Question

Watch Out for Potholes! A car with a mass of 1,480 kg is constructed so that its frame is supported by four springs. Each spring has a force constant of 18,000 N/m. Two people riding in the car have a combined mass of 156 kg. Find the frequency of vibration of the car after it is driven over a pothole in the road. SOLUTION Conceptualize Think about your experiences with automobiles. When you sit in a car, it moves downward a small distance because your weight is compressing the springs further. If you push down on the front bumper and release it, the front of the car oscillates a few times. Categorize We imagine the car as being supported by a single spring and model the car as a particle . Analyze First, let's determine the effective spring constant of the four springs combined. For a given extension x of the springs, the combined force on the car is the of the forces from the individual springs. Find an expression for the total force on the car: F total = (−kx) = − k x In this expression, x has been factored from the sum because it is the same for all four springs. The effective spring constant for the combined springs is the sum of the individual spring constants. Evaluate the effective spring constant (in N/m): keff = k = N/m Use this equation to find the frequency of vibration (in Hz):

Answer 1

Step-by-step explanation:

Given that,

Mass of car

Mc = 1480 kg.

The car has four spring and each of them have a Spring constant.

K = 18,000N/m

Then, the total spring constant is.

K = 4 × 18,000 = 72,000 N/m

Combine mass of people riding in the car

Mp = 156kg.

Total mass is mass of car plus mass of individuals in the car

M = Mp + Mc

M = 1480 + 156

M = 1636 kg

Frequency of car?

F = 1 / T

Where F is frequency and T is period

The period is calculated using

T = 2π√(m/k)

T = 2π √ (1636/72,000)

T = 2π √0.022722

T = 0.947 s

So, the frequency is

F = 1 / T

F = 1 / 0.947

F = 1.06 Hz