38. Our notation (and, implicitly, our choice of coordinate system) is as follows: the mass of the original

body is m; its initial velocity is 

v

0

= vˆi; the mass of the less massive piece is m

1

; ; its velocity is 

v

1

= 0;

and, the mass of the more massive piece is m

2

. We note that the conditions m

2

= 3m

1

(specified in the

problem) and m

1

+ m

2

= m generally assumed in classical physics (before Einstein) lead us to conclude

m

1

=

1

4

m

and

m

2

=

3

4

m .

Conservation of linear momentum requires

m

v

0

=

m

1



v

1

+ m

2



v

2

mvˆi =

0 +

3

4

m 

v

2

which leads to



v

2

=

4

3

v ˆi .

The increase in the system’s kinetic energy is therefore

∆K

=

1

2

m

1

v

2

1

+

1

2

m

2

v

2

2

−

1

2

mv

2

0

=

0 +

1

2

3

4

m



4

3

v



2

−

1

2

mv

2

=

1

6

m v

2

.