An object with total mass m total = 8.8 kg is sitting at rest when it explodes i

Question

An object with total mass mtotal = 8.8 kg is sitting at rest when it explodes into two pieces. The two pieces, after the explosion, have masses of m and 3m. During the explosion, the pieces are given a total energy of E = 49 J.

1) What is the speed of the smaller piece after the collision?

__________m/s

2) What is the speed of the larger piece after the collision?

__________m/s

3) If the explosion lasted for a time t = 0.02 s, what was the average force on the larger piece?

__________N

4) What is the magnitude of the change in momentum of the smaller piece?

__________kg-m/s

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

__________m/s

Explanation / Answer

let m1 = m = M/4 = 8.8/4 = 2.2 kg

m2 = 3*m = 3*M/4 = 3*8.8/4 = 6.6 kg

let v1 and v2 are the speeds of m1 and m2 after the explosion.

now Apply momentum conservation

0 = m1*v1 + m2*v2

0 = m*v1 + 3*m*v2

==> v1 = -3*v2

v2 = -v1/3

1) Total enrgy = 0.5*m1*v1^2 + 0.5*m2*v2^2

49 = 0.5*2.2*v1^2 + 0.5*6.6*(v1/3)^2

49 = 1.1*v1^2 + 0.367*v1^2

v1 = sqrt(49/1.467)

= 5.78 m/s

2) v2 = v1/3

= 5.78/3

= 1.93 m/s

3) Apply, impulse = chnage in momentum

F*t = m2*v2

F = m2*v2/t

= 6.6*1.93/0.02

= 635.8 N

4) delta P1 = m1*v1

= 2.2*5.78

= 12.7 kg.m/s

5) 0 m/s

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