Oscillations Car carrying four people find how much body rises

[GingerBread27]

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:

$$\omega_o=(2\pi\upsilon)/(\Delta(x))=(2\pi(17km/h)(1hr/60s)/(.004km)$$ This gives 445.059 rad/s.

I then tried to figure out k:

$$\kappa=(m1+m2)\omega_o^2=((1175 kg+(4*180kg))(445.059rad/s)^2$$ This gives 3.75e8.

Finally, I tried finding $$\Delta(x)=\Delta(F)/\kappa=(m_2*g)/(\kappa)=((180 kg*4)(9.8m/s^2))/(3.75*10^8)$$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!

 

[GingerBread27]

Help...Anyone lol...

 

[vtech]

your conversion for the first part seems to be off... recheck it... and make sure you convert to meter seconds... but you're on the right track

 

[mmayorga]

i just solved my homework problem with your equations and it worked. the only problem with your method is your unit conversions: to go from km/h to m/s you multiply by 1000/(60^2)

 

[asteriatic]

It looks like you have the right approach, but there may be some errors in your calculations. Here are some suggestions to check your work:

1. Make sure you are using consistent units throughout your calculations. In your first equation, you use kilometers per hour for speed, but in your second equation, you use meters per second. Make sure all your units are in the same system (either metric or standard) before plugging them into equations.

2. Double check your values for mass. In the problem statement, it says there are four 80 kg people, but in your calculations, you use four 180 kg people. This could be throwing off your final answer.

3. Check your conversions. In your first equation, you convert km/h to rad/s, but it looks like you may have forgotten to convert the distance from meters to kilometers. Make sure all your conversions are accurate.

4. Make sure you are using the correct formula for calculating the change in weight. In your final equation, you use the formula for calculating the change in force, but you need to use the formula for calculating the change in weight: \Delta(m)=m_1-m_2. This will give you the correct units for \Delta(x).

I hope this helps you find where you went wrong. Remember to always double check your units and conversions, and make sure you are using the correct formulas for the given situation. Good luck!