The front spring of a car‘s suspension system has a spring constant of 1.68×106 N/m and supports a mass of 204 kg. The wheel has a radius of 0.387 m. The car is traveling on a bumpy road, on which the distance between the bumps is equal to the circumference of the wheel. Due to resonance, the wheel starts to vibrate strongly when the car is traveling at a certain minimum linear speed. What is this speed?
The natural angular frequency of spring w sqrt (k/m) where Period T 2pi sqrt (m/k) and w 2pif 2pi/T the car travels on bumps - is like a sinusoidal motion with angular freq wr v / 2 pi r (v is linear velocity and r radius of wheel) so that every 2 bumps make a cycle at resonance rattling due to w wr maximu m amplitude sqrt (k/m) v / 2 pi r 90.748 v / 2.430 v 220.551 m/s
Less materials to waste. Plus the force created by that weight would be a hassle to stop and wear out your brakes quicker. Plus, inflated tires adjust to the road
Solid tires wouldn't provide much cushioning as air filled(pneumatic) tires do. The air inside them supports by absorbing the shock. A completely solid wouldn't be as flexible as a pneumatic tyre and so it would not be able to adapt to the road and there would be less grip.
A solid ruber tire would have the worst ride ever, it would also be unsafe cuz the tire woild get very hot, the tire could just slowly melt away. Ride and safty.
? yes, the period of spring T2pi*sqrt(m/k), where m204kg, k1.68·10^6 N/m; ? yes, circumference of the wheel C2pi*r, where r0.387m; ? yes, the speed should be vC/T r/sqrt(m/k) r*sqrt(k/m) 0.387* sqrt(1.68·10^6 / 204) 35.12 m/s; but not 220m/s !!!
