Final answer:
The spring constant of the spring is found using Hooke's Law and by applying the gravitational force of the bowling ball. By rearranging Hooke's Law to solve for the spring constant (k) and inserting the known values, we calculate that the spring constant is 125.046 N/m.
Step-by-step explanation:
The student's question involves calculating the spring constant of a spring that compresses by a certain distance under the influence of a known force. In this case, we can use Hooke's Law which states that the force (F) exerted by a spring is directly proportional to the displacement (x) from its equilibrium position and is given by the equation F = kx, where k is the spring constant.
To solve for the spring constant (k), we rearrange the formula to k = F/x. The force exerted by the bowling ball can be found by using the gravitational force equation F = mg, where m is the mass of the bowling ball and g is the acceleration due to gravity (9.8 m/s2). Therefore, the spring constant can be calculated as k = (m * g) / x.
Inserting the given values, we obtain k = (6.37 kg * 9.8 m/s2) / 0.5 m = 125.046 N/m. Thus, the spring constant of the spring must be 125.046 N/m.