A 4.20 kg object, travelling at 6.70 m/s to the right, suddenly explodes into two pieces. The 1.44 kg piece moves to the right at 9.10 m/s after the explosion; What is the speed of the 2.76 kg piece?
Question
A 4.20 kg object, travelling at 6.70 m/s to the right, suddenly explodes into two pieces. The 1.44 kg piece moves to the right at 9.10 m/s after the explosion; What is the speed of the 2.76 kg piece?
Solution
To solve this problem, we need to use the law of conservation of momentum. The total momentum before the explosion must be equal to the total momentum after the explosion.
Step 1: Calculate the initial momentum before the explosion. The initial momentum (P_initial) is the mass of the object times its velocity. P_initial = mass * velocity P_initial = 4.20 kg * 6.70 m/s = 28.14 kg*m/s
Step 2: Calculate the momentum of the 1.44 kg piece after the explosion. The momentum of the 1.44 kg piece (P_1.44) is its mass times its velocity. P_1.44 = 1.44 kg * 9.10 m/s = 13.104 kg*m/s
Step 3: Calculate the momentum of the 2.76 kg piece after the explosion. The momentum of the 2.76 kg piece (P_2.76) is the initial momentum minus the momentum of the 1.44 kg piece. P_2.76 = P_initial - P_1.44 P_2.76 = 28.14 kgm/s - 13.104 kgm/s = 15.036 kg*m/s
Step 4: Calculate the velocity of the 2.76 kg piece after the explosion. The velocity (v) of the 2.76 kg piece is its momentum divided by its mass. v = P_2.76 / mass v = 15.036 kg*m/s / 2.76 kg = 5.44 m/s
So, the speed of the 2.76 kg piece after the explosion is 5.44 m/s.
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