An object with total mass m_total - 14 kg is sitting at rest when it explodes in

Question

An object with total mass m_total - 14 kg is sitting at rest when it explodes into three pieces. One piece with mass m_1 -4.6 kg moves up and to the left at an angle of theta_1 - 21' above the x axis with a speed of w_1 - 28.6 m/s. A second piece with mass m_2 - 5.3 kg moves down and to the right an angle of theta_2 - 26' to the right of the -y axis at a speed of V_2 - 20.8 m/s. What is the magnitude of the final momentum of the system (all three pieces)? kg-m/s What is the mass of the third piece? kg What is the x-component of the velocity of the third piece? m/s What is the y-component of the velocity of the third piece? m/s What is the magnitude of the velocity of the center of mass of the pieces after the collision? m/s Calculate the increase in kinetic energy of the pieces during the explosion.

Explanation / Answer

(1)

initialy particle was in rest

so momentum Pi = 0

(2)

m3 = M-m1-m2 = 14 - 4.6 - 5.3

m3 = 4.1 kg

(3)

theta1(relative to +x) = 180 - 21 = 159 deg

theta2 = -64 deg

V3x = -(m1*v1*cos(theta1) + m2*v2*cos(theta2)) / m3

v3x = -(4.6*28.6*cos(159) + 5.3*20.8*cos(-64)) / 4.1

v3x = 18.17 m/s

(4)

v3y = -(4.6*28.6*sin(159) + 5.3*20.8*sin(-64)) / 4.1

v3y = 12.66 m/s

(5)

velocity of center of mass is conserved

so (Vcom)i = (Vcom)f = 0

because initialy particle was in rest

(6)

v3 = sqrt (v3x^2 + v3y^2)

v3 = sqrt (18.17^2 + 12.66^2)

v3 = 22.14 m/s

KE i = 0

KEf = 1/2 * (4.6*28.6^2 + 5.3*20.8^2 + 4.1*22.14^2)

increase in KE = 4032.66 J

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