Conservation of momentum of plate drop

In summary, the problem involves a plate shattering into 3 pieces of equal mass, with 2 pieces going off at equal speeds at right angles to each other. The challenge is to find the speed and direction of the third piece using the fact that net momentum is conserved if there is no external force acting on the system. Setting up a coordinate system and using the momentum vectors of the first two pieces, the total momentum of all three pieces can be determined to be 0. This can then be used to find the momentum vector of the third piece.
  • #1
romy
1
0
Hi, i was wondering if anybody can help me with the following problem:

A plate drops onto a smooth floor and shatters into 3 pieces of equal mass. 2 of the pieces go off with equal speeds v at right angles to one another. How do I find the speed and direction of the third piece?

I know that the net momentum is conserved if the net external force acting on the system is zero, how can I apply this, any suggestions to which equations I can use? :biggrin:
 
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  • #2
romy said:
I know that the net momentum is conserved if the net external force acting on the system is zero, how can I apply this, any suggestions to which equations I can use? :biggrin:
If momentum is conserved, then the change in momentum is 0 (i.e. [itex]\Delta p = 0[/itex]). What is the problem?
 
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  • #3
Since two pieces go at right angles to one another, set up a coordinates system using those directions as x and y axes: The velocity vectors are (v, 0) and (0, v) and so the momentum vectors are (mv,0) and (0,mv). The total momentum of those two pieces is (mv, mv).

The total momentum of all three pieces must be 0 since the only forces involved are vertical. What is the momentum vector of the third piece?
 

1. What is conservation of momentum of plate drop?

Conservation of momentum of plate drop is a physical principle that states that the total momentum of a system remains constant in the absence of external forces. In simpler terms, this means that when a plate is dropped, its initial momentum will be equal to its final momentum after it hits the ground.

2. How does conservation of momentum apply to plate drop?

When a plate is dropped, it has an initial momentum due to its mass and velocity. As it falls, this momentum is conserved and transferred to the ground upon impact. This means that the total momentum of the plate and the ground will be equal to the initial momentum of the plate before it was dropped.

3. What factors affect the conservation of momentum in a plate drop?

The main factors that affect the conservation of momentum in a plate drop are the mass and velocity of the plate, as well as the properties of the surface it is dropped onto. The greater the mass and velocity of the plate, the greater its initial momentum will be. The type of surface and its elasticity will also affect how much momentum is transferred to the ground upon impact.

4. Is conservation of momentum always applicable in a plate drop?

In theory, conservation of momentum is always applicable in a plate drop. However, in real-world scenarios, there may be other external forces at play, such as air resistance or friction, that can affect the conservation of momentum. These factors may cause the final momentum of the plate to be slightly different than the initial momentum.

5. What are some practical applications of conservation of momentum in plate drop?

Conservation of momentum in plate drop has many practical applications, such as in the design of safety equipment for falling objects, as well as in the study of impact and collision dynamics. It is also an important principle in understanding the mechanics of everyday objects, such as balls bouncing and cars crashing.

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