Your friends are travelling at 100 km/hr in a 1081 kg car with broken shock absorbers down a smooth concrete highway in Japan. Not unexpectedly, an earthquake hits lasting 1.45 minutes with changing intensity. Naturally, your friends are wearing their seatbelts and are being pushed about so forcefully that Susie, the driver of the car, pulls over to the side of the road and tries to stop. Unfortunately, the broken shock absorbers were not dampening the oscillation making Betty and Ken feel quite upset having never experienced such an intense tremble. George, has a body mass of 88.1 kg and a height of 186 cm, is an expert of vibration and estimates that the max amplitude occurred when the shaking reached about 1.7 Hz. Betty measures 65.3 kg and 169cm, Ken 79.1 kg and 179 cm, Susie 61.5 kg and 171 cm.When the car comes to a halt, they leave the car as fast as they can.
By what distance do the car's four undamaged coil springs raise the car's body as your friends get out?
To determine the distance by which the car's undamaged coil springs raise the car's body as your friends get out, we need to understand the relationship between the spring constant and the displacement of the spring.
The equation for the displacement of a spring is given by Hooke's Law:
F = k * x
Where:
F is the force applied by the spring,
k is the spring constant,
x is the displacement of the spring.
In this case, the displacement of the spring is what we are trying to find. We can rearrange the equation to solve for x:
x = F / k
To find F, we need to calculate the force applied by each coil spring. The force exerted by a spring is given by:
F = k * d
Where:
k is the spring constant, which we'll assume to be the same for all four coil springs,
d is the deflection or compression of the spring.
Since the car is at rest, the force applied by the coil springs must be equal to the weight of the car and its occupants:
F = m * g
Where:
m is the total mass of the car and occupants, and
g is the acceleration due to gravity (approximately 9.81 m/s²).
Now we can substitute F in the equation for x:
x = (m * g) / k
To calculate the displacement, we need to determine the spring constant (k), which depends on the characteristics of the coil springs. Unfortunately, the problem does not provide this information. Therefore, it's not possible to determine the exact distance by which the car's undamaged coil springs raise the car's body when your friends get out without additional information.
However, if you were provided with the spring constant (k) for each coil spring, you could calculate the displacement using the equation mentioned above.