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Determine the effective spring constant of the suspension system of a car. Consider a load of 4 passengers, each with a mass of 70 kg. The c
Question
Determine the effective spring constant of the suspension system of a car. Consider a load of 4 passengers, each with a mass of 70 kg. The car suspension system consists of four identical springs, each with a spring constant k. When all four people get into the car, the tires are depressed by about Δx = 2.0 cm.
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Physics
3 years
2021-08-21T15:16:58+00:00
2021-08-21T15:16:58+00:00 1 Answers
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Answer:
The value of spring constant for each spring of the suspension system of a car K = 343.35![Rendered by QuickLaTeX.com \frac{N}{cm}](https://documen.tv/wp-content/ql-cache/quicklatex.com-91ddad59e56a6eaf05060608524527f5_l3.png)
Explanation:
Total force on the springs = weight of the four passengers
⇒ F = 4 × 70 × 9.81
⇒ F = 2746.8 N
In the suspension system of the car the four springs are connected in parallel. So Equivalent spring constant is given by,
⇒
= 4 K ——– ( 1 )
Depression in the spring Δx = 2 cm
Now the force on the spring is given by
F =
× Δx
⇒
= ![Rendered by QuickLaTeX.com \frac{2746.8}{2}](https://documen.tv/wp-content/ql-cache/quicklatex.com-6c2bf2c1e27807b0db0d62bf15930757_l3.png)
⇒
= 1373.4 ![Rendered by QuickLaTeX.com \frac{N}{cm}](https://documen.tv/wp-content/ql-cache/quicklatex.com-91ddad59e56a6eaf05060608524527f5_l3.png)
Now the spring constant for each spring =![Rendered by QuickLaTeX.com \frac{K_{eq}}{4}](https://documen.tv/wp-content/ql-cache/quicklatex.com-95cf4af90a41e0da2371595970cf3103_l3.png)
⇒ K =![Rendered by QuickLaTeX.com \frac{1373.4}{4}](https://documen.tv/wp-content/ql-cache/quicklatex.com-9be6ea5ee558412114340a5dfc5b2ea5_l3.png)
⇒ K = 343.35![Rendered by QuickLaTeX.com \frac{N}{cm}](https://documen.tv/wp-content/ql-cache/quicklatex.com-91ddad59e56a6eaf05060608524527f5_l3.png)
This is the value of spring constant for each spring of the suspension system of a car.