College Physics
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.
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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.
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