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A massless spring (with force constant k = 199 N/m) connects a wall and a block of wood. The system is initially at rest, with the spring unstretched. The block has mass M = 58.1 g and is able to move without friction on a table. A gun is positioned to fire a bullet of mass m = 8.2 g into the block along the spring axis. After the gun is fired, the bullet gets embedded in the block, and the spring is compressed a maximum distance d = 0.89 m.

In meters per second, what is the speed of the bullet v before it enters the block?

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Step 1

Given values:

Spring constant, k = 199 N/m

Mass of the block, M = 58.1 g

Mass of the bullet, m = 8.2 g

Compression in the spring, d = 0.89 m

Let the speed of the bullet before it enters the block be u and the speed of the bullet after it embedded in the block be v.

Step 2

From the conservation of energy:

Kinetic energy lost by bullet = potential energy gain by spring

Step 3

From the conservation of linear momentum:...

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