# Conservation of Momentum of a plate

• henry3369
In summary, a plate drops onto a smooth floor and shatters into three pieces of equal mass with two pieces going off at equal speeds v at right angles to one another. The speed of the third piece can be found using the equation vf(m1 + m2 + m3) = m1v1+m2v2+m3v3, where v3 = vsqrt(2). To find the direction of the third piece, some sources suggest using arctan(y/x) while others suggest using arctan(z/x). However, a vector diagram can also be used to determine the direction of the third piece.
henry3369

## Homework Statement

A plate drops onto a smooth floor and shatters into three pieces of equal mass. Two of the pieces go off with equal speeds v at right angles to one another.

1. Find the speed of the third piece.

2. Find the direction of the third piece. Assume the motion of the two pieces at right angles to one another is in the positive x and y directions.

## Homework Equations

vf(m1 + m2 + m3) = m1v1+m2v2+m3v3

## The Attempt at a Solution

So I solved #1 to be v3 = vsqrt(2).

For #2, should the direction of the third piece be theta = arctan(z/x) or arctan(y/x)? I found some attempt of the solution online and they used arctan(y/x), which confuses me because wouldn't that find the resultant vector of the x and y component?

If you do arctan(y/x) you get theta = 135 degrees while arctan(z/x) gives 234.74 degrees. Which one is correct?

I don't even understand why you would need ANY equation to tell you the answer. Draw a vector diagram and it should be obvious. The SPEED will require an equation but not the direction, unless I am seriously misunderstanding something about the problem statement.

## 1. What is conservation of momentum of a plate?

Conservation of momentum of a plate refers to the principle that the total momentum of a plate before and after a collision or interaction will remain constant, provided there are no external forces acting upon it. This means that the combined momentum of the plate and any other objects involved in the collision will be equal before and after the interaction, regardless of any internal changes that may occur within the plate.

## 2. How is the conservation of momentum of a plate related to Newton's third law?

The conservation of momentum of a plate is closely related to Newton's third law, which states that for every action, there is an equal and opposite reaction. In the context of a plate, this means that when two objects collide, the force exerted by one object on the other will be equal and opposite to the force exerted by the other object on the first. As a result, the total momentum of the system will remain constant.

## 3. What factors can affect the conservation of momentum of a plate?

There are several factors that can affect the conservation of momentum of a plate, including the mass and velocity of the plate, the angle at which it is moving, and any external forces acting upon it. Additionally, the elasticity and shape of the plate can also play a role in the conservation of momentum, as these factors can impact the amount of energy absorbed or transferred during a collision.

## 4. How is the conservation of momentum of a plate used in real-world applications?

The conservation of momentum of a plate is a fundamental principle in physics and is used in many real-world applications. For example, it is used in the design of car safety features, such as airbags, to help reduce the impact force on passengers during a collision. It is also used in sports, such as billiards and pool, to predict the paths of balls after collisions.

## 5. Can the conservation of momentum of a plate be violated?

No, the conservation of momentum of a plate is a fundamental law of physics and cannot be violated. However, it may appear to be violated in certain situations due to external forces that are not accounted for or due to the transfer of energy between objects. In these cases, the total momentum of the system may remain constant, but the momentum of individual objects may change due to internal energy changes.

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