Final answer:
To find the spring constant, equate the gravitational potential energy lost by the bowling ball to the elastic potential energy of the spring when compressed. Solve for the spring constant using the equation GPE = 0.5 * k * x² where GPE equals the product of the ball's mass, gravitational acceleration, and height dropped, and x is the spring compression.
Step-by-step explanation:
To find the spring constant of the spring for a 7.08 kg bowling ball dropped from 2.10 m and compressing the spring by 0.525 m, we can equate the gravitational potential energy lost by the ball to the elastic potential energy stored in the spring when compressed.
The gravitational potential energy (GPE) lost by the ball is GPE = mgh, where m is mass, g is the acceleration due to gravity (approximately 9.81 m/s²), and h is the height.
GPE = (7.08 kg)(9.81 m/s²)(2.10 m)
The elastic potential energy (EPE) of the spring is EPE = 0.5 * k * x², where k is the spring constant we want to determine, and x is the compression of the spring.
EPE = 0.5 * k * (0.525 m)²
Since GPE = EPE, we can solve for k: k = (2 * GPE) / (x²)
k = (2 * (7.08 kg)(9.81 m/s²)(2.10 m)) / (0.525 m)²
Now, we just calculate using the values provided:
k = (2 * (7.08 kg) * (9.81 m/s²) * (2.10 m)) / (0.275 m)²
Calculate the values in the numerator and denominator separately and then divide to find the spring constant k.