Question

Compact car has a mass of 1260 kgkg . Assume that the car has one spring on each wheel, that the springs are identical, and that the mass is equally distributed over the four springs.

A. What is the spring constant of each spring if the empty car bounces up and down 1.6 times each second?Express your answer using two significant figures.in N/m.B. What will be the car's oscillation frequency while carrying four 70 kg passengers?Express in two sig figs in Hz.

Answer 1

Answer

given,

mass of the car, m = 1260 Kg

mass on each spring = 1260/4 = 315 Kg

a) frequency, f = 1.6 Hz

  spring constant, k = ?

  $f = \dfrac{1}{2\pi} \sqrt{\dfrac{k}{m}}$

squaring both side

  $k = 4 \pi^2 f^2 m$

  $k = 4 \pi^2\times 1.6^2\times 315$

      k = 3.18 x 10⁴ N/m

b) frequency of the spring if 4 mass of 70 Kg sit in the car

  mass on each spring, $m = \dfrac{1260 + 4\times 70}{4}$

              m = 385 Kg

 now,

$f = \dfrac{1}{2\pi} \sqrt{\dfrac{k}{m}}$

$f = \dfrac{1}{2\pi} \sqrt{\dfrac{3.18\times 10^{4}}{385}}$

      f = 1.45 Hz

hence, frequency of the spring is equal to 1.45 Hz