An object initially at rest suddenly explodes in two fragments of masses $2.6 \mathrm {~kg}$ and $3.3 \mathrm {~kg}$ that move in opposite directions.If the speed of the first fragment is $3.6 \mathrm {~m} / \mathrm { s }$ find the internal energy of the explosion.
A)30 J
B)30 kJ
C)38 J
D)38 kJ

Question

Quizplus · Accepted Answer

The internal energy of the explosion can be calculated using the conservation of momentum and the kinetic energy formula. Since the object was initially at rest, its initial momentum was 0. After the explosion, the momentum of the two fragments must still sum to 0 because momentum is conserved. Let's denote the masses as $m_1 = 2.6 \, \mathrm{kg}$ and $m_2 = 3.3 \, \mathrm{kg}$, and their velocities as $v_1 = 3.6 \, \mathrm{m/s}$ and $v_2$, respectively. From the conservation of momentum:$$m_1v_1 = m_2v_2$$Solving for $v_2$, we get:$$v_2 = \frac{m_1v_1}{m_2} = \frac{2.6 \times 3.6}{3.3} \approx 2.85 \, \mathrm{m/s}$$The total kinetic energy (internal energy of the explosion) is the sum of the kinetic energies of the two fragments:$$E = \frac{1}{2}m_1v_1^2 + \frac{1}{2}m_2v_2^2$$Substituting the values:$$E = \frac{1}{2} \times 2.6 \times (3.6)^2 + \frac{1}{2} \times 3.3 \times (2.85)^2 \approx 30 \, \mathrm{J}$$Therefore, the internal energy of the explosion is approximately 30 J.

An Object Initially at Rest Suddenly Explodes in Two Fragments 2.6 kg2.6 \mathrm {~kg}2.6 kg

An Object Initially at Rest Suddenly Explodes in Two Fragments $2.6 \mathrm {~kg}$