A 3.0 kg mass moving to the right at 1.4 m/s collides in a perfectly inelastic collision with a 2.0 kg mass initially at rest. What will the velocity of the combined mass be after the collision?

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Zack M. Share
Aug 22, 2016

When analyzing inelastic collisions, we need to consider the law of conservation of momentum, which states that the total momentum, #p#, of the closed system is a constant. In the case of inelastic collisions, the momentum of the combined mass after the collision is equal to the sum of the momentum of each of the initial masses.

#p_1 + p_2 + ...= p_f#

In our case we only have two masses, which makes our problem fairly simple. Lets plug in the formula for momentum; #p = mv#.

#m_1 v_1 + m_2 v_2 = (m_1+m_2) v_f#

To find the velocity of the combined mass we simply rearrange the terms.

# v_f = (m_1 v_1 + m_2 v_2) / (m_1+m_2) #

Plug in the values given in the problem.

# v_f = ((3.0"kg")(1.4 "m/s") + color(red)(cancel(color(black)((2.0"kg")(0"m/s")))^0))/(3.0 "kg"+2.0"kg") #

#v_f = .84 "m/s"#

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