A `10 g` rubber ball and a `10g` clay ball are each thrown at a wall with equal speeds. The rubber ball bounces, the clay ball sticks. Which ball receives a greater impulse from the wall ?

Options

A. The clay ball recieves a greater impulse because it sicks.
B. The rubber ball receive a greater impulse because it bounces.
C. They receive equal impulses because they have equal momenta.
D. Neither receives an impulse because the wall doesn't move.

Answer

To determine which ball receives a greater impulse from the wall, we can analyze the situation using the principles of momentum and impulse.

### Step-by-step Solution:

1. **Understanding Impulse**:
Impulse is defined as the change in momentum of an object when a force is applied over a period of time. Mathematically, impulse (I) can be expressed as:
\[ I = \Delta p = p_f - p_i \]
where \( p_f \) is the final momentum and \( p_i \) is the initial momentum.

2. **Initial Momentum Calculation**:
For both the rubber ball and the clay ball, they have the same mass \( m = 10 \, g = 0.01 \, kg \) and are thrown at the same speed \( v_i \). The initial momentum for both balls is:
\[ p_i = m \cdot v_i \]

3. **Final Momentum for the Rubber Ball**:
When the rubber ball hits the wall, it bounces back. If we assume it bounces back with the same speed but in the opposite direction, its final momentum \( p_f \) will be:
\[ p_f = m \cdot (-v_i) = -m \cdot v_i \]
Thus, the change in momentum (impulse) for the rubber ball \( I_1 \) is:
\[ I_1 = p_f - p_i = (-m \cdot v_i) - (m \cdot v_i) = -2m \cdot v_i \]

4. **Final Momentum for the Clay Ball**:
The clay ball sticks to the wall, so its final momentum \( p_f \) is 0. Therefore, the impulse \( I_2 \) for the clay ball is:
\[ I_2 = p_f - p_i = 0 - (m \cdot v_i) = -m \cdot v_i \]

5. **Comparing Impulses**:
Now we can compare the impulses received by both balls:
- For the rubber ball:
\[ I_1 = -2m \cdot v_i \]
- For the clay ball:
\[ I_2 = -m \cdot v_i \]
Since \( -2m \cdot v_i < -m \cdot v_i \), we conclude that:
\[ |I_1| > |I_2| \]
This indicates that the rubber ball receives a greater impulse from the wall than the clay ball.

### Conclusion:
The rubber ball receives a greater impulse from the wall because it bounces back, resulting in a larger change in momentum compared to the clay ball, which sticks to the wall.