c) Change any of the given parameters to make the collision opposite from part b.(For example if you determined that the collision is elastic make it inelastic. And if you determined that the collision was inelastic make it elastic.)
c) Change any of the given parameters to make the collision opposite from part b.(For example if you determined that the collision is elastic make it inelastic. And if you determined that the collision was inelastic make it elastic.)
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Solve #4 problem c
![**Transcription for Educational Website**
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### Physics Problem: Collision Analysis
**Problem Statement:**
A large mass \( m_A = 2.50 \, \text{kg} \) traveling at \( 25.0 \, \text{m/s} \) crashes head-on into a smaller mass \( m_B = 7.50 \, \text{kg} \) which is originally at rest. The masses can slide without friction on the level surface. After the collision, \( m_A \) reverses direction, recoiling with a speed of \( 5.00 \, \text{m/s} \) in the opposite direction.
**a) Find the velocity of \( m_B \) after the collision.**
\[ m_A v_A + m_B v_B = m_A v_A' + m_B v_B' \]
\[ (2.50)(25 \, \text{m/s}) + (7.50)(0 \, \text{m/s}) = (2.50)(-5 \, \text{m/s}) + (7.50)v_B \]
\[ v_B = \frac{(2.50)(25) + (2.50)(-5)}{7.50} = 10 \, \text{m/s} \]
**b) Determine whether the collision is elastic or inelastic.**
*Energy Calculations:*
- **Initial Kinetic Energy:**
\[ \frac{1}{2}(2.5)(25)^2 + \frac{1}{2}(7.5)(0)^2 = 781.25 \, \text{J} \]
- **Final Kinetic Energy:**
\[ \frac{1}{2}(2.5)(5)^2 + \frac{1}{2}(7.5)(10)^2 = 406.25 \, \text{J} \]
*Conclusion:*
The collision is **inelastic**, as initial kinetic energy is greater than final kinetic energy and energy is not conserved.
**c) Change any of the given parameters to make the collision opposite from part b. (For example, if you determined the collision is inelastic, make it elastic, and vice versa.)**
\[ v_A' = \left(\frac{m_A - m_B}{m_A + m_B}\right) v_A \]
\[ v_A](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd9ac933e-a222-4210-8a67-76a29c4a48c0%2Fd3497917-ea4c-4916-ad91-4e7245635605%2F20cpydqb_processed.png&w=3840&q=75)
Transcribed Image Text:**Transcription for Educational Website**
---
### Physics Problem: Collision Analysis
**Problem Statement:**
A large mass \( m_A = 2.50 \, \text{kg} \) traveling at \( 25.0 \, \text{m/s} \) crashes head-on into a smaller mass \( m_B = 7.50 \, \text{kg} \) which is originally at rest. The masses can slide without friction on the level surface. After the collision, \( m_A \) reverses direction, recoiling with a speed of \( 5.00 \, \text{m/s} \) in the opposite direction.
**a) Find the velocity of \( m_B \) after the collision.**
\[ m_A v_A + m_B v_B = m_A v_A' + m_B v_B' \]
\[ (2.50)(25 \, \text{m/s}) + (7.50)(0 \, \text{m/s}) = (2.50)(-5 \, \text{m/s}) + (7.50)v_B \]
\[ v_B = \frac{(2.50)(25) + (2.50)(-5)}{7.50} = 10 \, \text{m/s} \]
**b) Determine whether the collision is elastic or inelastic.**
*Energy Calculations:*
- **Initial Kinetic Energy:**
\[ \frac{1}{2}(2.5)(25)^2 + \frac{1}{2}(7.5)(0)^2 = 781.25 \, \text{J} \]
- **Final Kinetic Energy:**
\[ \frac{1}{2}(2.5)(5)^2 + \frac{1}{2}(7.5)(10)^2 = 406.25 \, \text{J} \]
*Conclusion:*
The collision is **inelastic**, as initial kinetic energy is greater than final kinetic energy and energy is not conserved.
**c) Change any of the given parameters to make the collision opposite from part b. (For example, if you determined the collision is inelastic, make it elastic, and vice versa.)**
\[ v_A' = \left(\frac{m_A - m_B}{m_A + m_B}\right) v_A \]
\[ v_A
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