I tried doing this problem but couldn't get the right answer. I don't get how the answer is 2.19cm. Is the distance referring to the vertical or horizontal distance
Four people, each with a mass of 73.5 kg, are in a car with a mass of 1190 kg. An earthquake strikes. The driver manages to pull of the road and stop, as the vertical oscillations of the ground surface make the car bounce up and down on its suspension springs. When the frequency of the shaking is 1.50 Hz, the car exhibits a maximum amplitude of vibration. The earthquake ends and the four people leave the car as fast as they can. By what distance does the car's undamaged suspension lift the car's body as the people get out?
Wo = sqrt(k/m)
2 pi * 1.5 = Wo = 9.42 radians/s
so
9.42 = sqrt (k/(1190+4*73.5) )
88.8 = k/1484
k = 131,780 Newtons/meter
newtons lost = 4 * 73.5 * 9.81 = weight (not mass) of people
newtons lost = 2884 Newtons
elongation = F/k = 2884/131,780 = .022 meters = 2.2 centimeters, about an inch
why are we using the newton lost but not the newton remaining
To solve this problem, we need to apply the concept of resonance frequency. Resonance occurs when an object is subjected to a periodic force at its natural frequency, causing it to vibrate with a maximum amplitude.
In this case, the car is vibrating vertically with a frequency of 1.50 Hz. The maximum amplitude refers to the maximum displacement of the car from its equilibrium position.
To find the distance the car's undamaged suspension lifts the car's body as the people get out, we can use the formula:
Amplitude = (mass * gravity * displacement) / (spring constant)
Where:
- Amplitude is the maximum displacement of the car's body (given).
- Mass is the total mass of the car and the four people (1190 kg + 4 * 73.5 kg).
- Gravity is the acceleration due to gravity (approximately 9.8 m/s^2).
- Displacement is the distance we want to find.
- Spring constant is a measure of the stiffness of the car's suspension system.
By rearranging the formula, we can solve for the displacement:
Displacement = (Amplitude * spring constant) / (mass * gravity)
Since we have the amplitude (maximum displacement) given in the problem (2.19 cm) and the mass of the car and people, we need to find the spring constant. Unfortunately, the problem does not provide the spring constant, so we cannot calculate the displacement without that information.
Therefore, the answer cannot be determined without knowing the spring constant of the car's suspension system.