Question

A bullet traveling horizontally at a very high speed embeds itself in a wooden block that is sitting at rest on a very slippery sheet of ice. You want to find the speed of the block just after the bullet embeds itself in the block. (a) What should you choose as the system to analyze? (b) Which of the following statements is true? (1) After the collision, the speed of the block with the bullet stuck in it is the same as the speed of the bullet before the collision. (2) The momentum of the block with the bullet stuck in it is the same as the momentum of the bullet before the collision. (3) The initial momentum of the bullet is greater than the momentum of the block with the bullet stuck in it.

Short answer

a) System we choose is bullet and block.

b) (2)The momentum of the block with the bullet stuck in it, is the same as the momentum of the bullet before the collision. This statement is true.

Step-by-step solution

System to analyze

Part a)

A bullet traveling at speed embeds in the wooden block. So we find the speed of a bullet, the speed of the wooden block after the bullet embeds. So, the system to analyze is bullet and wooden block.

Law of conservation of momentum

Part b)

Statement: The total momentum before the collision equals the total momentum after the collision.

Mathematically representation can be written as,

$$\begin{gathered} P_i=P_f \\ {m}_1{m}_1+m_2{u}_2=m_1{v}_1+m_2{v}_2 \end{gathered}$$

Where $m_1{m}_2$are the mass of bodies,are$u_1{u}_2$ the speed of bodies before the collision, and$v_1{v}_2$ are the speed of bodies after the collision.

Statement 1)

After the collision, the speed of the block with thebullet stuck in it is the same as the speed of the bullet before the collision.

Where v is the final speed of the block with the bullet stuck in it.

Momentum before collision$P_i=m_1{u}_1$

Momentum after collision$P_f=\left(m_1+m_2\right)v=\left(m_1+m_2\right)u_1$

So the momentum of the system is

$P_i<P_f$

It does not follow the law of conservation of momentum.

Thus, the statement is false.

Statement 2)

The momentum of the block with the bullet stuck in it is the same as the momentum of the bullet before the collision.

$P_i=P_f$

It follows the law of conservation of momentum.

Thus, this statement is true.

Statement 3)

The initial momentum of the bullet is greater than the momentum of the block with the bullet stuck in it.

$P_i>P_f$

It does not follow the law of conservation of momentum.

Thus, this statement is false.