An object with total mass m total = 7.5 kg is sitting at rest when it explodes i
ID: 1786857 • Letter: A
Question
An object with total mass mtotal = 7.5 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 = 41 J.
1)
What is the speed of the smaller piece after the collision?
m/s
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5.72713
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5.72713
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Friday, November 17 at 7:02 PM
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Correct!
2)
What is the speed of the larger piece after the collision?
m/s
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17.18139
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17.18139
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Friday, November 17 at 7:14 PM
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3)
If the explosion lasted for a time t = 0.028 s, what was the average force on the larger piece?
N
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3451.618527
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3451.618527
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Friday, November 17 at 7:08 PM
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4)
What is the magnitude of the change in momentum of the smaller piece?
kg-m/s
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5)
What is the magnitude of the velocity of the center of mass of the pieces after the collision?
Explanation / Answer
1)
given that : m + 3m = 7.5 kg
m = 7.5/4 = 1.875 kg
m1 = m
v1f = ?
m3 = 3m
v2f = ?
using conservation of momentum
0 = m1 v1i + m2 v2i
- m v1i = (3m) v2i
v1i = - 3 v2i eq-1
using conservation of energy
41 = (0.5) m1 v1i2 + (0.5) m2 v2i2
41 = (0.5) (1.875) v1i2 + (0.5) (3 x 1.875) (- v1i/3)2
v1i = 5.73 m/s
2)
using eq-1
v2i = v1i /3 = 5.73/3 = 1.92 m/s
3)
Favg = average force = change in momentum of smaller mass /t = m1 v1i/t = (1.875) (5.73)/0.028 = 383.7 N
4)
change in momentum of smaller mass = (1.875) (5.73) = 10.7 kgm/s
5)
velocity of center of mass before and after collision remain same. before collision the velocity of center of mass was zero. it remains zero even after explosion