You have a job at a forensics laboratory investigating an accident at a railroad

Question

You have a job at a forensics laboratory investigating an accident at a railroad station. Your task is to determine the response of the safety system that prevented a railroad car from crashing into the station. A passenger car broke away from a train and rolled into the station because the brakes on the car failed. The safety system, a large horizontal spring at the end of the track, grabbed onto the car and prevented it from crashing into the platform. To determine the cause of passengers’ injuries, you need to know the frequency and amplitude of the car's oscillation after hitting the spring based on the car’s mass (1900 kg ) and speed (9 mph ) and the spring constant of the spring (3×104 N/m ). What is the amplitude of the car's oscillation?

Explanation / Answer

angular frequency

W=sqrt(K/m)=sqrt(30000/1900)=15.8 rad/sec

frequency

f=W/2pi=15.8/2pi

f=2.51 Hz

Amplitude

A=Vmax/W=(9*0.44704)/15.8

A=0.255 m or 25.5 cm

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