A 6.0-kg object, initially at rest in free space, "explodes" into three segments of equal mass. Two of these segments are observed to be moving with equal speeds of 20 m/s with an angle of 60° between their directions of motion. How much kinetic energy is released in this explosion?
A) 2.4 kJ
B) 2.9 kJ
C) 2.0 kJ
D) 3.4 kJ
E) 1.2 kJ

Question

Quizplus · Accepted Answer

Since the three segments have equal mass, each segment will have a mass of 2.0 kg.
Let the two segments moving with equal speeds be labeled A and B, and let the third segment be labeled C.
From the conservation of momentum, we have:
0 = m(A)v(A)cos(60°) + m(B)v(B)cos(60°)
0 = m(A)v(A)sin(60°) - m(B)v(B)sin(60°)
m(C)v(C) = m(A)v(A)sin(60°) + m(B)v(B)sin(60°)
Solving these equations for v(A), v(B), and v(C), we get:
v(A) = -v(B) = 20/(2√3) ≈ 5.77 m/s
v(C) = 40/(2√3) ≈ 11.54 m/s
The kinetic energy released in the explosion is given by:
KE = (1/2)m(A)v(A)² + (1/2)m(B)v(B)² + (1/2)m(C)v(C)²
Substituting the values, we get:
KE ≈ 2.0 kJ
Therefore, the best choice is C.

A 60-Kg Object, Initially at Rest in Free Space, "Explodes" into into Three