Mess Kit Momentum Question

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In summary, the 8 kg mess kit on a frictionless surface explodes into two 4 kg parts moving at 2.5 m/s due north and 4.5 m/s at 30° north of east. To find the original speed of the mess kit, we must use the equation PM = p1m1 + p2m2 and find the components of the total momentum in the x- and y-directions. Then, we can use the Pythagorean theorem to find the magnitude of the original velocity.
  • #1
A 8.0 kg mess kit sliding on a frictionless surface explodes into two 4 kg parts, one moving at 2.5 m/s, due north, and the other at 4.5 m/s, 30° north of east. What was the original speed of the mess kit?

Known equations:
PM= p1m1+p2m2

I tried to give this question a shot but to no avail. I tried to switch the axis to make the problem easier, but still got the wrong answer. 8(unknown velocity) = 4(4.5kg)(cos60) + 4(2.5)cos0 adn I got 2.375m/s, but this wasn't right...so I tried it from the same perspective on the y-axis 8(unknown velocity in y direction) = 4(4.5kg)sin60 + 4(2.5)sin0(this drops off) and got 1.9485m/s...this wasn't the same as the other velocity so I know I am doing something wrong...any pointers?
 
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  • #2
rosstheboss23 said:
I tried to give this question a shot but to no avail. I tried to switch the axis to make the problem easier, but still got the wrong answer. 8(unknown velocity) = 4(4.5kg)(cos60) + 4(2.5)cos0 adn I got 2.375m/s, but this wasn't right...
That gives you one component of the velocity (assuming your arithmetic is correct).
so I tried it from the same perspective on the y-axis 8(unknown velocity in y direction) = 4(4.5kg)sin60 + 4(2.5)sin0(this drops off) and got 1.9485m/s...
That gives you the other component.

In summary:

Find the components of the total momentum: x-components (east) and y-components (north). Once you have the components of the total momentum and then the components of the original velocity, then you can find the magnitude.
 
  • #3
So I found the components of the total momentum, but how would I relate that back to the original momentums of the problem to find the velocity of the 8kg messkit? Would I add the x and y direction momentums (p=19 for x) and (p=15.588 for y) and then divide by 8?...when I did that I got 4.324m/s for the initial 8kg mass's velocity. I'm not sure if that is right though.
 
  • #4
rosstheboss23 said:
So I found the components of the total momentum, but how would I relate that back to the original momentums of the problem to find the velocity of the 8kg messkit? Would I add the x and y direction momentums (p=19 for x) and (p=15.588 for y) and then divide by 8?...when I did that I got 4.324m/s for the initial 8kg mass's velocity. I'm not sure if that is right though.
Do like this: Find the x- and y-components of the momentum of each 4 kg piece. Add the x-components up to get the x-component of the total momentum, which is the x-component of the original momentum; use that to find the x-component of the original velocity. Do the same thing for the y-components to find the y-component of the original velocity.

Once you have the components of the velocity vector, find the magnitude like any other vector: Use the Pythagorean theorem.
 
  • #5
Infinite thank yous. :)
 

1. What is "Mess Kit Momentum Question"?

"Mess Kit Momentum Question" is a hypothetical situation used to explain the concept of momentum in physics. It involves a person sitting on a stool and holding a tray with a mess kit (a set of utensils and a plate). The person then extends their arms and releases the mess kit, causing it to move in a certain direction.

2. How does "Mess Kit Momentum Question" relate to momentum?

As the person releases the mess kit, it gains momentum in the direction it was released. This is because momentum is the product of an object's mass and velocity, and the mess kit has both mass and velocity as it moves. The question helps to visualize and understand how momentum works in real-life scenarios.

3. Can you change the momentum of the mess kit in "Mess Kit Momentum Question"?

Yes, the momentum of the mess kit can be changed by altering either its mass or velocity. For example, if the person on the stool changes the direction in which they release the mess kit or increases its weight, the momentum will change accordingly.

4. How is momentum conserved in "Mess Kit Momentum Question"?

In "Mess Kit Momentum Question," the initial momentum of the person and the stool is equal to the final momentum of the person, stool, and mess kit combined. This is due to the law of conservation of momentum, which states that in a closed system, the total momentum remains constant.

5. What are some real-life examples of "Mess Kit Momentum Question"?

One possible example is a person sitting on a skateboard and holding a ball. If they throw the ball in one direction, the skateboard will move in the opposite direction due to the conservation of momentum. Another example could be a person throwing a frisbee while standing on a moving boat – the momentum of the frisbee will be added to the momentum of the boat, causing it to move in a different direction.

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