By accident, a large plate is dropped and breaks into three pieces. The pieces f

Question

By accident, a large plate is dropped and breaks into three pieces. The pieces fly apart parallel to the floor, with v1 = 2.75 m/s and v2 = 1.80 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.

Explanation / Answer

In the drawing, it shows m1 & m2 falling at an angle to the floor but m3 has no angle, and just has a velocity of 2.75m/s pointing south with a mass of 1.3kg.

We can get two equations. One for the north south momentum, and one for the east west momentum.

m1v1 cos 25 + m2v2 cos45 = m3v3
m1 2.75m/s cos 25 + m2 1.80 m/s cos45 = 130kg 3.07 m/s

m1v1 sin 25 = m2 v2 sin 45
m1 2.75 m/s sin 25 = m2 1.80 m/s sin 45
m1 = m2 1.80 m/s sin 45/(2.75 m/s sin 25) =1.095 m2

1.095 m2 2.75 m/s cos 25 + m2 1.80 m/s cos45 = 1.30kg 3.07 m/s
m2 = =1kg

m1 = 0.896 m2 = 1.095 * 1 kg = 1.095 kg

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