An object with total mass m total = 17.2 kg is sitting at rest when it explodes

Question

An object with total mass mtotal = 17.2 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 1 = 20° above the –x axis with a speed of v1 = 25.4 m/s. A second piece with mass m2 = 5.1 kg moves down and to the right an angle of 2 = 25° to the right of the -y axis at a speed of v2 = 20.8 m/s.

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

=0 kg-m/s

2) What is the mass of the third piece?

7.2 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) 0. ("An object... is sitting at rest...)
2) m3 = 17.2kg - 4.9kg - 5.1kg = 7.2 kg
3) x-momentum:
0 = 4.9kg * 25.4m/s * cos(160º) + 5.1kg * 20.8m/s * cos295º + 7.2kg * V * cos
0 = -62.574kg·m/s + 7.2kg * V * cos
V * cos = 8.69 m/s x-component

4) y-momentum:
0 = 4.9kg * 25.4m/s * sin(160º) + 5.1kg * 20.8m/s * sin295º + 7.2kg * V * sin
0 = -53.57kg·m/s + 7.2kg * V * sin
V * sin = 7.44 m/s y-component

5) system momentum still = 0, so velocity of c.o.m. = 0.

6) velocity of third mass is V = (8.69² + 7.44²) m/s = 11.438 m/s
Ek = ½ * 4.9kg * (25.4m/s)² + ½ * 5.1kg * (20.8m/s)² + ½ * 7.2kg * (7.44m/s)² =

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