An object with total mass m total = 15.3 kg is sitting at rest when it explodes

Question

An object with total mass mtotal = 15.3 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 = 25.6 m/s. A second piece with mass m2 = 5.3 kg moves down and to the right an angle of 2 = 25° to the right of the -y axis at a speed of v2 = 23 m/s.

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.

36/2017 Homework Collisions, Impulse, and Reference Frames Dmalkhayat@gmail.com account log aff help 1 PM Fliplt Physics PHYS 2210 Spring 2017 (Gerton macmillan learning University of Utah Umit Checkpo Problems Homework: Collisions, Impulse, And Reference Frames Print Assignment View 00 until Monday, March 20 a Standard Exertbe Ball Hits Wal Explosion Standard Exertse Ball Hits Wall 2 Cptional Standard Exerthe Explosion Standard Exertbe Explosion 2 Cptional An object with total mass m 15.3 kg is sitting at rest when it explodes into three pieces. One piece with mass m 4,9 kg moves up and to the left at an angle of e 20" above the -x axis with a speed of v1 25.6 m/s. A second piece with mass m2 5.3 kg moves down and to the right an angle of 62 25 to the right of the y axis at a speed of Z3 m/s. 1) What is the magnitude of the final momentum of the system (all three pieces)? g m/s Submit 2) What is the mass of the third piece? g Subin 3) What is the X component of the velocity of the thrd piece? 2.8 m/s Submit 4) What is the y component of the velocity of the third plece? Sub 5) What is the magnitude of the velocity of the center of mass of the pieces after the collision? Submit 6) Calculate the increase in kinetic energy of the pieces during the explosion Submit https:/wwww.flipitphysics.com/CourseMiewProblem?unitltemID 2359384&enrollmentID; 236799

Explanation / Answer

4. The Y component of momentum

Py = m1v1 sin theta - m2 v2 cos theta

Py = m3V3 = 4.9 * 25.6 * sin 20 - (5.3 * 23 * cos 25)

m3V3 = 67.57 kg m/s

remaining mass m3 = 15.3 - 4.9 -5.3 = 5.1 kgs

so y-component of the velocity of the third piece = 67.57/5.1

V3 y = 13.24 m/s

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5) System momentum still = 0

SO its velocity of the center of mass = 0

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6) velocity of third mass is V3^2 = v1^2 + v2^2

The sum of all x components of momentum must be zero

the first two fragments have x momenta of , Vx = Vcos(24)

(4.9 * (-25.6 cos 20) + (5.3 * 23 sin 25) = 66.35 kg-m/s

so its velocity = 66.35/ 5.1 = 13 m/s

V = sqrt( 13^2 + 13.24^2)

V = 18.55 m/s

Increase in kinetic energy

Ek = 1/2 * 4.9* (25.6)^2 + 1/2 * 5.4 * (23)^2 + 1/2 * 5.1 * (18.55)^2

Ek = 3911.39 J

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