Final answer:
To determine the spring constant (k) for a car's suspension system, Hooke's Law (F = -kx) is used, treating force (F) as analogous to y from the straight line equation and k as the slope (m). Given the force caused by an 80.0-kg person and the displacement of 1.20 cm, we calculate the spring constant to be 65,333.33 N/m.
Step-by-step explanation:
The question involves applying Hooke's Law to find the spring constant (k) of a car's suspension system using a provided graph of the restoring force versus displacement. Hooke's Law is mathematically similar to the equation of a straight line (y = mx + b), with force (F) being analogous to y, spring constant (k) to the slope (m), and displacement (x) to x, without the y-intercept (b) since the line passes through the origin. To determine the spring constant, we use the formula F = -kx, which describes the relationship between force and displacement in a spring system that complies with Hooke's Law.
The strategy to find the spring constant is based on the observation that when an 80.0-kg person settles into a car, it displaces the spring by 1.20 cm. We can convert this into meters (1.20 cm = 0.012 m) and calculate the weight force (w) exerted by the person using w = mg, with g being the acceleration due to gravity (9.80 m/s²). The force thus calculated can be substituted into Hooke's Law to solve for k.
Using the given values, we calculate the person's weight w = (80.0 kg)(9.80 m/s²) = 784 N.
Substituting w for F and 0.012 m for x in Hooke's Law, we have 784 N = k(0.012 m).
Solving for k, we find that the spring constant k = 784 N / 0.012 m = 65,333.33 N/m.