Final answer:
Using Hooke's Law, the displacement of the pickup truck's springs under a 1000 kg load is calculated to be 7.55 cm. The spring constant is 1.30 × 10⁵ N/m, and the force exerted by the load is 9810 N.
Step-by-step explanation:
The question is about calculating the displacement of vehicle springs under a load, which is a problem related to Hooke's Law in physics. Hooke's Law states that the displacement of a spring is directly proportional to the force applied to it, assuming the spring is within its elastic limit. This can be represented by the formula Δx = F / k, where Δx is the displacement, F is the force, and k is the spring constant. In this case, the maximum load of the vehicle is 1000 kg, which will exert a gravitational force (weight) equal to the mass multiplied by the acceleration due to gravity (F = m × g, with g approximately 9.81 m/s²).
The spring constant is given as 1.30 × 10⁵ N/m. To find the displacement, we first calculate the force exerted by the 1000 kg load: F = 1000 kg × 9.81 m/s² = 9810 N. Next, we use Hooke's Law to find the displacement: Δx = 9810 N / (1.30 × 10⁵ N/m) = 0.0755 m or 7.55 cm. Therefore, the truck's springs will be depressed by 7.55 cm under the maximum load.