Inelastic collisions

Imagine a collision between two objects with masses m1 and m2. The two objects have initial velocities vi1 and vi2 and final velocities vf1 and vf2. Momentum conservation for these two colliding objects can be written as Read the text aloud
(11.3)
m 1 v i1 + m 2 v i2 = m 1 v f1 + m 2 v f2
m1  = mass of object 1 (kg)
vi1  = initial velocity of object 1 (m/s)
vf1  = final velocity of object 1 (m/s)
m2  = mass of object 2 (kg)
vi2  = initial velocity of object 2 (m/s)
vf2  = final velocity of object 2 (m/s)
Conservation
of momentum
(two objects)
There are two basic types of collisions in physics: elastic and inelastic. In an inelastic collision, some of the initial kinetic energy of the objects is transformed into heat and/or works to deform the shape of the objects. Auto collisions are nearly always inelastic, because of the damage caused to the cars. In the special case of a perfectly inelastic collision, the two objects stick together after impact. Read the text aloud Show Symmetry and collisions
Perfectly inelastic collision between two balls
A perfectly inelastic collision is depicted in the illustration above. These collision problems are solved in the same way as any other collision problem, using the conservation of momentum. Moreover, in the perfectly inelastic collision case the final velocities of the two objects are set to be equal—because the objects stick together! Read the text aloud
A 100 kg hockey player, moving at 2 m/s, collides head-on with a 75 kg hockey player moving at 1 m/s. After impact, they become entangled and slide together. What is their velocity after impact?
Asked: final velocity vf after collision
Given: m1 = 100 kg, m2 = 75 kg,
vi1 = +2 m/s, vi2 = −1 m/s,
vf1 = vf2 = vf, since they move together after the (inelastic) collision
Relationships: Conservation of momentum: m1vi1 + m2vi2 = m1vf1 + m2vf2
Solution: Equate the final velocities: m1vi1 + m2vi2 = (m1 + m2)vf.
Divide both sides by (m1 + m2): m 1 v i1 + m 2 v i2 m 1 + m 2 = ( m 1 + m 2 ) v f m 1 + m 2 Cancel terms to solve for vf  and substitute the values: v f = m 1 v i1 + m 2 v i2 m 1 + m 2 = ( 100 kg )( 2 m/s )+( 75 kg )( 1 m/s ) 100 kg+75 kg =+0.71 m/s
Answer: vf = +0.71 m/s, in the same direction as the 100 kg player.
Read the text aloud
Two cars collide head-on, partially crumpling the front end of each. The cars bounce off each other from the collision, ending 1.3 m apart. What type of collision is this?
  1. elastic
  2. inelastic
  3. perfectly inelastic
  4. There is not enough information to determine the type of collision.
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Two 1 kg balls, traveling at +1 m/s and −1 m/s, respectively, collide with each other and stick together after impact. What is their velocity after the collision?
  1. −1 m/s
  2. 0 m/s
  3. +1 m/s
  4. +2 m/s
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