A 2.0kg object initially at rest explodes breaking into two pieces of mass 5.0kg and 15.0kg. If the 15.0kg piece moves with a speed 2m/s what is the speed of the 5.0kg piece?
A. -6 m/s
B. 15 m/s
C. -5 m/s
D. 20 m/s
assuming the original mass was really 20.0 kg,
total momentum must remain at zero, so
15.0*2 + 5.0v = 0
Yes the original mass was 20.0kg my mistake. According to my calculations the answer will be -6m/s.
To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before the explosion must be equal to the total momentum after the explosion.
The total momentum before the explosion can be calculated by multiplying the mass of the object (2.0 kg) by its initial velocity (which is 0 since it is at rest):
Total momentum before = (mass of object) x (initial velocity)
= (2.0 kg) x (0 m/s)
= 0 kg·m/s
The total momentum after the explosion can be calculated by summing up the individual momenta of the two pieces:
Total momentum after = (mass of 5.0 kg piece) x (speed of 5.0 kg piece) + (mass of 15.0 kg piece) x (speed of 15.0 kg piece)
= (5.0 kg) x (speed of 5.0 kg piece) + (15.0 kg) x (2 m/s)
= 5(speed of 5.0 kg piece) + 30
Since the total momentum before the explosion is equal to the total momentum after the explosion, we can set up the equation:
0 kg·m/s = 5(speed of 5.0 kg piece) + 30
To solve for the speed of the 5.0 kg piece, we can rearrange the equation:
5(speed of 5.0 kg piece) = -30
(speed of 5.0 kg piece) = -30/5
(speed of 5.0 kg piece) = -6 m/s
Therefore, the speed of the 5.0 kg piece is -6 m/s.
So, the correct answer is A. -6 m/s.