Proof of KE loss in inelastic collision

Click For Summary
SUMMARY

The discussion focuses on proving that a perfectly inelastic collision results in a greater loss of kinetic energy compared to a partially inelastic collision. The conservation of momentum equations are provided for both scenarios: for perfectly inelastic collisions, the equation is \(P_{inelastic} : m_1v_{1i} + m_2v_{2i} = (m_1 + m_2)v_f\), while for partially inelastic collisions, it is \(P_{partial} : m_1v_{1i} + m_2v_{2i} = m_1v_{1f} + m_2v_{2f}\). The kinetic energy formula \(KE = \frac{1}{2}mv^2\) is essential for comparing energy before and after the collisions.

PREREQUISITES
  • Understanding of conservation of momentum
  • Familiarity with kinetic energy calculations
  • Knowledge of perfectly inelastic and partially inelastic collisions
  • Basic algebra for manipulating equations
NEXT STEPS
  • Analyze the kinetic energy loss in perfectly inelastic collisions using the formula \(KE = \frac{1}{2}mv^2\)
  • Explore the differences in momentum conservation between perfectly inelastic and partially inelastic collisions
  • Investigate real-world examples of inelastic collisions in physics
  • Learn about energy conservation principles in various types of collisions
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and collision theory, as well as educators looking for examples to illustrate concepts of kinetic energy and momentum.

Xizel
Messages
4
Reaction score
0

Homework Statement


Prove that a perfectly inelastic collision loses more kinetic energy than a partially inelastic collision. Given: $$m_1, m_2, v_{1i}, v_{2i}, v_{1f}, v_{2f}$$

Homework Equations


$$KE = \frac{1}{2}mv^2$$

The Attempt at a Solution


From conservation of momentum:
$$P_{inelastic} : m_1v_{1i} + m_2v_{2i} = (m_1 + m_2)v_f$$
$$P_{partial} : m_1v_{1i} + m_2v_{2i} = m_1v_{1f} + m_2v_{2f}$$

I'm not sure how to progress from this. Thanks.
 
Physics news on Phys.org
Compare energy before collision with energy after collision for each case.
 

Similar threads

  • · Replies 15 ·
Replies
15
Views
2K
  • · Replies 1 ·
Replies
1
Views
856
  • · Replies 9 ·
Replies
9
Views
1K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 9 ·
Replies
9
Views
3K
  • · Replies 3 ·
Replies
3
Views
23K
  • · Replies 12 ·
Replies
12
Views
3K
  • · Replies 3 ·
Replies
3
Views
12K