A 93.0 kg person steps into a car, causing it to sink 2.3 cm. When the car goes over a road bump, the car and the driver vibrate at a frequency of 0.727 Hz. Assuming no damping, what is the mass of the car?
A: 1550B: 1810C: 1900D: 2780E: 3150F: 3400G: 8590H: 75000 Approach
When the person steps into the car and the car sinks by 2.3 cm due to the weight of the person being exerted on the springs. This allows the spring constant of to be calculated. Once the spring constant is known, the mass of the car can be calculated from the frequency of the spring formula.
From function NoFontMessage F=kx, the spring constant is k=xmg. Now for springs, the frequency of oscillation is given by f=1/2pi*sqrt(k/m) where m=mcar+mperson. Putting in the values, the mass of the car can be calculated.