https://file.aiquickdraw.com/mathbot/file/1730506564617d7yp96r9.jpg

To solve this problem, we need to find the change in the linear momentum of the ball when it rebounds from the wall.

### Given dataTo solve this problem, we need to find the change in the linear momentum of the ball when it rebounds from the wall.

### Given 
- Mass of the ball, \( m = 0.57 \, \text{kg} \)
- Initial speed of the ball before hitting the wall, \( v_i = 6.5 \, \text{m/s} \) (moving towards the wall)
- Final speed of the ball after rebounding from the wall, \( v_f = 1.3 \, \text{m/s} \) (moving away from the wall)

### Approach:
Linear momentum (\( p \)) is given by:
\[
p = m \cdot v
\]

The change in linear momentum \( \Delta p \) is the difference between the final and initial momenta:
\[
\Delta p = p_f - p_i = m \cdot v_f - m \cdot v_i
\]

Since the ball rebounds in the opposite direction, we need to assign a negative sign to the final speed (or direction) to indicate the change in direction. Therefore:
- Initial velocity \( v_i = +6.5 \, \text{m/s} \)
- Final velocity \( v_f = -1.3 \, \text{m/s} \)

### Calculation:
Substitute the values into the formula:
\[
\Delta p = 0.57 \cdot (-1.3) - 0.57 \cdot (6.5)
\]

Breaking it down:
1. Calculate \( m \cdot v_f \):
   \[
   0.57 \cdot (-1.3) = -0.741 \, \text{kg} \cdot \text{m/s}
   \]

2. Calculate \( m \cdot v_i \):
   \[
   0.57 \cdot 6.5 = 3.705 \, \text{kg} \cdot \text{m/s}
   \]

3. Now find \( \Delta p \):
   \[
   \Delta p = -0.741 - 3.705 = -4.446 \, \text{kg} \cdot \text{m/s}
   \]

The magnitude of the change in linear momentum is:
\[
|\Delta p| = 4.446 \, \text{kg} \cdot \text{m/s}
\]

### Answer:
The magnitude of the change in linear momentum of the ball is **4.446 kg·m/s**.

Would you like further details, or do you have any questions?

### Related Questions:
1. What is linear momentum, and how is it calculated?
2. Why does the direction of velocity matter in momentum calculations?
3. How would the change in momentum differ if the ball stuck to the wall instead of rebounding?
4. What role does mass play in calculating momentum?
5. How would the answer change if the mass of the ball were different?

### Tip:
Remember, momentum is a vector quantity—it has both magnitude and direction. This is why direction changes (like in a rebound) significantly affect momentum calculations.

A 0.57 kg ball is moving horizontally with a speed of 6.5 m/s when it strikes a vertical wall. The ball rebounds with a speed of 1.3 m/s. What is the magnitude of the change in linear momentum of the ball?

Learn how to calculate the change in linear momentum of a 0.57 kg ball moving at 6.5 m/s before and 1.3 m/s after rebounding from a wall. This problem involves key concepts in linear momentum, vector direction in momentum, and the impact of mass and speed on momentum change.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation