By accident, a large plate is dropped and breaks into three pieces. The pieces f
ID: 1630641 • Letter: B
Question
By accident, a large plate is dropped and breaks into three pieces. The pieces fly apart parallel to the floor, with v1 = 2.85 m/s and v2 = 1.75 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.
m1 = kg m2 = kg V1 25.0°I V2 2] 7n 45.0° 2 M3 = 1.30 kg 3.07 m/sExplanation / Answer
Solution:
As we know;
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.
Hence,
In x - direction:
=> m3 x 0 = m1 x (v1 sin250) - m2 x (v2 cos450)
=> 1.3 x 0 = m1 x 2.85 sin250 - m2 x 1.75 cos450
=> 0 = 1.204 m1 - 1.237m2
=> m1 = 1.0277 m2
In y - direction:
m3v3 = m1v1cos25 + m2v2sin45
=> 3.07 x 1.3 = m1 2.583 + m2 1.237
=> 3.991 = 2.583 m1 + 1.237 m2
On solving these two equations:
m1 = 1.0544 kg
m2 = 1.026 kg
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