Question

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.

Answer 1

`18.18\ \text{m/s}`

`6.82\ \text{m/s}`

Step-by-step explanation:

`m_1` = Mass of large object = 8 kg

`m_2` = Mass of smaller object = 3 kg

When large mass is moving

`u_1` = 25 m/s

`u_2` = 0

For completely inelastic collision we have the relation

`m_1u_1+m_2u_2=(m_1+m_2)v\\\Rightarrow v=(m_1u_1+m_2u_2)/(m_1+m_2)\\\Rightarrow v=(8* 25+3* 0)/(8+3)\\\Rightarrow v=18.18\ \text{m/s}`

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

When smaller mass is moving

`u_1` = 0

`u_2` = 25 m/s

`v=(m_1u_1+m_2u_2)/(m_1+m_2)\\\Rightarrow v=(8* 0+3* 25)/(8+3)\\\Rightarrow v=6.82\ \text{m/s}`

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