By accident, a large plate is dropped and breaks into three pieces. The pieces fly apart parallel to the floor, with v1 = 3.05 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.

Question

By accident, a large plate is dropped and breaks into three pieces. The pieces fly apart parallel to the floor, with v1 = 3.05 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.

Answer 1

To find the masses of pieces 1 and 2, we can use the principle of conservation of momentum.

Momentum is the product of mass and velocity: p = mv.

Before the collision, the plate is dropped and its momentum has only a vertical component. This means that the total momentum of the plate before the collision is zero in the horizontal direction.

After the collision, the total momentum of the plate must still be zero in the horizontal direction since there is no net external force acting on it in that direction.

We have the following information:

v1 = 3.05 m/s (velocity of piece 1)
v2 = 1.95 m/s (velocity of piece 2)

Let m1 be the mass of piece 1 and m2 be the mass of piece 2.

Using the principle of conservation of momentum, we can write the equation:

m1v1 + m2v2 = 0

Now, let's plug in the values:

m1(3.05) + m2(1.95) = 0

Simplifying the equation, we get:

3.05m1 + 1.95m2 = 0

To solve this equation, we need one more piece of information.

Answer 2

To find the masses of pieces 1 and 2, we can use the concept of conservation of momentum.

We know that the total momentum before the collision is equal to the total momentum after the collision. Since there is no initial momentum parallel to the floor, the final momentum parallel to the floor must also be zero.

Before the collision, the vertical components of the momentum of pieces 1 and 2 add up to the total momentum of the plate. Let's call the mass of piece 1 as m1, and the mass of piece 2 as m2.

The momentum of piece 1 is given by p1 = m1 * v1, and the momentum of piece 2 is p2 = m2 * v2. The total momentum before the collision is m1v1 + m2v2.

Since the total momentum after the collision is zero, we have:

m1v1 + m2v2 = 0

Since v1 = 3.05 m/s and v2 = 1.95 m/s, we can substitute these values into the equation:

m1 * 3.05 + m2 * 1.95 = 0

Now, we need additional information to solve for the masses of pieces 1 and 2.

Answer 3

so we do not have the directions of 1 and 2

we know that the total east (x) momentum must be zero and the total north (y) momentum must be zero