Question

The length that a hanging spring stretches varies directly as the weight placed at the end of the spring. If a weight of 7 lb stretches a certain spring 15 in., how far will the spring stretch if the weight is increased to 31 lb? Round your answer to the nearest integer if necessary.

Answer 1

The stretch length of the spring with a 31 lb weight will be approximately 66 inches, which is found by using direct variation based on the initial scenario where a 7 lb weight stretches the spring to 15 inches.

Step-by-step explanation:

The length that a spring stretches varies directly with the weight placed on the end, according to Hooke's Law. In the given scenario, a weight of 7 lb stretches the spring 15 in. We can use the direct variation to find out how far the spring will stretch with a weight of 31 lb. To solve this, we set up a proportion using the known length and weight (15 in. / 7 lb = x in. / 31 lb). Solving for 'x' gives us the stretch length for the 31 lb weight.

By cross-multiplying and dividing by 7 lb, we get x = (15 in. * 31 lb) / 7 lb. The calculation leads to x = 66.4285714 in. Rounding this to the nearest whole number, we find that the spring will stretch approximately 66 inches with a 31 lb weight attached. This demonstrates the direct proportionality between weight and stretch length for a spring.