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 shown in the figure below. When the main leaf spring is compressed by distance y g, the helper spring engages and then helps to support any additional load. Suppose the leaf spring constant is 5.20 x 105 N/m, the helper spring constant is 3.70 x 105 N/m, and y, = 0.500 m. Truck body "Helper" spring Main leaf spring Axle (a) What is the compression of the leaf spring for a load of 4.20 x 105 N? (b) How much work is done in compressing the springs?

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### Explanation of Helper Springs in Truck Suspensions

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 shown in the figure below. When the main leaf spring is compressed by the distance \( y_0 \), the helper spring engages and then helps to support any additional load.

#### Diagram Description
In the diagram:

- **Truck body**: The upper part of the figure (labeled in green) represents the body of the truck.
- **Main leaf spring**: This is a primary suspension component mounted on the axle and attached to the truck body. It is shown in gold color.
- **Helper spring**: This is a secondary spring, depicted in gray, which engages when the main leaf spring is compressed beyond a certain point.
- **Axle**: The central horizontal component connecting the wheel to the springs.

The distance \( y_0 \) (0.500 m) indicates the initial compression needed for the helper spring to engage.

Suppose the leaf spring constant is \( 5.20 \times 10^5 \) N/m, and the helper spring constant is \( 3.70 \times 10^5 \) N/m. These constants determine the stiffness of the springs.

#### Questions for Calculation
(a) **What is the compression of the leaf spring for a load of \( 4.20 \times 10^5 \) N?**
   - Enter your answer in meters.

(b) **How much work is done in compressing the springs?**
   - Enter your answer in joules.
Transcribed Image Text:### Explanation of Helper Springs in Truck Suspensions 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 shown in the figure below. When the main leaf spring is compressed by the distance \( y_0 \), the helper spring engages and then helps to support any additional load. #### Diagram Description In the diagram: - **Truck body**: The upper part of the figure (labeled in green) represents the body of the truck. - **Main leaf spring**: This is a primary suspension component mounted on the axle and attached to the truck body. It is shown in gold color. - **Helper spring**: This is a secondary spring, depicted in gray, which engages when the main leaf spring is compressed beyond a certain point. - **Axle**: The central horizontal component connecting the wheel to the springs. The distance \( y_0 \) (0.500 m) indicates the initial compression needed for the helper spring to engage. Suppose the leaf spring constant is \( 5.20 \times 10^5 \) N/m, and the helper spring constant is \( 3.70 \times 10^5 \) N/m. These constants determine the stiffness of the springs. #### Questions for Calculation (a) **What is the compression of the leaf spring for a load of \( 4.20 \times 10^5 \) N?** - Enter your answer in meters. (b) **How much work is done in compressing the springs?** - Enter your answer in joules.
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