An object with total mass m total = 8.9 kg is sitting at rest when it explodes i
ID: 1376320 • Letter: A
Question
An object with total mass mtotal = 8.9 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?
2) What is the speed of the larger piece after the collision?
3) If the explosion lasted for a time t = 0.02 s, what was the average force on the larger piece?
4) What is the magnitude of the change in momentum of the smaller piece?
Explanation / Answer
Total Mass M = 8.9 kg
Mass of small piece m = M/ 4 = 8.9 / 4= 2.225 kg
Mass of larger piece m ' = 3 m = 3 M / 4 = 6.675 kg
Initial velocity of the object u = 0
Initial kinetic energy of the object K = 0
Total energy of the pieces after collision K ' = (1/2) m v 2 + ( 1/ 2)m' v' 2
According to problem K ' = 49 J
So, (1/2) m v 2 + ( 1/ 2)m' v' 2 = 49 J
1.1125 v 2 + 3.3375 v' 2 = 49 J -------( 1)
From law of conservation of linear momentum , Mu = m v + m ' v '
0 = ( M / 4 ) v + (3M /4) v '
From this ( M / 4 ) v = - (3M /4) v '
v = -3v' -----( 2)
Substitute equation ( 2) in equation ( 1) you get ,
1.1125 (-3v') 2 + 3.3375 v' 2 = 49 J
10.0125 v' 2 + 3.3375 v' 2=49
13.35 v' 2 = 49
v' 2 = 3.67
v ' = 1.915 m / s
(1).The speed of the smaller piece after the collision v = -3v '
= -5.747 m / s
2) The speed of the larger piece after the collision v ' = 1.915 m / s
3) The explosion lasted for a time t = 0.02 s
The average force on the larger piece F = Change in momentum / time
= m'(v'-0) / t
= 12.78 / 0.02
= 639.13 N
4) The magnitude of the change in momentum of the smaller piece = m (v - 0 )
= m v
= 12.78 kg m/s