Momentum Broken Plate Problem

[jacksonpeeble]

Momentum "Broken Plate" Problem

Homework Statement

By accident, a large plate is dropped and breaks into three pieces. The pieces fly apart parallel to the floor, with v1 = 3.10 m/s and v2 = 1.95 m/s. As the plate falls, its momentum has only a vertical component, and no component parallel to the floor. After the collision, the component of the total momentum parallel to the floor must remain zero, since the net external force acting on the plate has no component parallel to the floor. Using the data shown in the drawing, find the masses of pieces 1 and 2.

Homework Equations

(See below)

The Attempt at a Solution

This question has been posted multiple times at https://www.physicsforums.com/showthread.php?t=115200, https://www.physicsforums.com/showthread.php?t=50774, and http://answers.yahoo.com/question/index?qid=20061028143914AAiNoia. Therefore, I have a step-by-step process to follow.

I am simply wondering if somebody can take me through the "whys" regarding this problem. As an online AP Physics student, I am having trouble applying some of the concepts in the online and book material. Specifically, could somebody please take me through the existing procedure with a better explanation of what is happening at each step, up to the answer?

Thank you very much for your time in advance!

 

[rl.bhat]

Take the components m1v1 and m2v2 along x and y-axis.
As you can see from the figure, net x components is zero and net y component is equal to m3v3.
You have two equations and two unknowns. Now solve foe m1 and m2.

 

[kerimek]

I would like to start by clarifying the concept of momentum. Momentum is a physical quantity that describes the motion of an object and is defined as the product of an object's mass and velocity. In other words, it is a measure of how difficult it is to stop an object in motion.

Now, let's look at the scenario provided in the problem. We have a large plate that is dropped and breaks into three pieces. As the plate falls, its momentum has only a vertical component and no component parallel to the floor. This means that the total momentum of the plate before and after the collision remains the same, but the direction of the momentum changes.

The law of conservation of momentum states that in a closed system, the total momentum remains constant. This means that the total momentum of the system (the plate and its pieces) before the collision is equal to the total momentum after the collision.

Now, let's look at the given data in the drawing. We have two pieces, v1 and v2, with velocities of 3.10 m/s and 1.95 m/s respectively. We can calculate the total momentum of these two pieces by multiplying their mass and velocity, as momentum = mass x velocity.

So, we have:

Total momentum before collision = (mass of piece 1) x (velocity of piece 1) + (mass of piece 2) x (velocity of piece 2)

= m1v1 + m2v2

After the collision, the two pieces will move in opposite directions, but their total momentum must still be equal to the total momentum before the collision. This means that the total momentum after the collision will be:

Total momentum after collision = (mass of piece 1) x (velocity of piece 1) - (mass of piece 2) x (velocity of piece 2)

= m1v1 - m2v2

Since the total momentum remains the same, we can equate the two equations as follows:

m1v1 + m2v2 = m1v1 - m2v2

This allows us to solve for the mass of piece 2, which is given by:

m2 = (m1v1 - m1v2)/v2

Similarly, we can solve for the mass of piece 1, which is given by:

m1 = (m2v2 + m1v2)/v1

Now