Question

A gadget of mass 21.85 kg floats in space without motion. Because of some internal malfunction, the gadget violently breaks up into 3 fragments flying away from each other. The first fragment has mass m1 = 6.42 kg and speed v1 = 6.8 m/s while the second fragment has mass m2 = 8.26 kg and speed v2 = 3.54 m/s. The angle between the velocity vectors ~v1 and ~v2 is θ12 = 64 ◦ . What is the speed v3 of the third fragment? Answer in units of m/s.

Answer 1

Answer:

$v_3=8.622\ m.s^{-1}$

Explanation:

Given:

• mass of the gadget, $m=21.85\ kg$

• mass of fragment 1, $m_1=6.42\ kg$

• mass of fragment 2, $m_2=8.26\ kg$

• velocity of fragment 1, $v_1=6.8\ m.s^{-1}$

• velocity of fragment 2, $v_2=3.54\ m.s^{-1}$

• angle between the velocity 1 & 2, $\theta=64\ ^{\circ}$

Now the mass of the third part:

$m_3=m-(m_1+m_2)$

$m_3=21.85-(6.42+8.26)$

$m_3=7.17\ kg$

The momentum of the gadget before and after collision is equal:

$m_3.v_3=m_1.v_1\cos\ \frac{\theta}{2} +m_2.v_2\cos \frac{\theta}{2}$

$7.17\times v_3=(6.42\times6.8+8.26\times3.54)\times \cos \frac{64}{2}$

$v_3=8.622\ m.s^{-1}$

Refer schematic for more clarity.

Answer 2

The speed of third fragment of the given gadget is 8.62 m/s.

The given parameters:

• total mass of the gadget, Mt = 21.85 kg
• mass of first fragment, m₁ = 6.42 kg
• mass of the second fragment, m₂ = 8.26 kg
• speed of the first fragment, v₁ = 6.8 m/s
• speed of the second fragment, v₂ = 3.54 m/s
• angle between the first and second fragment, θ = 64⁰

The mass of the third fragment is calculated as follows;

$m_3 = 21.85-(6.42 + 8.26)\\\\m_3 = 7.17 \ kg$

Apply the principle of conservation of linear momentum to determine the speed of the third fragment as follows;

$m_3v_3 = m_1v_1 cos(\frac{\theta}{2} ) \ + \ m_2v_2 cos(\frac{\theta}{2} )\\\\7.17v_3 = 6.42\times 6.8 \times cos(\frac{64}{2} ) \ + 8.26 \times 6.8 \times cos(\frac{64}{2} )\\\\7.17 v_3 = 61.82 \\\\v_3 = \frac{61.82}{7.17} \\\\v_3 = 8.62 \ m/s$

Thus, the speed of third fragment of the given gadget is 8.62 m/s.

Learn more about conservation of linear momentum here: https://brainly.com/question/22698801