Final answer:
The depression of the pickup truck under a maximum load of 1000 kg, with a spring constant of 1.30 × 10^5 N/m, is calculated using Hooke's Law and is found to be 7.538 cm.
Step-by-step explanation:
The bumper height requirements for trucks weighing between 3000 and 5000 pounds generally vary based on state laws and regulations. However, the question posed relates more to the physics of springs in a pickup truck's suspension. We are asked about how much the truck will be depressed by its maximum load of 1000 kg, given that the spring constant is 1.30 × 105 N/m.
To calculate the depression of the truck, we use Hooke's Law, which states that the force (F) exerted by a spring is directly proportional to the distance (x) the spring is stretched or compressed from its rest position, which is expressed as F = kx, where k is the spring constant.
In this scenario, the force applied by the load (F) is equal to the mass (m) of the load times the acceleration due to gravity (g), or F = mg. With the given mass of 1000 kg and the standard gravity constant 9.8 m/s2, the force would be 1000 kg × 9.8 m/s2 = 9800 N.
Therefore, we can rearrange Hooke's Law to solve for depression (x): x = F / k. Substituting the values we have, we get x = 9800 N / (1.30 x 105 N/m) = 0.07538 m, or 7.538 cm.