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fill out the table with the values remember that for completely inelastic collisions we use the equation m 1 ​ v 1i ​ +m 2 ​ v 2i ​ =(m 1 ​ +m 2 ​ )v f ​

To fill out the table using the given information and formula for completely inelastic collisions, let’s go through the necessary steps:

1. **Extract the mass values**:
   - \( m_1 = 0.314 \, \text{kg} \)
   - \( m_2 = 0.253 \, \text{kg} \)

2. **Use the formula for completely inelastic collisions**:
   \[
   m_1 \cdot v_{1i} + m_2 \cdot v_{2i} = (m_1 + m_2) \cdot v_f
   \]
   where:
   - \( v_{1i} \) and \( v_{2i} \) are the initial velocities of carts 1 and 2.
   - \( v_f \) is the final common velocity after collision.

3. **Calculate initial and final momentum** for each trial in the "Completely Inelastic" section and then verify other types (Inelastic, Elastic, Explosion) based on different formulas.

I'll now compute these values for the trials in the "Completely Inelastic" section and display them in the table format.I have calculated and filled out the table for the "Completely Inelastic" collision trials, showing the initial and final momenta for each cart and the total initial and final momentum for each trial.

Would you like me to proceed with calculations for other types of collisions (Inelastic, Elastic, and Explosion), or do you have specific questions on this part?

Here are some related questions you might consider:
1. How do the calculated final momenta compare to the initial momenta in these inelastic collisions?
2. Would using a different collision equation change the results?
3. What do the small differences in total initial and final momenta indicate about energy loss or experimental accuracy?
4. How does the mass ratio of the carts affect the momentum distribution after the collision?
5. How would the calculations differ if both carts had initial velocities?

**Tip:** In collisions, total momentum is conserved, but kinetic energy conservation depends on the type of collision (elastic or inelastic).

fill out the table with the values remember that for completely inelastic collisions we use the equation m₁v₁ᵢ + m₂v₂ᵢ = (m₁ + m₂)v_f

Learn how to calculate momentum for different types of collisions, including completely inelastic, inelastic, elastic, and explosion. This problem covers key physics concepts and the conservation of momentum theorem. Suitable for high school physics students.

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