Question

Four people who each have mass 80 kg ride in a 1000kg car. The car travels on a road that has large bumps, equally spaced 16m apart. The car bounces on its spring suspension with maximum amplitude when traveling at 36 km/h. If the car stops, and the people get out, by how much does the car body rise on its suspension?

Answer 1

Given that speed of car = 36 km/hr = 36*5/18 = 10 m/sec

d = distance traveled between bumps = 16 m

T = time interval between each bumps = d/v = 16/10 = 1.6 sec

Now Time period in SHM is given by:

T = 2*pi/w = 2*pi*sqrt (M_net/k)

M_net = mass of car + people = Mc + 4*Mp

T = 2*pi*sqrt ((Mc + 4*Mp)/k)

k = (Mc + 4*Mp)*(4*pi^2)/T^2

k = (1000 + 4*80)*4*pi^2/1.6^2

k = spring constant = 20356.06 N/m

Now Compression on spring when people were inside will be given by:

Fnet = k*xi

xi = Fnet/k = (Mc + 4*Mp)*g/k

Compression on spring after people get out

xf = Mc*g/k

We need car's body rise during suspension, So

dx = xi - xf

dx = (1000 + 4*80)*9.81/20356.06 - 1000*9.81/20356.06

dx = 0.154 m = rise in the body of car

Let me know if you've any query.