Two masses of 0.25 kg each moves toward each other with speed 3 `ms^(-1)` collide and stick together. Find the final velocity

Options

A. `0.5 ms^(-1)`
B. `2 ms^(-1)`
C. `1 ms^(-1)`
D. `0.25 ms^(-1)`

Answer

To solve the problem of two masses colliding and sticking together, we can use the principle of conservation of momentum. Here’s a step-by-step solution:

### Step 1: Identify the masses and their velocities
- Mass of object A (m1) = 0.25 kg
- Velocity of object A (v1) = 3 m/s (moving to the right)
- Mass of object B (m2) = 0.25 kg
- Velocity of object B (v2) = -3 m/s (moving to the left, hence negative)

### Step 2: Write the formula for conservation of momentum
The principle of conservation of momentum states that the total momentum before the collision is equal to the total momentum after the collision. Mathematically, this can be expressed as:
\[ m_1 v_1 + m_2 v_2 = (m_1 + m_2) V \]
where \( V \) is the final velocity of the combined masses after the collision.

### Step 3: Substitute the known values into the equation
Substituting the values we have:
\[ (0.25 \, \text{kg}) \cdot (3 \, \text{m/s}) + (0.25 \, \text{kg}) \cdot (-3 \, \text{m/s}) = (0.25 \, \text{kg} + 0.25 \, \text{kg}) \cdot V \]

### Step 4: Calculate the left-hand side
Calculating the left-hand side:
\[ 0.25 \cdot 3 + 0.25 \cdot (-3) = 0.75 - 0.75 = 0 \]

### Step 5: Simplify the right-hand side
The right-hand side becomes:
\[ (0.25 + 0.25) \cdot V = 0.5 \cdot V \]

### Step 6: Set the two sides equal to each other
Now we can set the two sides equal to each other:
\[ 0 = 0.5 \cdot V \]

### Step 7: Solve for V
To find \( V \), we can divide both sides by 0.5:
\[ V = 0 \]

### Conclusion
The final velocity \( V \) of the two masses after they collide and stick together is **0 m/s**. This means that the two masses come to a complete stop after the collision.

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