The body of a car, of mass 1200 kg, rests on four identical springs…

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The body of a car, of mass $1200\ \text{kg}$ , rests on four identical springs. When a load of $300\ \text{kg}$ is put in, the body sinks by $2.5\ \text{cm}$ . Find (a) the spring constant of the four springs together and (b) the spring constant of each spring. (c) The loaded car goes over a bump. With what period does it bounce? Take $g = 9.8\ \text{m/s}^2$ .

Need a reminder? The key ideaShow

A hanging spring rests at a stretch $d$ with $kd = mg$ , and $T = 2\pi\sqrt{m/k} = 2\pi\sqrt{d/g}$ . In parallel $k = k_1 + k_2$ ; in series $\dfrac{1}{k} = \dfrac{1}{k_1} + \dfrac{1}{k_2}$ . A piece of a spring has a larger $k$ : $k \times$ length stays the same.

The worked solution

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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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The body of a car, of mass 1200 kg, rests on four identical springs…

The worked solution

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