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 v_1 = 3.10 m/s and v_2 = 1.70 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. m_1 = kg m_2 = kg

Explanation / Answer

balancing total momentum along x axis to zero:
m2*v2*cos(45)=m1*v1*sin(25)

==>m2=1.0899*m1...(1)

balancing total momentum along y axis:

m2*v2*sin(45)+m1*v1*cos(25)=m3*v3

==>1.0899*m1*1.7*sin(45)+m1*3.1*cos(25)=1.3*3.07

==>m1=1.3*3.07/(1.0899*1.7*sin(45)+3.1*cos(25))=0.96876 kg

m2=1.0899*m1=1.0559 kg

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