# What is the work required to stretch the spring from a length of 21 inches to a length of 26 inches if a spring has a natural length of 18 inches and a force of 20 lbs is required to stretch and hold the spring to a length of 24 inches?

Please check my maths and my units as I am...metric!!! :-)

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To find the work required to stretch the spring from a length of 21 inches to 26 inches, we need to calculate the work done in stretching the spring from 21 inches to 24 inches, and then from 24 inches to 26 inches.

First, let's find the work done to stretch the spring from 18 inches to 24 inches. The change in length is 24 inches - 18 inches = 6 inches. The force required to stretch the spring to a length of 24 inches is given as 20 lbs. So, the work done is:

Work = Force × Distance Work = 20 lbs × 6 inches

Next, let's find the work done to stretch the spring from 24 inches to 26 inches. The change in length is 26 inches - 24 inches = 2 inches. To find the force required, we can use Hooke's Law, which states that the force required to stretch a spring is directly proportional to the change in length.

So, the force required to stretch the spring by 2 inches can be calculated using:

Force = k × Change in length

Where "k" is the spring constant. We can find "k" using the information given for the force required to stretch the spring to 24 inches:

20 lbs = k × (24 inches - 18 inches)

Now, solve for "k".

Then, once you have "k", you can find the force required to stretch the spring from 24 inches to 26 inches:

Force = k × 2 inches

Finally, calculate the work done using the force and distance.

Add the work done in both steps to find the total work required to stretch the spring from 21 inches to 26 inches.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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