Calculating Common Velocity of Two Identical Blocks After Collision

In summary, the formula for calculating the common velocity of two identical blocks after collision is v = (m1v1 + m2v2) / (m1 + m2), where v is the common velocity, m1 and m2 are the masses of the two blocks, and v1 and v2 are their respective velocities before the collision. The direction of the common velocity can be determined by considering the conservation of momentum. This formula cannot be used for non-identical blocks and the units for the common velocity will depend on the units used for mass and velocity. There is no limit to the number of blocks that can be used in this formula, but it is usually used for two blocks at a time.
  • #1
dalcde
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Homework Statement


Two identical blocks of the same mass travel at velocities of 3v and 2v on a smooth surface as shown (same direction).
Two blocks move together after collision. What is their common velocity?

Homework Equations


Conservation of momentum

The Attempt at a Solution


Let v' be the common velocity.

3mv+2mv = 2mv'
v'= 2.5v

Therefore the veloctiy is 2.5v. Answer given is 1.5v.
 
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  • #2
From the information given the answer should be 2.5 v.
 
  • #3
Thank you
 

1. What is the formula for calculating the common velocity of two identical blocks after collision?

The formula for calculating the common velocity of two identical blocks after collision is: v = (m1v1 + m2v2) / (m1 + m2), where v is the common velocity, m1 and m2 are the masses of the two blocks, and v1 and v2 are their respective velocities before the collision.

2. How do you determine the direction of the common velocity after collision?

The direction of the common velocity after collision can be determined by considering the conservation of momentum. If the total momentum of the system is conserved, the direction of the common velocity will be in the same direction as the initial momentum of the two blocks.

3. Can you use this formula for non-identical blocks?

No, this formula is specifically for calculating the common velocity of two identical blocks after collision. For non-identical blocks, you would need to use the formula for conservation of momentum and solve for the final velocity of the system.

4. What are the units for the common velocity?

The units for the common velocity will depend on the units used for mass and velocity in the formula. If mass is given in kilograms and velocity in meters per second, then the common velocity will have units of meters per second.

5. Is there a limit to the number of blocks that can be used in this formula?

No, this formula can be used for any number of identical blocks, as long as their masses and velocities before the collision are known. However, for simplicity, it is usually used for two blocks at a time.

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