what would the length of a spring be if a 4 lb weight stretched a spring to 20in and a 16 lb weight stretched a spring 26in
To find the length of a spring under different weights, you can use Hooke's Law, which states that the elongation (change in length) of a spring is directly proportional to the applied force (weight in this case).
Let's denote:
- L1 as the initial length of the spring
- L2 as the length of the spring when a weight of 4 lb is applied
- L3 as the length of the spring when a weight of 16 lb is applied
From the information given, we have:
L2 = L1 + 20 inches
L3 = L1 + 26 inches
To solve for L1, we need to eliminate L1 from these two equations. We can do this by subtracting the first equation from the second equation:
L3 - L2 = (L1 + 26) - (L1 + 20)
6 inches = 26 - 20
6 inches = 6
Therefore, since 6 inches = 6 inches, we know that the initial length of the spring (L1) does not affect the stretch length. So, regardless of the initial length, when a weight of 4 lb stretches the spring by 20 inches, then a weight of 16 lb will stretch the spring by an additional 6 inches.
Hence, when a 16 lb weight is applied to the spring, the length will be 26 + 6 = 32 inches.