An initially stationary device lying on a frictionless floor explodes into two pieces and slides across the floor. One piece is moving in positive x-direction then other piece is moving in

Options

A. positive y- direction
B. negative y-direction
C. negative x-direction
D. at angle from x-direction

Explanation

To solve the problem of an initially stationary device that explodes into two pieces on a frictionless floor, we will use the principle of conservation of momentum. Here’s a step-by-step solution:

### Step 1: Understand the Initial Conditions
The device is initially stationary, which means its initial momentum is zero.

**Hint:** Remember that momentum is the product of mass and velocity. If the device is stationary, its velocity is zero.

### Step 2: Define the Masses and Velocities
Let the masses of the two pieces after the explosion be \( m_1 \) and \( m_2 \). After the explosion, one piece moves in the positive x-direction with velocity \( v_1 \), and the other piece moves in the negative x-direction with velocity \( v_2 \).

**Hint:** Assign directions carefully; positive x-direction is typically to the right, and negative x-direction is to the left.

### Step 3: Apply the Conservation of Momentum
According to the conservation of momentum, the total momentum before the explosion must equal the total momentum after the explosion. Since the initial momentum is zero, we can write:

\[ 0 = m_1 v_1 + m_2 v_2 \]

**Hint:** The momentum before the explosion is zero, so the sum of the momenta after the explosion must also equal zero.

### Step 4: Rearrange the Equation
From the equation \( m_1 v_1 + m_2 v_2 = 0 \), we can express \( v_2 \) in terms of \( v_1 \):

\[ m_1 v_1 = -m_2 v_2 \implies v_2 = -\frac{m_1}{m_2} v_1 \]

**Hint:** The negative sign indicates that the second piece is moving in the opposite direction to the first piece.

### Step 5: Interpret the Result
The result \( v_2 = -\frac{m_1}{m_2} v_1 \) shows that the second piece moves in the negative x-direction, confirming that it is indeed moving in the opposite direction to the first piece.

**Hint:** Check the signs of the velocities to ensure they match the directions you assigned earlier.

### Conclusion
Thus, we conclude that the second piece moves in the negative x-direction after the explosion.

**Final Answer:** The second piece is moving in the negative x-direction.