Question

# An object with total mass mtotal = 17.4 kg is sitting at rest when it explodes...

An object with total mass mtotal = 17.4 kg is sitting at rest when it explodes into three pieces. One piece with mass m1 = 4.9 kg moves up and to the left at an angle of θ1 = 21° above the –x axis with a speed of v1 = 25.9 m/s. A second piece with mass m2 = 5.1 kg moves down and to the right an angle of θ2 = 26° to the right of the -y axis at a speed of v2 = 21.4 m/s.

)What is the magnitude of the final momentum of the system (all three pieces)? kg-m/s

2)What is the mass of the third piece? kg

3)What is the x-component of the velocity of the third piece? m/s

4)What is the y-component of the velocity of the third piece?   m/s

5)What is the magnitude of the velocity of the center of mass of the pieces after the collision?   m/s

6)Calculate the increase in kinetic energy of the pieces during the explosion. J

1) Conserving momentum:

pf = pi = 0 kg-m/s

2) m3 = M - m1 - m2 = 17.4kg - 4.9kg - 5.1kg = 7.4 kg

Convert the angles to standard:

θ1 = 21° above the –x axis = 159º

θ2 = 26° to the right of the -y axis = 296º

3) Conserve momentum horizontally:

0 = 4.9kg*25.9m/s*cos159º + 5.1kg*21.4m/s*cos296º + 7.4kg*V*cosΘ3

V*cosΘ3 = 9.95 m/s ◄ x-component

4) Conserve momentum vertically:

0 = 4.9kg*25.9m/s*sin159º + 5.1kg*21.4m/s*sin296º + 7.4kg*V*sinΘ3

V*sinΘ3 = 7.11 m/s ◄ y-component

5) 0

6) KE = Σ ½mv²

KE = ½(4.9*25.9² + 5.1*21.4² + 7.4*(9.95² + 7.11²)) J = 3365 J

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