- #1
GingerBread27
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A 1175 kg car carrying four 80 kg people travels over a rough "washboard" dirt road with corrugations 4.0 m apart which causes the car to bounce on its spring suspension. The car bounces with maximum amplitude when its speed is 17 km/h. The car now stops, and the four people get out. By how much does the car body rise on its suspension owing to this decrease in weight?
I first tried figuring the natural frequency of the car:
[tex]\omega_o=(2\pi\upsilon)/(\Delta(x))=(2\pi(17km/h)(1hr/60s)/(.004km)[/tex] This gives 445.059 rad/s.
I then tried to figure out k:
[tex]\kappa=(m1+m2)\omega_o^2=((1175 kg+(4*180kg))(445.059rad/s)^2[/tex] This gives 3.75e8.
Finally, I tried finding [tex]\Delta(x)=\Delta(F)/\kappa=(m_2*g)/(\kappa)=((180 kg*4)(9.8m/s^2))/(3.75*10^8)[/tex]This gives 1.8e-5 m, or .00188 cm, this is wrong, where did I go wrong? Help!
PS This is the first time I use Latex so if it looks odd I'm sorry!
I first tried figuring the natural frequency of the car:
[tex]\omega_o=(2\pi\upsilon)/(\Delta(x))=(2\pi(17km/h)(1hr/60s)/(.004km)[/tex] This gives 445.059 rad/s.
I then tried to figure out k:
[tex]\kappa=(m1+m2)\omega_o^2=((1175 kg+(4*180kg))(445.059rad/s)^2[/tex] This gives 3.75e8.
Finally, I tried finding [tex]\Delta(x)=\Delta(F)/\kappa=(m_2*g)/(\kappa)=((180 kg*4)(9.8m/s^2))/(3.75*10^8)[/tex]This gives 1.8e-5 m, or .00188 cm, this is wrong, where did I go wrong? Help!
PS This is the first time I use Latex so if it looks odd I'm sorry!