a) Differentiate between perfectly elastic and perfectly inelastic collisions.
b) A body of mass m, moving with a velocity u1 undergoes a heat on perfectly inelastic collision with a body of mass m2 initially at rest. Show that the ratio of final k.e and initial ke, of the system is m1/m1 + m2.
Answers
Elastic and Inelastic Collisions
• A collision in which the objects stick together after collision
is called a perfectly inelastic collision.
– The objects do not bounce at all.
– If we know the total momentum before the collision, we can calculate the final momentum and velocity of the now-joined objects.
• For example:
– The football players who stay together after colliding.
– Coupling railroad cars.
Four railroad cars, all with the same mass of
20,000 kg, sit on a track. A fifth car of identical
mass approaches them with a velocity of 15 m/s.
This car collides and couples with the other four
cars. What is the initial momentum of the system?
a) 200,000 kg·m/s
b) 300,000 kg·m/s
c) 600,000 kg·m/s
d) 1,200,000 kg·m/s
m5 = 20,000 kg v5 = 15 m/s pinitial = m5v5
= (20,000 kg)(15 m/s) = 300,000 kg·m/s
Four railroad cars, all with the same mass of
20,000 kg, sit on a track. A fifth car of identical
mass approaches them with a velocity of 15 m/s.
This car collides and couples with the other four
cars. What is the initial momentum of the system?
a) 200,000 kg·m/s
b) 300,000 kg·m/s
c) 600,000 kg·m/s
d) 1,200,000 kg·m/s
m5 = 20,000 kg v5 = 15 m/s pinitial = m5v5
= (20,000 kg)(15 m/s) = 300,000 kg·m/s