Ch- 14- sec8 An 1150 kg automobile has springs with k= 16,000N/m. one ofthe tire

Question

Ch- 14- sec8 An 1150 kg automobile has springs with k= 16,000N/m. one ofthe tires is not properly balanced; it has a little extra mass onone side compared to the other, causing the car to shake at certainspeeds. if the tire radius 42 cm, at what speed will the wheelshake most? - Thanks Ch- 14- sec8 An 1150 kg automobile has springs with k= 16,000N/m. one ofthe tires is not properly balanced; it has a little extra mass onone side compared to the other, causing the car to shake at certainspeeds. if the tire radius 42 cm, at what speed will the wheelshake most? - Thanks

Explanation / Answer

Car will shake most when tire "bounces" at the spring's resonant oscillation period. Tire will "bounce" once per rotation, so car's speed can be determined from the given tire radius. Mass Supported By Each Of 4 Springs = m =      = (1/4)*{Total Car Mass}      = (1/4)*(1150 kg)      = 287.5 kg Resonant Oscillation Period Of Each Spring = T =      = 2**[ m/k ]      = 2**[ (287.5)/(16000) ]      = 0.842246 sec Car Speed AtSpring Resonance = v =    = 2**{Tire Radius}/T   (

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