# MCAT Collisions of a wooden block and bullet

• Joseph Phan
In summary, the conversation is discussing a physics problem about a sharpshooter firing a gun at a wooden block with a bullet lodges inside. The question asks which statement is not true, and the answer is (C) if the bullet has the same mass as the block, the block will not move after the collision. The conversation then delves into understanding the type of collision and how the final velocity of the block is related to the initial velocity of the bullet. It is concluded that the final block mass will always be greater than the initial block mass due to the two masses being combined during the collision. The important concept to grasp is the type of collision and how it relates to the conservation of momentum.
Joseph Phan
Thread moved from the technical PF forums so no Homework Help Template is shown
Hi guys,
I'm currently going over Berkerley Review Physics example problem and got confused on a question:
Ex. 4.1a : A sharpshooter fires a gun at a wooden block of mass M. If the bullet, of mass (m), becomes lodged inside the block, then which of the following is NOT true?

The answer was: (C) If the bullet has the same mass as the block, the block will NOT move after the collision, which I deemed as correct as a false statement

But why is (D) a correct statement: The block can never move faster than the bullet's impact speed, after the collision.

I was trying to solve this conceptual problem mathematically using Δv2 = -(Δv1 m1 ) / (m2), and though that if the block was lighter than the bullet, wouldn't the velocity of the block be greater than the bullet?

The bullet was lodged inside the block. So what type of collision was it?

Inelastic collision. So the block will NEVER be lighter than the bullet. Got it Thanks!

Joseph Phan said:
Inelastic collision. So the block will NEVER be lighter than the bullet. Got it Thanks!
No, the block can be lighter that the bullet; There's no constraint on the masses. But the nature of the collision dictates how the final velocity of the block will be related to the initial velocity of the bullet. You should be able to write the appropriate equation to find the velocity of the combined bullet+block.

My bad, I worded that poorly. I meant the final block, m2, must always be greater than m1 because the the final block will include the mass of both the bullet and the block.

Joseph Phan said:
My bad, I worded that poorly. I meant the final block, m2, must always be greater than m1 because the the final block will include the mass of both the bullet and the block.
Okay, that is true. Although I wouldn't distinguish a "final block" that's different from the initial block. Presumably the block remains the block and the bullet remains the bullet. It's just that the two are combined into a single joined mass during the collision.

But the important insight is to recognize the type of collision taking place, and to tie the outcome (the final velocity) to the conservation of momentum.

## 1. How do collisions between a wooden block and bullet differ from other types of collisions?

Collisions between a wooden block and bullet are categorized as inelastic collisions, meaning that the objects involved stick together after impact. This is different from elastic collisions, where the objects bounce off each other without any loss of energy.

## 2. What factors affect the outcome of a collision between a wooden block and bullet?

The outcome of a collision between a wooden block and bullet is influenced by factors such as the mass and velocity of the objects, the angle of impact, and the material properties of the objects.

## 3. How does the conservation of momentum apply to collisions between a wooden block and bullet?

The law of conservation of momentum states that in a closed system, the total momentum before a collision is equal to the total momentum after the collision. In the case of a wooden block and bullet, this means that the combined momentum of the two objects before impact will be equal to the momentum of the block and bullet together after impact.

## 4. How does the conservation of energy apply to collisions between a wooden block and bullet?

The law of conservation of energy states that energy cannot be created or destroyed, only transferred from one form to another. In a collision between a wooden block and bullet, some of the kinetic energy of the objects will be converted into other forms of energy, such as heat and sound.

## 5. How can understanding collisions between a wooden block and bullet be useful in real-world applications?

Understanding collisions between a wooden block and bullet can have practical applications, such as in the design of bulletproof vests or car safety features. It can also be used in forensic investigations to determine the cause and trajectory of bullet impacts.

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