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30. Easy Guided Online Tutorial One object is at rest, and another is moving. The two collide in a one-dimensional, completely inelastic collision. In other words, they stick together after the collision and move off with a common velocity. Momentum is conserved. The speed of the object that is moving initially is 25 m/s. The masses of the two objects are 3.0 and 8.0 kg. Determine the final speed of the two-object system after the collision for the case when the large-mass object is the one moving initially and the case when the small-mass object is the one moving initially.

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Answer:

[tex]18.18\ \text{m/s}[/tex]

[tex]6.82\ \text{m/s}[/tex]

Explanation:

[tex]m_1[/tex] = Mass of large object = 8 kg

[tex]m_2[/tex] = Mass of smaller object = 3 kg

When large mass is moving

[tex]u_1[/tex] = 25 m/s

[tex]u_2[/tex] = 0

For completely inelastic collision we have the relation

[tex]m_1u_1+m_2u_2=(m_1+m_2)v\\\Rightarrow v=\dfrac{m_1u_1+m_2u_2}{m_1+m_2}\\\Rightarrow v=\dfrac{8\times 25+3\times 0}{8+3}\\\Rightarrow v=18.18\ \text{m/s}[/tex]

Speed of the combined mass when the larger object is moving is [tex]18.18\ \text{m/s}[/tex]

When smaller mass is moving

[tex]u_1[/tex] = 0

[tex]u_2[/tex] = 25 m/s

[tex]v=\dfrac{m_1u_1+m_2u_2}{m_1+m_2}\\\Rightarrow v=\dfrac{8\times 0+3\times 25}{8+3}\\\Rightarrow v=6.82\ \text{m/s}[/tex]

Speed of the combined mass when the smaller object is moving is [tex]6.82\ \text{m/s}[/tex]

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