Final answer:
The spring constant of the springs is 22752 N/m. The work done on the springs when the truck is loaded is 81.732 J.
Step-by-step explanation:
To find the spring constant of the springs, we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position. The formula for Hooke's Law is F = -kx, where F is the force exerted by the spring, k is the spring constant, and x is the displacement from the equilibrium position.
In this case, the displacement of the truck's rear is 8.5 cm (or 0.085 m) when a load of sand with a mass of 200 kg is placed in the truck. To find the spring constant, we can rearrange the formula to solve for k:
k = F / x = (mg) / x = (200 kg)(9.8 m/s^2) / 0.085 m = 22752 N/m
The spring constant of the springs is therefore 22752 N/m.
The work done on the springs when the truck is loaded can be calculated using the formula for work: W = (1/2)kx^2. Since the displacement of the springs is 0.085 m, we can substitute the given values into the formula to calculate the work:
W = (1/2)(22752 N/m)(0.085 m)^2 = 81.732 J
Therefore, the work done on the springs when the truck is loaded is 81.732 Joules.