Exploding Pumpkin: Solving for Third Fragment's Velocity, Direction, and Mass

In summary: You can also solve this by arranging the momentum vectors in a triangle and using Law of Cosines and/or Law of Sines.
  • #1
Forerunner546
3
0

Homework Statement


A pumpkin of mass 3.30kg at rest on a smooth frictionless plane, explodes into 3 pieces in the horizontal plane. A .50kg piece flies to the North at 3.2m/s. A 1.4kg piece flies off (SW) at 4.1m/s.

What is the speed, direction and mass of the third piece?

Homework Equations


M1V1o + M2V2o = M1V1f + M2V2f

The Attempt at a Solution


I assumed the piece was 1.4kg as I subtracted the original pumpkins mass by the known fragmentary masses. I used the conservation of momentum to subtract the original pumpkins mass and velocity by the unknown fragment and equaled it to the two known pieces. M1V1o - M3V3f = M1V1f + M2V2f

This yielded -5.2 as a velocity which seems wrong, and I have no idea how to find the direction of the third piece and no angles were included.
 
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  • #2
The FIRST thing you should always do in working on such problems is to draw a force diagram. For unknown forces you estimate at direction and magnitude from the known forces/directions. Do that and present it here and then we can help you work on the problem.
 
  • #3
They do give angles, just not in the sense you may be used to. Get a Compass Rose and find direction of North and South West, then figure out what angles these are.
 
  • #4
Here’s a diagram
 

Attachments

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  • #5
Forerunner546 said:
This yielded -5.2 as a velocity which seems wrong
Can't tell where you are going wrong if you do not post your working.
 
  • #6
Forerunner546 said:

Homework Statement


A pumpkin of mass 3.30kg at rest on a smooth frictionless plane, explodes into 3 pieces in the horizontal plane. A .50kg piece flies to the North at 3.2m/s. A 1.4kg piece flies off (SW) at 4.1m/s.

What is the speed, direction and mass of the third piece?

Homework Equations


M1V1o + M2V2o = M1V1f + M2V2f

The Attempt at a Solution


I assumed the piece was 1.4kg as I subtracted the original pumpkins mass by the known fragmentary masses. I used the conservation of momentum to subtract the original pumpkins mass and velocity by the unknown fragment and equaled it to the two known pieces. M1V1o - M3V3f = M1V1f + M2V2f

This yielded -5.2 as a velocity which seems wrong, and I have no idea how to find the direction of the third piece and no angles were included.
Forerunner546 said:
Here’s a diagram
6f89413f-811d-487b-be47-b9f7cdc691cb-jpeg.jpg


Hello @Forerunner546 . :welcome:

Your equations are vector equations, because momentum is a vector quantity. So is velocity.

What is the initial momentum ?
 

Attachments

  • 6f89413f-811d-487b-be47-b9f7cdc691cb-jpeg.jpg
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    25.3 KB · Views: 542
  • #7
SammyS said:
View attachment 234263

Hello @Forerunner546 . :welcome:

Your equations are vector equations, because momentum is a vector quantity. So is velocity.

What is the initial momentum ?
There is no initial momentum
 
  • #8
Forerunner546 said:
There is no initial momentum
Right. So write out the momentum conservation equations for two orthogonal directions.
 
  • #9
Forerunner546 said:
There is no initial momentum
By this I assume that you mean: the initial momentum is zero.

That's correct.

You can also solve this by arranging the momentum vectors in a triangle and using Law of Cosines and/or Law of Sines.
 

Related to Exploding Pumpkin: Solving for Third Fragment's Velocity, Direction, and Mass

What is momentum?

Momentum is a physics concept that describes the tendency of an object to keep moving in the same direction at the same speed.

How is momentum calculated?

Momentum is calculated by multiplying an object's mass by its velocity. The formula is p = m x v, where p is momentum, m is mass, and v is velocity.

What is the unit of momentum?

The unit of momentum is kilogram-meters per second (kg·m/s).

What is the law of conservation of momentum?

The law of conservation of momentum states that in a closed system, the total momentum before an event must equal the total momentum after the event. This means that momentum is conserved and cannot be created or destroyed.

How does momentum relate to collisions?

In collisions, momentum is transferred from one object to another. According to the law of conservation of momentum, the total momentum of the objects before and after the collision must be equal.

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