An object with total mass m total = 17.6 kg is sitting at rest when it explodes

Question

An object with total mass mtotal = 17.6 kg is sitting at rest when it explodes into three pieces. One piece with mass m1= 4.5 kg moves up and to the left at an angle of 1 = 24° above the –x axis with a speed of v1 = 26.9 m/s. A second piece with mass m2 = 5.2 kg moves down and to the right an angle of 2 = 29° to the right of the -y axis at a speed of v2 = 22.7 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

given,

total mass = 17.6 kg

m1 = 4.5 kg

1 = 24°

v1 = 26.9 m/s

m2 = 5.2 kg

2 = 29°

v2 = 22.7 m/s

initial momentum of the system = 0 kg.m/s (since the system was in rest)

by conservation of momentum

initial momentum = final momentum

final momentum = 0 kg m/s

magnitude of the final momentum of the system = 0 kg.m/s

total mass = m1 + m2 + m3

17.6 = 4.5 + 5.2 + m3

m3 = 7.9 kg

mass of third piece = 7.9 kg

final horizontal momentum = m1 * v1 * cos(theta1) + m2 * sin(theta2) + m3 * v

0 = 4.5 * 26.9 * cos(24) - 5.2 * 22.7 * sin(29) + 7.9 * v

v = -6.754 m/s

x-component of the velocity of the third piece = -6.754 m/s

final vertical momentum = m1 * v1 * sin(theta1) + m2 * cos(theta2) + m3 * v

0 = 4.5 * 26.9 * sin(24) - 5.2 * 22.7 * cos(29) + 7.9 * v

v = 6.836 m/s

y-component of the velocity of the third piece = 6.836 m/s

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