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A car of mass 1500 kg rests equally on four springs, so each corner carries 375 kg…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A car of mass rests equally on four springs, so each corner carries . A shock absorber at each corner gives a damping force . The designer wants the bounce after a bump to fall to one tenth of its size within . (a) What is the least for each shock absorber? (b) A worn shock absorber has a third of this . What fraction of the bounce is left after ?
Need a reminder? The key ideaShow
With a damping force , the amplitude falls as and the energy as . A periodic force drives the body at its own frequency; the amplitude is largest at resonance, when the driving frequency equals the natural frequency.
The worked solution
Have you tried it?
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.
(a) We want , so from :
(b) With the exponent is . So the fraction left is . Nearly half the bounce is still there after a whole second.
Why it matters. A car with worn shock absorbers keeps bouncing after every bump. The tyres then grip the road badly.
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