8) A) A cart of mass m1 = 2.00 kg rolls along the floor with a velocity of 14.0

Question

8) A) A cart of mass m1 = 2.00 kg rolls along the floor with a velocity of 14.0 m/s in the positive direction. It hits a second cart, of mass 5.00 kg, and bounces back with a velocity of 6.00 m/s in the opposite direction. If the second cart was initially at rest, what is its final velocity? Show ALL work.

a) 2.00 m/s b) 4.00 m/s c) 6.00 m/s d) 8.00 m/s  

B) Is it elastic or inelastic, and why?

a) Inelastic, because momentum is not conserved. b) Elastic, because momentum is conserved. c) Inelastic, because kinetic energy is not conserved. d) Elastic, because kinetic energy is conserved.

Explanation / Answer

given
m1 = 2 kg
m2 = 5 kg
u1 = 14 m/s
u2 = 0
v1 = 6 m/s
v2 = ?
from the conservation of linear momentum
initial momentum = final momentum
Pi = Pf
m1*u1 + m2*u2 = m1*v1+m2*v2
2*14+5*0=2*-6+5*v2
v2 = 8 m/s
Ans-----------------D

B) It is elastic collision
because linear momentum and kinetic energy is conserved.

initial KE = 1/2*m1*u1^2+1/2*m2*u2^2
=0.5*2*14^2+0.5*5*0 =196 J

final KE =1/2*m1*v1^2+1/2*m2*v2^2
= 0.5*2*6^2+0.5*5*8^2
=196

initial momentum = final momentum
initial KE = final KE

So, It is elastic collision

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