Question

A body of mass 15.0 kg is traveling at 5.3 m/s along the positive x-axis with no external force acting. At a certain instant an internal explosion occurs, splitting the body into two chunks of 7.5 kg mass each. The explosion gives the chunks an additional 16 J of kinetic energy. Neither chunk leaves the line of original motion. Determine the speed and direction of motion of each of the chunks after the explosion. Enter the larger velocity.

Enter the smaller velocity.

Answer 1

step 1 we have given here that,

two chunks of 7.5kg each

velocity = 5.3 m/s

kinetic energy =16 J

step 2

applying the consevation of momentum we will have,

mv0 = m1v1 + m2v2

on substitution of values we will have ,

10.6 - v1 = v2 ..............................1

now given that change in kinetic energy

K = 0.5 m1(v1^ + v^2 - 2v0^2)

on substituation we will get ,

16 J = 0.5 * 7.5* (v1^ + v^2 - 2* 5.3*5.3 )

v2^2 = 60.44667 - v1^2 .................................2

from one and 2 equaiton we have ,

(10.6 - v1)^2 = 60.44667 - v1^2

now on solving these equations we will get as,

51.913323 +2 v1^2 - 21.2v1 = 0

on solving this quadratic equation we will get as

v1 = 6.76059 m/s so at this v2 =3.839404 m/s

v1 = 3.839404 m/s so at this v2 = 3.839404 m/s

as in both the cases the velocity comes out to be postive so that they both will move in forward along the positive x-axis though their velocity is not same

the larger velocity. = 6.76059 m/s

the smaller velocity.= 3.839404 m/s