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 vi-3.05 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. m1 = m2 = ky kg 25 .0° 1 45.0 m3 = 1.30 kg 3.07 m/s Additional Materials Section 7.2

Explanation / Answer

North south momentum

m1v1 cos 25 degree + m2v2 cos45 degree = m3v3

m1*3.05 cos 25 degree + m2*1.80 cos 45 degree = 1.30*3.07 eq1

East west momentum

m1v1 sin 25 degree = m2 v2 sin 45 degree

m1*3.05 sin 25 degree = m2 *1.80*sin 45 degree

m1 = m2*1.80*sin45 degree/(3.05*sin 25 degree)

m1 = 0.987 m2

Putting in eq1,

0.987*m2*3.05 cos 25 degree + m2*1.80 cos 45 degree = 1.30*3.07

m2 = 1.30*3.07/(0.987*3.05cos* 25 degree + 1.80* cos 45 degree )

m2 = 0.997 kg

m1 = 0.987*0.997

= 0.984 kg

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