A car with bad shocks has a mass of 1500 kg. Before you go for a drive with thre

Question

A car with bad shocks has a mass of 1500 kg. Before you go for a drive with three of your friends you notice that the car sinks a distance of 6.0 cm when all four of you get in the car. You estimate that the four of you together have a mass of 347? kg. As you are driving down the highway at 65 mph you notice that the car is starting to bounce up and down with large amplitude. You realize that there is a periodic series of small bumps and dips in the road that is driving the bouncing. What is the distance (in meters, to two significant figures) between adjacent bumps on the road, assuming that damping by the shocks is negligible?

Explanation / Answer

distance between adjacent bumps=VxT
now
Assuming the behaviour of car to be similar to that of spring
force F=mg=kx

==>267*9.8=k*0.06

where k is the spring constant

==>k=43610
Time period of oscillation of car=

T=2??(m/k)=2??(1500+267)/43610=1.27068s

Now ,velocity of car=65mph=65*1.61km/h=65*1.61*1000/3600m/s

=29.1m/s

?distance between adjacent bumps=29.1*1.27068

=36.97687366443452

=37m.......ANS

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