Momentum/exploding block

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In summary, the conversation discussed the initial momentum of a 2kg block that explodes into two smaller blocks. The first block, weighing 1.2 kg, moves east at 10 m/s, while the second block, weighing 0.8 kg, moves at an angle north of west at 22 m/s. The equation for momentum conservation, p initial = p final, was mentioned. The correct answer for the initial momentum was determined to be 13 kg m/s, while a friend's answer of 29.6 kg m/s was deemed incorrect due to the cancellation of horizontal components in opposite directions.
  • #1
kaitamasaki
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Homework Statement



A 2 kg block moves north at an unknown velocity. It then explodes into two blocks, the first one being 1.2 kg and moves EAST at 10 m/s, the second one is 0.8 kg and moves 22 m/s at an angle North of West.

What is the initial MOMENTUM of the 2kg block?

Homework Equations



p initial = p final (momentum conserved)

The Attempt at a Solution



The answer i got was 13 kg m/s, and some friends of mine got 29.6 kg m/s. The reason i got 13 is because I think/thought the two horizontal components of the exploded blocks cancel out each other because they are in separate directions (velocity is a vector and therefore one being negative one being positive, so I thought only the vertical component of the second block's momentum mattered).

Any help is appreciated Thank You!
 
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  • #2
You are correct; your friend is not. Good reasoning.
 
  • #3


I would first like to clarify that the initial momentum of the 2 kg block is a vector quantity, meaning it has both magnitude and direction. Therefore, simply stating the value of the initial momentum without specifying the direction is not enough to fully answer the question.

To calculate the initial momentum of the 2 kg block, we can use the equation p = mv, where p is momentum, m is mass, and v is velocity. Since the initial velocity of the 2 kg block is unknown, we cannot directly calculate its initial momentum. However, we can use the principle of conservation of momentum to find the initial momentum indirectly.

According to the principle of conservation of momentum, the total momentum of a system (in this case, the 2 kg block before it explodes) remains constant before and after a collision or explosion. This means that the initial momentum of the 2 kg block is equal to the final momentum of the two smaller blocks.

Using the given information, we can calculate the final momentum of the two smaller blocks. The first block has a mass of 1.2 kg and a velocity of 10 m/s in the east direction. The second block has a mass of 0.8 kg and a velocity of 22 m/s at an angle north of west. To find the horizontal and vertical components of the second block's velocity, we can use trigonometry. The horizontal component is 22 cos(45°) = 15.56 m/s and the vertical component is 22 sin(45°) = 15.56 m/s. Therefore, the final momentum of the two smaller blocks can be calculated as:

p final = (1.2 kg)(10 m/s) + (0.8 kg)(15.56 m/s) = 12 + 12.45 = 24.45 kg m/s

Since the initial momentum of the 2 kg block is equal to the final momentum of the two smaller blocks, we can conclude that the initial momentum of the 2 kg block is also 24.45 kg m/s. This means that both you and your friends were correct in your calculations, as long as the direction of the initial momentum is taken into account.

In summary, the initial momentum of the 2 kg block is 24.45 kg m/s in an unknown direction. It is important to always consider both magnitude and direction when dealing with vector quantities like momentum.
 

1. What is momentum?

Momentum is a physics concept that refers to the quantity of motion possessed by an object. It is calculated by multiplying an object's mass by its velocity.

2. How is momentum related to an exploding block?

In the context of an exploding block, momentum is related to the force produced by the explosion. As the block explodes, the force causes the individual pieces to move with a certain velocity, resulting in a change in momentum.

3. Can momentum be conserved in an exploding block scenario?

Yes, according to the law of conservation of momentum, the total momentum of a system remains constant unless acted upon by an external force. In an exploding block, the momentum of the individual pieces may change, but the total momentum of the system will remain the same.

4. How does the mass of the block affect its momentum?

The mass of the block directly affects its momentum. A larger mass will result in a greater momentum, while a smaller mass will result in a lower momentum, assuming the velocity remains constant.

5. What factors can affect the momentum of an exploding block?

The momentum of an exploding block can be affected by factors such as the mass and velocity of the individual pieces, the force of the explosion, and any external forces acting on the system. Additionally, the type of material the block is made of can also impact its momentum.

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