Collisions?

Question

An explosion breaks an object into two pieces, one of which has 1,5 times the mass of the other. If 17,500 J were released in the explosion, how much kinetic energy did each piece acquire?

Answer 1

let the two pieces weigh x,1.5x and thier velocities be v1 and v2.
using law of conservation of momentum:
x.v1 + 1.5x . (v2)=0


therefore if we r bothered only abt speeds(i.e neglecting signs) we get-
v1 = 1.5 v2 ............. result1
v1/v2= 1.5

the ratio of ke's of each piece is:
.5 x * v1*v1
--------------------
.5 * 1.5 x * v2*v2

using result 1 we get the above ratio as 1.5

therefore the total energy is shared by the two pieces in the ratio of 1.5:1

smaller piece gets 1.5*17500/2.5 = 10500j
larger piece gets the remaining 7000j

Answer 2

The total kinetic energy is

0.5*m1*v1^2 + 0.5*m2*v2^2 = E (17,500 J)

By momentum conservation,

m1*v1 = m2*v2, or v2 = (m1/m2)*v1

Plug this in for v2 in the energy eq:

0.5*m1*v1^2 + 0.5*m2*(m1/m2)^2*v1^2 = E

Let m2 = 1.5* m1 (m1/m2 = 1/1.5) and plug that in:

0.5*m1*v1^2 + 0.5*1.5*m1*(1/1.5)^2*v1^2 = E

v1^2*( 0.5*m1 + 0.5*m1/1.5) = E

v1^2 = E/(2.5*m1/3)

The energy in m1 is 0.5*m1*v1^2 = 0.5*m1*E/2.5*m1/3) = 0.6*E The other will have E - this or 0.4*E.

(Check the math--I did it quickly)