A 28.0-kg body is moving in the direction of the positive x axis with a speed of

Question

A 28.0-kg body is moving in the direction of the positive x axis with a speed of 360 m/s when, owing to an internal explosion, it breaks into three pieces. One part, whose mass is 9.5 kg, moves away from the point of explosion with a speed of 342 m/s along the positive y axis. A second fragment, whose mass is 3.0 kg, moves away from the point of explosion with a speed of 328 m/s along the negative x axis. What is the speed of the third fragment? Ignore effects due to gravity. How much energy was released in the explosion?

Explanation / Answer

Given

masses m = 28 kg , moving in the +ve x direction with velocity v = 360 m/s

after an internal explosion , m breaks in to three pieces say m1,m2,m3 moving in different directions with diffrerent velocities

from conservation of momentum the total momentum of the system before and after the explosion is same

momentum isa vector quantity so , the components of the momentum can be calculated

initial momentum before explosion is  

P = Px + py

p = 28*360 + 0 = 10080 i + 0 j

now masses of pieces and their velcoicities are

m1 = 9.5 kg, v1 = 342 m/s along +y direction

m2 = 3.0 kg, v2 = 328 m/s along -x direction

m3 = (m-(m1+m2)) = 28-(9.5+3) = 15.5kg , v3 = ?

from conservation of momentum , for Vx3

Px = m1*vx1+m2*vx2+m3*vx3

10080 = m1*0 + 3(-328)+15.5(vx3)

Vx3 = 713.80 m/s

for Vy3

Py = m1*vy1+m2*vy2+m3*vy3

10080 = 9.5*342 + m2*0+15.5(vy3)

Vy3 = 440.70 m/s

the speed of third piece is v = sqrt(vx3^2+vy3^2) = sqrt(713.80^2+440.70^2) m/s = 838.88 m/s

---

the initial kinetic energy of the 28 kg block is  

k.e_i = 0.5*28*360^2 J = 1814400 J

final k.e , k.e_f = 0.5(m1*v1^2+m2*2^2+m3*v3^2)

= 0.5(9.5*342^2+3*328^2+15.5*838.88^2) J

= 6170782.322 J

the energy difference is

k.e_f - k.e_i = 6170782.322 -1814400 J = 4356382.322 J

the energy released in the explosion is 4356382.322 J

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.