An isolated 3 kg object is moving in the positive y direction along the -y axis at 2 m/s; when it reaches the origin it breaks into two pieces sending a 1 kg fragment in the +y direction at a speed of 3.7 m/s. what are the velocity and direction of the other piece immediately after the "explosion"?
To find the velocity and direction of the other piece immediately after the "explosion", we can use the principle of conservation of momentum. The total momentum before the explosion should be equal to the total momentum after the explosion.
Let's denote the velocity of the other piece as V. Since the 1 kg fragment is moving in the positive y direction at a speed of 3.7 m/s, we know its momentum is given by:
Momentum of fragment = mass × velocity = (1 kg) × (3.7 m/s) = 3.7 kg·m/s
The total momentum before the explosion is the momentum of the isolated object, which is moving in the negative y direction at 2 m/s. Since the object has a mass of 3 kg, its momentum is given by:
Momentum of object = mass × velocity = (3 kg) × (-2 m/s) = -6 kg·m/s
According to the principle of conservation of momentum, the total momentum before the explosion (-6 kg·m/s) should be equal to the total momentum after the explosion (3.7 kg·m/s for the fragment + mass of the other piece × V).
-6 kg·m/s = 3.7 kg·m/s + (mass of the other piece) × V
Now, we can solve for V:
-6 kg·m/s - 3.7 kg·m/s = (mass of the other piece) × V
-9.7 kg·m/s = (mass of the other piece) × V
Dividing both sides of the equation by the mass of the other piece:
V = (-9.7 kg·m/s) / (mass of the other piece)
The mass of the other piece can be found by subtracting the mass of the fragment (1 kg) from the initial mass (3 kg):
mass of the other piece = 3 kg - 1 kg = 2 kg
Plugging in the values:
V = (-9.7 kg·m/s) / (2 kg) = -4.85 m/s
Therefore, the velocity of the other piece immediately after the explosion is -4.85 m/s, and since it is negative, it is moving in the negative y direction (opposite direction of the fragment).