Truck suspensions often have "helper springs" that engage at high loads. One such arrangement is a leaf spring with a helper coil spring mounted on the axle, as in the figure below. The helper spring engages when the main leaf spring is compressed by distance yo, and then helps to support any additional load. Consider a leaf spring constant of 6.05 x 105 N/m, helper spring constant of 3.60 x 105 N/m, and y₁ = 0.500 m. Ⓒ Truck body m WWW.C Axle (a) What is the compression of the leaf spring for a load of 4.55 X 105 N? (b) How much work is done compressing the springs?

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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**Truck Suspension and Helper Springs**

Truck suspensions often include "helper springs" to manage high loads effectively. In this illustration, a leaf spring with a helper coil spring is mounted on the axle. The helper spring engages after the main leaf spring compresses by a specified distance \( y_0 \), providing additional support.

### Diagram Explanation
- **Truck Body:** The structure supported by the springs.
- **Helper Coil Spring:** Positioned above the axle, it activates to support extra loads after initial compression of the leaf spring.
- **Leaf Spring:** Installed beneath the axle, provides primary suspension.
- **Axle:** Connects the truck's wheels, pivotal in load distribution.

### Given Values
- **Leaf Spring Constant:** \( 6.05 \times 10^5 \, \text{N/m} \)
- **Helper Spring Constant:** \( 3.60 \times 10^5 \, \text{N/m} \)
- **Initial Compression Distance (\( y_0 \)):** \( 0.500 \, \text{m} \)

### Questions

(a) **Compression of the Leaf Spring:** For a load of \( 4.55 \times 10^5 \, \text{N} \), calculate the compression.

(b) **Work Done in Compressing the Springs:** Determine the energy required. 

This setup ensures efficient load management in trucks, enhancing safety and performance.
Transcribed Image Text:**Truck Suspension and Helper Springs** Truck suspensions often include "helper springs" to manage high loads effectively. In this illustration, a leaf spring with a helper coil spring is mounted on the axle. The helper spring engages after the main leaf spring compresses by a specified distance \( y_0 \), providing additional support. ### Diagram Explanation - **Truck Body:** The structure supported by the springs. - **Helper Coil Spring:** Positioned above the axle, it activates to support extra loads after initial compression of the leaf spring. - **Leaf Spring:** Installed beneath the axle, provides primary suspension. - **Axle:** Connects the truck's wheels, pivotal in load distribution. ### Given Values - **Leaf Spring Constant:** \( 6.05 \times 10^5 \, \text{N/m} \) - **Helper Spring Constant:** \( 3.60 \times 10^5 \, \text{N/m} \) - **Initial Compression Distance (\( y_0 \)):** \( 0.500 \, \text{m} \) ### Questions (a) **Compression of the Leaf Spring:** For a load of \( 4.55 \times 10^5 \, \text{N} \), calculate the compression. (b) **Work Done in Compressing the Springs:** Determine the energy required. This setup ensures efficient load management in trucks, enhancing safety and performance.
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