What Is the Initial Speed of the Bullet in a Bullet-Block Collision Problem?

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The problem involves a bullet of mass 0.0100 kg colliding with a block of mass 5 kg, becoming embedded, and moving a distance of 6 m on a rough table with a kinetic friction coefficient of 0.300. To find the bullet's initial speed, conservation of momentum and work-energy principles are applied. The first equation relates the bullet's initial speed to the combined mass's velocity after the collision and the work done against friction. The discussion emphasizes the need for two equations to solve for the two unknowns, the bullet's initial speed and the velocity after the collision. Using the work-energy principle is suggested as a starting point for the solution.
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Homework Statement


A bullet of mass 0.0100kg moving horizontally strikes a block of M=5kg and becomes embedded. If the block bullet move a distance of 6 m on a rough horizontal table. The coefficient of kinetic friction is 0.300. What is the speed of the bullet before striking the block ?


Homework Equations



m1v1= ( M+m) V2 - fkd (1)



The Attempt at a Solution



I got two unknowns and one equation. I do not have V2 and v1 so l am stuck.
 
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Nyasha said:

Homework Equations



m1v1= ( M+m) V2 - fkd (1)
This looks like some mix of momentum conservation and work. No good!

I got two unknowns and one equation. I do not have V2 and v1 so l am stuck.
Find two equations:
(1) Conservation of momentum for the collision.
(2) Energy/work applied after the collision.

Hint: Use equation 2 first.
 

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