A 7.00 g bullet, when fired from a gun into a 1.10 kg block of wood held in a vise, penetrates the block to a depth of 9.60 cm. This block of wood is next placed on a frictionless horizontal surface, and a second 7.00 g bullet is fired from the gun into the block. To what depth will the bullet penetrate the block in this case

Explanation:

The given data is as follows.

    Mass of bullet 1, = 7 g =

   Mass of block of wood, M = 1.10 kg

   Bullet penetrates to depth, = 9.60 cm =

  Mass of bullet 2, = 7 g =

  Velocity of bullet = v

Let us assume that depth of penetration of the bullet is .

According to the law of conservation of energy,

            Kinetic energy = Potential energy

        Kinetic energy =

and,       Potential energy = mgh

so, for bullet 1

            .......... (1)

For bullet 2,

     Kinetic energy of bullet 1 - kinetic energy of bullet 2 = Potential energy

Using equation (1), we get

Putting the given values into the above formula as follows.

                   =

                   = 0.0953 m

or,                = 9.53 cm    (as 1 m = 100 cm)

Thus, we can conclude that the bullet will penetrate at a depth of 9.53 cm.

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