Question

the length that a hanging spring stretches varies directly with the weight placed at the end of the spring. if a weight of 22lb stretches a certain spring 5in. , how far will the spring stretch if the weight is increased to 42lb ?

Answer 1

The length that a hanging spring stretches varies directly with the weight placed at the end of the spring. Using direct variation, we can set up a proportion to find the length of the spring when the weight is increased to 42 pounds. Solving the proportion gives us a length of approximately 9.55 inches.

Step-by-step explanation:

To solve this question, we can use the concept of direct variation. According to the question, the length that a hanging spring stretches varies directly with the weight placed at the end of the spring. This means that we can set up a proportion between the weight and the length of the spring.

We can start by setting up the proportion: Weight1/Length1 = Weight2/Length2. Substitute the given values into the proportion: 22lb/ 5in = 42lb/ x.

Now we can cross multiply and solve for x: (22 lb)(x) = (42 lb)(5 in). Simplifying this equation gives us: 22x = 210. Dividing both sides by 22 gives us: x = 9.55 in. Therefore, the spring will stretch approximately 9.55 inches if the weight is increased to 42 pounds.