The spring stretches from 10cm to 22cm when a force of 4N is applied.if it obeys Hooke's law ,its total length in cm when a force of 6N is applied is?

Answer 1

According to Hooke's law, the force applied is directly proportional to the extension of the spring. Mathematically, this can be represented as:

F = kx

where F is the force applied, k is the spring constant, and x is the extension of the spring.

To find the spring constant, we can use the given information that the spring stretches from 10cm to 22cm when a force of 4N is applied. The extension of the spring is:

x = 22cm - 10cm = 12cm = 0.12m

The force applied is 4N, so we can rearrange the equation to solve for k:

k = F/x = 4N / 0.12m = 33.33 N/m

Now, we can determine the extension of the spring when a force of 6N is applied. Rearranging the equation, we have:

x = F/k = 6N / 33.33 N/m = 0.18m

To find the total length of the spring, we add the original length to the extension:

Total length = Original length + Extension
Total length = 10cm + 18cm = 28cm

Therefore, when a force of 6N is applied, the total length of the spring is 28cm.