U3AOS1 Topic 12: Collisions

Collision questions are almost like momentum questions, but now there's just an extra step which is classifying the collision as Elastic or Inelastic.


The difference between Elastic and Inelastic collisions is very simple and is shown in the table below.


Elastic Inelastic



An elastic collision is when

KE is conserved


KEi=KEfKE_{i} = KE_{f}



An inelastic collision is when

KE is NOT conserved


KEi≠KEfKE_{i} \neq KE_{f}



If energy is always conserved then why won't the initial and final KEs be the same?


This is because the energy can get dissipated in the form of heat, sound etc.

Therefore the energy in the entire system is still conserved.




When solving collision questions the first thing generally is to calculate the speeds using the momentum equations.

From here calculate the initial and final kinetic energy.


KEi=KEfKE_{i} = KE_{f}

v2v^212m1(u1)2+12m2(u2)2=12m1(v1)2+12m2(v2)2\frac{1}{2}m_1(u_1)^2+\frac{1}{2}m_2(u_2)^2 = \frac{1}{2}m_1(v_1)^2 +\frac{1}{2}m_2(v_2)^2


(this is assuming there are only two objects if there are more just add more m, u and v values)





SOLVING COLLISIONS FULLY:



1. Calculate all speed and mass variables using momentum equations

2. Substitute all variables into kinetic energy equations

3. Determine whether the collision is elastic or inelastic





Created with GeoGebra®, by Tom Walsh, Link



Use the calculator below to assist you

Example 1

If Cart A is travelling at 5m/s West and Cart B is travelling 1m/s East toward each other until they crash and move together at 3m/s West. Assume both carts have a mass of 50kg. Is the collision elastic or inelastic?


The question is asking to determine whether the collision is elastic or not.


Therefore, the initial and final energies must be checked.

If they are equal then the collision is elastic.


We are given that both masses travel at the same velocity after the collision. 




Step 1: Label the direction so that West is negative and the East is positive

−←→+



Step 2: Write down all known variables

m1=m2=50kg,u1=−5,u2=1,u3=−3m_1 = m_2 = 50kg, u_1 = -5, u_2 = 1, u_3 = -3

Step 3: Choose the appropriate equation


12m1u12+12m2u22=12m(1+2)u32\frac{1}{2}m_1u_1^2 + \frac{1}{2}m_2u_2^2 = \frac{1}{2}m_{(1+2)}u_3^2


Step 4: Substitute values


12(50)(−5)2+12(50)(1)2=12(50+50)∗(−3)2\frac{1}{2}(50)(-5)^2 + \frac{1}{2}(50)(1)^2 = \frac{1}{2}(50+50)*(-3)^2




Step 5: Solve carefully


12(50)(25)+12(50)(1)=12(100)∗(9)\frac{1}{2}(50)(25) + \frac{1}{2}(50)(1) = \frac{1}{2}(100)*(9)

≠

625+25≠450625 + 25 \neq 450

The collision is inelastic because the initial and final energy are not equal.