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College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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![**Collision Analysis of a Toy Car**
A 0.300 kg toy car moving with a speed of 0.820 m/s collides with a wall. The figure shows the force exerted on the car by the wall over the course of the collision.
**Problem Statement:**
What is the magnitude of the velocity, or final speed, of the car after the collision?
**Graph Analysis:**
- **X-Axis (Time, s):** The time interval ranges from 0 to 0.02 seconds.
- **Y-Axis (Force, N):** The force exerted is measured from 0 to 45 Newtons.
- **Graph Description:** The force applied to the car increases linearly, reaches a maximum of 45 N at approximately 0.01 seconds, and then decreases linearly back to zero at 0.02 seconds. This creates a triangular shape.
**Calculation:**
To find the final speed of the car, consider using the impulse-momentum theorem, which relates the change in momentum to the impulse experienced. The area under the force-time graph will give the impulse.
\[ \text{Impulse} = \Delta p = F \cdot \Delta t \]
Calculate the area under the triangular force-time graph to determine the impulse, then use it to find the change in velocity.
**Final Speed Calculation Box:**
\[ \text{Final Speed} = \quad \text{m/s} \]
**Note:** Ensure to integrate or calculate the area of the triangle for accurate results. Use tools like calculators for numerical computations.](https://content.bartleby.com/qna-images/question/518a9830-87bc-492b-a0d3-d0bffb9858cc/f04f64fc-f6be-4e06-afc6-d968f5436ff1/zxxa1o_thumbnail.jpeg)
Transcribed Image Text:**Collision Analysis of a Toy Car**
A 0.300 kg toy car moving with a speed of 0.820 m/s collides with a wall. The figure shows the force exerted on the car by the wall over the course of the collision.
**Problem Statement:**
What is the magnitude of the velocity, or final speed, of the car after the collision?
**Graph Analysis:**
- **X-Axis (Time, s):** The time interval ranges from 0 to 0.02 seconds.
- **Y-Axis (Force, N):** The force exerted is measured from 0 to 45 Newtons.
- **Graph Description:** The force applied to the car increases linearly, reaches a maximum of 45 N at approximately 0.01 seconds, and then decreases linearly back to zero at 0.02 seconds. This creates a triangular shape.
**Calculation:**
To find the final speed of the car, consider using the impulse-momentum theorem, which relates the change in momentum to the impulse experienced. The area under the force-time graph will give the impulse.
\[ \text{Impulse} = \Delta p = F \cdot \Delta t \]
Calculate the area under the triangular force-time graph to determine the impulse, then use it to find the change in velocity.
**Final Speed Calculation Box:**
\[ \text{Final Speed} = \quad \text{m/s} \]
**Note:** Ensure to integrate or calculate the area of the triangle for accurate results. Use tools like calculators for numerical computations.
Expert Solution
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