An object with total mass m total = 7.5 kg is sitting at rest when it explodes i

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

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