Let’s look at a simplified model of a car that’s dropped onto the ground. Model the suspension as a single linear spring and the rest of the vehicle as a single lumped mass. The car is dropped from a height of h1 = 0.9m. What is the maximum mass m for which the suspension does not bottom out? Assume a maximal allowable suspension travel of 10 cm and a spring constant of k = 2.4x10^6 N/m.

Elements Of Electromagnetics
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Author:Sadiku, Matthew N. O.
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Let’s look at a simplified model of a car that’s dropped onto the ground.

Model the suspension as a single linear spring and the rest of the vehicle as a single lumped mass. The car is dropped from a height of h1 = 0.9m.

What is the maximum mass m for which the suspension does not bottom out? Assume a maximal allowable suspension travel of 10 cm and a spring constant of k = 2.4x10^6 N/m.

### Physics of Spring-Mass Systems

This image illustrates two separate systems for analyzing gravitational effects and spring mechanics.

**Left Diagram: Car on a Surface**

- A car is shown resting on a flat surface.
- The gravitational force (`g`) is acting downward on the car.

**Right Diagram: Mass-Spring System**

- This diagram features a mass (`m`) attached to a vertical spring.
- The gravitational force (`g`) also acts downward on this mass-spring system.
- **Spring Mechanics**:
  - The spring is initially at rest with a length `h1` from the ground when no force is applied.
  - Under the weight of the mass `m`, the spring compresses to a length `h2`.
  
**Common Variables**:
- `g`: Acceleration due to gravity, acting downward in both diagrams.
- `m`: Mass attached to the spring, subject to gravitational force.

This setup is often used to examine concepts like equilibrium, oscillation, Hooke's Law, and energy transfer in physics.
Transcribed Image Text:### Physics of Spring-Mass Systems This image illustrates two separate systems for analyzing gravitational effects and spring mechanics. **Left Diagram: Car on a Surface** - A car is shown resting on a flat surface. - The gravitational force (`g`) is acting downward on the car. **Right Diagram: Mass-Spring System** - This diagram features a mass (`m`) attached to a vertical spring. - The gravitational force (`g`) also acts downward on this mass-spring system. - **Spring Mechanics**: - The spring is initially at rest with a length `h1` from the ground when no force is applied. - Under the weight of the mass `m`, the spring compresses to a length `h2`. **Common Variables**: - `g`: Acceleration due to gravity, acting downward in both diagrams. - `m`: Mass attached to the spring, subject to gravitational force. This setup is often used to examine concepts like equilibrium, oscillation, Hooke's Law, and energy transfer in physics.
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