Inelastic and Elastic Collisions

This web page discusses both Inelastic and Elastic collisions.

Inelastic Collisions:

• Two objects hit one another and stick together. Example: windshield and bug
• Equation: m1v1+m2v2=(m1+m2)Vc, where m=mass, v=velocity, and Vc= the change in velocity
• Example:  A 1450-kg truck is going 5.6 m/s east collides inelastically with a stationary 3400-kg bus.  What is the final velocity?
• m1v1+ m2v2=(m1+m2)Vc
• 1450kg(5.6m/s)+3400kg(0m/s)=(1450kg+3400kg)Vc
• 8120=4850Vc
• Vc=1.67 m/s

 

Elastic Collisions:

• Two objects collide and bounce off of each other.  Example: bowling ball and bowling pin
• Equation: m1v1+m2v2=m1v1’+m2v2’, where m=mass and v=velocity
• Example: A 1978 Pinto with a mass of 1000-kg going east at 5 m/s collides with a stationary truck whose mass is 3100-kg.  The truck’s velocity after the collision is 1.4 m/s.
• m1v1+m2v2=m1v1’+m2v2’
• 1000kg(5m/s)+3100kg(0m/s)=1000kg(v1’)+3100kg(1.4m/s)
• 5000kg-m/s+0kg-m/s=1000(v1’)+4340kg-m/s
• 5000=1000(v1’)+4340
• 660=1000(v1’)
• v1’=0.66 m/s

 

Inelastic and Elastic Practice:

• A 90-kg fullback is moving south with a speed of 5.0 m/s has a perfectly inelastic collisions with a 95-kg opponent running north at 3.0 m/s.
• m1v1+m2v2=(m1+m2)Vc
• 90(5)+95(-3)=(90+95)Vc (the 3 is negative because the two objects are going in opposite directions)
• 165=185Vc
• Vc= 0.89 m/s

 

• Two 0.40-kg soccer balls collide elastically in a head-on collision.  The first ball starts at rest, and the second ball has a speed of 3.5 m/s.  After the collision, the second ball is at rest. 
• m1v1+m2v2=m1v1’+m2v2’
• .40(0)+.40(3.5)=.40(v1)+.40(0)
• 1.4=.40(v1)
• v1= 3.5 m/s