Help me please......?

Question

A railroad freight car whose mass is 70,000kg collides qith a stationary caboose car, there is no friction with the rails. the cars couple 2gether and 20% of the initial kinectic energy is transformed into thermal energy,sound,bending of metals,vibrations,e.t.c. find the MASS of the caboose?

Answer 1

First let's use the conservation of linear momentum :

70000*V = V'*(70000 + X) .....(*)

X = mass of the carboose

V = speed of the railroad

V' = speed of the couple

Initial kinetic energy = 70000*V^2 / 2

Final kinetic energy = (70000 + X)*V'^2 / 2

Final kinetic energy = 80/100*initial energy

80/100*(70000*V^2 / 2) = (70000 + X)*V'^2 / 2

4/5*(70000*V^2) = (70000 + X)*V'^2 ....(**)

Dividing (*) and (**)

4/5*V = V'

5*V' = 4V

and replacing on :

70000*V = V'*(70000 + X) .....(*)

X = 17500 kg

Hope that helps

Answer 2

from the statement
the initial kinetic energy
0.8*.5*70000*v1^2=.5*(70000+m)*v2^2
0.8*70000*v1^2=(70000+m)*v2^2

we also know that
70000*v1=(70000+m)*v2
v1=(70000+m)*v2/70000
v1^2=(70000+m)^2*v2^2/70000^2

plugging in and using m in units of kg*1000

0.8*70*(70+m)^2*v2^2/70^2=(70+m)*v2^2

simplify
(70+m)*v2^2*(1-(70+m)/87.5)=0

if I divide both sides by
(70+m)*v2^2
I have
(1-(70+m)/87.5)=0
87.5-70 = m
17500 kg is the mass of the caboose

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