Conservation of momentum and Impulse

In summary, the conversation discusses a large plate breaking into three pieces and flying apart parallel to the floor. The momentum of the plate has only vertical components before the collision, but after the collision, the component parallel to the floor must remain zero. Given the velocities and angles of the three pieces, the mass of the other two pieces can be solved for using the equations P=mv and conservation of momentum.
  • #1
leftyguitarjo
52
0

Homework Statement


A large plate is dropped and breaks into three large pieces. The pieces fly apart parallel to the floor. As the plate falls, its momentum has only vertical components, none parallel to the floor. After the collision, the component of momentum parallel to the floor must remain zero since the external force acting on the plate has no parallel component. As viewed from above, piece one has a component velocity of 3m/s at an angle of 115 degrees to the horizontal. Piece two has a velocity of 1.79m/s at an angle of 45 degrees. The third has a velocity of 3.07m/s at -90 degrees and a mass of 1.3 Kg.

What is the mass of the other two pieces?



Homework Equations


P=mv
J=F[tex]\Delta[/tex]t=[tex]\Delta[/tex]p
conservation of momentum


The Attempt at a Solution



First, I drew a picture.

http://www.imagecross.com/image-hosting-viewer-01.php?id=8714untitled1.JPG

then I solved for the velocity in the X and Y directions using sin and cos

I am stuck on the meat of the problem

(x direction)0=mv1+mv2+mv3
=m1.26+m1.26+1.3(0)

y direction 0=m2.71+m1.26+1.3(3.07)

I am lost at this point.
 
Last edited:
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  • #2
The velocities in your momentum equation should have signs. Two velocities should have opposite signs when they are pointed in opposite directions. Furthermore the masses are not necessarily all the same, are they?
 
  • #3
Dick said:
The velocities in your momentum equation should have signs. Two velocities should have opposite signs when they are pointed in opposite directions. Furthermore the masses are not necessarily all the same, are they?

This was just the way my teacher had it set up. I may have copied it down wrong.

If someone would be as kind as to tell me the correct setup, that would be great.
 
  • #4
Call the two unknown masses m1 and m2 (instead of both m). Now for the velocity components call the velocity component positive if it is up or to the right and negative if it is down or to the left. With these changes your equations are correct. Now just solve them for m1 and m2.
 
  • #5
Dick said:
Call the two unknown masses m1 and m2 (instead of both m). Now for the velocity components call the velocity component positive if it is up or to the right and negative if it is down or to the left. With these changes your equations are correct. Now just solve them for m1 and m2.

some of velocities should have negative values then!

I am familiar with adding vectors, so this concept is not new to me. Its the whole conservation of momentum part I've yet to fully grasp.

BUT, do I solve for both X any Y directions?
 
  • #6
You have two unknowns, m1 and m2. So you need two equations to solve for them. The x and y momentum components are those two equations.
 
  • #7
Dick said:
You have two unknowns, m1 and m2. So you need two equations to solve for them. The x and y momentum components are those two equations.

0=m(1)2.71+m(2)1.26+1.3(-3.07)
0=m(1)-1.26+m(2)1.26+1.3(0)

does this look like an good start then?
 
  • #8
Looks great. Write m(1)*(-1.26) instead of m(1)-1.26, ok? Otherwise the '-' looks like a subtraction instead of a sign on the 1.26.
 

1. What is the conservation of momentum?

The conservation of momentum is a fundamental law of physics that states that the total momentum of a closed system remains constant over time, unless acted upon by an external force.

2. How is momentum calculated?

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

3. What is the relationship between conservation of momentum and Newton's third law of motion?

Newton's third law of motion states that for every action, there is an equal and opposite reaction. This means that when two objects interact, the total momentum of the system remains constant. This is an example of the conservation of momentum.

4. What is impulse?

Impulse is the change in momentum of an object. It is calculated by multiplying the force applied to an object by the time it is applied. The formula for impulse is J = FΔt, where J is impulse, F is force, and Δt is the change in time.

5. How is the conservation of momentum applied in real-life scenarios?

The conservation of momentum is applied in various real-life scenarios, such as collisions between objects, rocket propulsion, and sports. For example, in a car crash, the total momentum before the crash will be equal to the total momentum after the crash, demonstrating the conservation of momentum. In rocket propulsion, the momentum of the gases expelled by the rocket will be equal and opposite to the momentum gained by the rocket, allowing it to move forward. In sports, the conservation of momentum is seen in actions such as throwing a ball or swinging a bat.

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