nn An object with total mass m total = 14.2 kg is sitting at rest when it explod

Question

nn

An object with total mass mtotal = 14.2 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 = 5.3 kg moves down and to the right an angle of 2 = 28° to the right of the -y axis at a speed of v2 = 21.5 m/s.

1)

What is the magnitude of the final momentum of the system (all three pieces)?

2)

What is the mass of the third piece?

3)

What is the x-component of the velocity of the third piece?

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

5)

What is the magnitude of the velocity of the center of mass of the pieces after the collision?

6)

Calculate the increase in kinetic energy of the pieces during the explosion.

Explanation / Answer

1)

as the system was at rest initially

and NO external force is acting on the system

magnitude of final momentum = 0 Kg.m/s

2)

mass of third mass is m3

m1 + m2 + m3 = mtotal

4.6 + 5.3 + m3 = 14.2

m3 = 4.3 Kg

the mass of third piece is 4.3 Kg

3)

Now , using conservation of momnetum in x direction

- m1 * v1 cos( theta1) + m2 * v2 * sin(theta2) + m3 * v3x = 0

-4.6 * 25.2 * cos(23) + 5.3 * 21.5 * sin(28) + 4.3 * v3x = 0

solving for v3x

v3x = 12.4 m/s

the x-component of the velocity of the third piece is 12.4 m/s

4)

for conservation of momentum in y direction

m1 * v1 * sin( theta1) - m2 * v2 * cos(theta2) + m3 * v3y = 0

4.6 * 25.2 * sin(23) - 5.3 * 21.5 * cos(28) + 4.3 * v3y = 0

solving for v3y

v3y = 12.74 m/s

the y-component of the velocity of the third piece is 12.74 m/s

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