An object with total mass m total = 16.2 kg is sitting at rest when it explodes

Question

An object with total mass mtotal = 16.2 kg is sitting at rest when it explodes into three pieces. One piece with mass m1 = 4.6 kg moves up and to the left at an angle of 1 = 23° above the –x axis with a speed of v1 = 25.2 m/s. A second piece with mass m2 = 5.1 kg moves down and to the right an angle of 2 = 28° to the right of the -y axis at a speed of v2 = 23.6 m/s.

1)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

Explanation / Answer

1) magnitude of final momentum will be zero because the inital momentum is zero

2) mass of the third piece = M- (m1+m2) = 17.5 - (4.5+5.1) = 7.9 kg

3) conserving the momentum in x- direction we have

4.5*(-26.4) cos 22 + 5.1 *22.1 * sin 27 + 7.9 Vx = 0

Vx = 7.465 m/s

4) cosnerving the momentum in y - direction we have

4.5*(26.4) sin 22 + 5.1 *-22.1 * cos 27 + 7.9 Vy = 0

Vy = 7.078 m/s

velocity of the third piece = sqrt(7.465^2 + 7.078^2) = 10.28 m/s

5) magnitude of velocity of COM

V = m1v1 + m2v2 + m3v3 / M

V = 4.5*26.4 + 5.1*22.1 + 7.9*10.28 / 17.5

V = 17.87 m/s

6) Increase in KE = 0.5 MV^2 = 0.5*17.5*17.87^2 = 2794.14 J

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