A car with a total mass of 1800kg (including passengers) is driving down a washboard road with bumps spaced 4.4m apart. The ride is roughest
The force that the spring exerts is k*x, where x is the distance
of compression.
If the spring is compressed an infinitesimal distance dx, the
energy required to do this is:
dE = F*d = (k*x)*dx
If the spring is compressed a finite distance d, the total energy
required would be given by the integral of this equation from x=0
to x=d:
E = integral of {k*xdx) from x=0 to x=d
= 1/2*k*x^2 (evaluated from x = 0 to x=d)
= 1/2*k*d^2
If the car is stopped completely, then all of its kinetic energy is
captured by the spring, so
1/2*m*v^2 = 1/2*k*d^2, or
m*v^2 = k*d^2, or
k=m*v^2/d^2
= (1800kg)*((5.5)*(5.5)/(4.4)^2
=54450/19.36
= 2812.5 N/m
A car with a total mass of 1800kg (including passengers) is driving down a washboard road...
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