An object with total mass m total = 14.8 kg is sitting at rest when it explodes

Question

An object with total mass mtotal = 14.8 kg is sitting at rest when it explodes into three pieces. One piece with mass m1 = 4.8 kg moves up and to the left at an angle of ?1 = 22? above the ?x axis with a speed of v1 = 27.7 m/s. A second piece with mass m2 = 5.1 kg moves down and to the right an angle of ?2 = 27? to the right of the -y axis at a speed of v2 = 20.7 m/s.

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

What is the mass of the third piece?

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

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

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

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

Explanation / Answer

a)

the momentum is zero because the object is sitting at the rest

b)

m = m1 + m2 + m3

m3 = 14.8-4.8-5.1

m3 = 4.9kg

the mass of the third piece is 4.9 kg

c)

the x component of the velocity of third piece is

x - momentum = 0

so

0 = 4.8 * 27.7 * cos(158 degree) + 5.1 * 20.7* cos(297 degree)+ 4.9 * v3 cos(theta)

v3 *cos(theta) = 75.35 / 4.9 = 15.37 m /s

the x-component of the velocity of the third piece is 15.37 m/s

c)

y- momentum = 0

0 = 4.8 * 27.7 * sin(158 degree) + 5.1 * 20.7* sin(297 degree)+ 4.9 * v3 sin(theta)

v3 sin( theta ) = 44.26 / 4.9 = 9 m/s

the y-component of the velocity of the third piece is 9 m/s

d)

system momentum still = 0, so velocity of center of mass of the piece after collision is = 0m/s

e)

velocity of third mass

v3 = sqrt( 15.37^2 + 9^2)

v3 = 17.81 m/s

delta K = 0.5 * 4.8 * 27.7^2 + 0.5 * 5.1 * 20.7^2 + 0.5 * 4.9 * 17.81^2

delta k = 3711.27 J

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