How do you calculate inelastic collisions?

Answer 1

Given perfect inelasticity, we go back to first principles.

For inelastic collisions momentum is conserved, but energy is lost. Hence, recall,

#m_"A"nu_"A" + m_"B"nu_"B" = m_"A"nu_"A"' + m_"B"nu_"B"'#

To demonstrate, I will do a problem.

Two asteroids strike head-on: before the collision, asteroid A (#m_"A" = 7.5*10^12"kg"#) has velocity #(3.3"km")/"s"# and asteroid B (#m_"B" = 1.45*10^13"kg"#) has velocity #(1.4"km")/"s"# in the opposite direction. If the asteroids stick together, what is the velocity (magnitude and direction) of the new asteroid after the collision?#^1#

Given,

#m_"A" = 7.5*10^12"kg"#, and

#nu_"A" = (3.3"km")/"s" * (10^3"m")/"km" = (3.3*10^3"m")/"s"#

#m_"B" = 1.45*10^13"kg"#, and

#nu_"B" = (-1.4"km")/"s" * (10^3"m")/"km" = (-1.4*10^3"m")/"s"#

Now, recall what we talked about!

#m_"A"nu_"A" + m_"B"nu_"B" = m_"A"nu_"A"' + m_"B"nu_"B"'#

#nu_"A"' = nu_"B"' = nu'#

Hence,

#(m_"A"nu_"A" + m_"B"nu_"B")/(m_"A" + m_"B") = nu' = (2.0*10^2"m")/"s"#

is the velocity of the compound asteroid after the collision (in the positive direction).

1: Giancoli, D. C. (2014). Physics: Principles with Applications. Boston: Pearson. pg. 195

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Answer 2

Isabella Alvarez

Use the equation: ( m_1 \cdot v_{1i} + m_2 \cdot v_{2i} = (m_1 + m_2) \cdot v_f )

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.