There are three different types of impacts, elastic impacts, plastic impacts, and an oblique impact which is an impact that is in between a plastic and elastic impact. Elastic impacts and plastic impacts are completely theoretical. However, they are needed to help describe real life impacts.

The coefficient of restitution determines what will happen during an impact. Basically the coefficient of restitution relates the restitution impulse R to the deformation impulse P. To calculate the coefficient of restitution equation 1 would be used.

**(Eq 1) ** $e=\frac{∫Rdt}{∫Pdt}=\frac{(v_B)_2-(v_A)_2}{(v_A)_1-(v_B)_1}$

(v_{A})_{1} = initial velocity of particle A

(v_{A})_{2} = final velocity of particle A

(v_{B})_{1} = initial velocity of particle B

(v_{B})_{2} = final velocity of particle B

e = coefficient of restitution

An elastic impact deformation means that deformation impulse equals the restitution impulse, or in other words the coefficient of restitution equals 1. A plastic impact on the other hand has no restitution impact. Which means the particles after the impact will stay together, and this will cause the coefficient of restitution to equal 0.

Note when dealing with impact problems you also have to take in consideration of a modified equation for conservation of linear momentum. This equation can be seen in equation 2.

**(Eq 2)** $m_B(v_B)_1+m_A(v_A)_1=m_B(v_B)_2+m_A(v_A)_2$

m_{A} = Mass of particle A

m_{B} = Mass of particle B