(Conservation of Linear Momentum) Find u1 speed

AI Thread Summary
In a one-dimensional completely inelastic collision involving a 2 kg particle moving at speed u1 and a 3 kg particle at rest, 60 J of kinetic energy is lost. The conservation of linear momentum is expressed as m1u1 + m2u2 = m1v1 + m2v2, leading to the equation 2u1 = 5V. The kinetic energy loss is calculated as the difference between initial and final kinetic energy, resulting in the equation Kfinal - Kinitial = 60 J. To find u1, one can substitute the expression for V from the momentum equation into the energy equation. This approach allows for solving the two equations with two unknowns effectively.
paola8
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1. A particle of mass m1 = 2 kg moving at speed u1 makes a one-dimensional completely inelastic collision with a particle of mass m2 = 3 kg, intially at rest.

If 60 J of kinetic energy are lost, find u1?
2. Conservation of linear momentum:
m1u1 + m2u2 = m1v1 + m2v2


3. Using the conservation of linear momentun formula...
2u1 + 3(0) = (m1 + m2)V
2u1 = 5V

I'm just not sure where the 60 J of ke lost fits in. The loss in kinetic energy of 60 J means
Kfinal - Kinitial

which is
[.5(m1 + m2)v^2] - [((.5)m1u^2) + ((.5)m2(0)]

But there still remains the unknown variable of u, meaning I went in a circle.
 
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You have two equations and two unknowns. There are many ways to solve this. One is way is substituting your answer for v in terms of u1 from the momentum equation into your energy equation. Then solve for u1.
 
Thanks! Once again, I'm left feeling dumb after such a simple solution.
 
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