Final answer:
The new force exerted by the floor on the box after substituting the weights can be calculated using Newton's second law of motion. The force is equal to the mass times acceleration. By converting the weights to mass and using the value of acceleration due to gravity, the new force is approximately 30.5 lb.
Step-by-step explanation:
To calculate the new force exerted by the floor on the box after substituting the 11.0 lb weight with the 30.5 lb weight, we can use Newton's second law of motion, which states that force is equal to mass times acceleration. We can assume that the acceleration remains constant.
Let's convert the weights to mass using the formula W = mg, where W is the weight, m is the mass, and g is the acceleration due to gravity (approximately 9.8 m/s²).
For the 11.0 lb weight, the mass is 11.0 lb / 9.8 m/s² ≈ 1.12 kg.
For the 30.5 lb weight, the mass is 30.5 lb / 9.8 m/s² ≈ 3.11 kg.
Since the weight is related to the force, the new force exerted by the floor on the box is approximately 3.11 kg * 9.8 m/s² = 30.5 lb * (9.8 m/s² / 9.8 m/s²) ≈ 30.5 lb.