equation'1'

    Initial Kinetic Energy is #1/2m_1u_1^2#
    Final Kinetic Energy is #1/2m_1v_1^2+1/2m_2v_2^2#

    So, #1/2m_1u_1^2 = 1/2m_1v_1^2+1/2m_2v_2^2#
    #rArr# #m_1u_1^2 = m_1v_1^2+m_2v_2^2#
    #rArr# #m_1u_1^2-m_1v_1^2 = m_2v_2^2#
    #rArr# #m_1(u_1^2-v_1^2) = m_2v_2^2#
    #rArr# #m_1(u_1-v_1)(u_1+v_1) = m_2v_2^2#

    From Equation '1', #m_1(u_1-v_1)=m_2v_2#

    #rArr# #m_2v_2(u_1+v_1)=m_2v_2^2#
    #rArr# #u_1+v_1=v_2#

    Now, #v_2=u_1+v_1#

    From Equation '1', #m_1(u_1-v_1)=m_2v_2#

    So, #m_1(u_1-v_1)=m_2(u_1+v_1)#
    #rArr# #m_1u_1-m_1v_1=m_2u_1+m_2v_1#
    #rArr# #v_1= (u_1(m_1-m_2))/(m_1+m_2)#

    now, solve the equation '1' using #v_1=v_2-u_1# to get #v_2#

    I think, #v_2=(2m_1u_2)/(m_1+m_2)#

    Final momentum of of #m_1# is #m_1v_1# and Final momentum of #m_2# is #m_2v_2#

    :D

    PS : Sorry if the math is clumsy, I'm new here.

    Shiva Reddy · 2 · Oct 24 2014
  • What is an elastic collision?

    Answer:

    Elastic collision is the collision where there occurs no loss in net kinetic energy as the result of collision.

    Explanation:

    Total Kinetic energy before the collision= Total kinetic energy after the collision

    For example,

    Bouncing back of a ball from the floor is an example of elastic collision.

    Some other examples are:-
    #=>#collision between atoms
    #=>#collision of billiard balls
    #=>#balls in the Newton's cradle... etc.

    Reyan Roberth · 1 · Jun 4 2018

Questions

Momentum and Collisions