Calculating Work Required to Stretch a Spring by Additional Distance

In summary, the conversation is about a problem involving a spring and the calculation of work needed to stretch it a certain distance. The person is having trouble getting the correct answer and asks for help. They explain their process of finding the spring constant and the total work needed, but are still getting the wrong answer. Another person points out a mistake in the units and suggests a simpler solution using the equations. The final answer is determined to be 48 J.
  • #1
RGBolton95
Hey everyone,

I'm really hoping somebody will be able to help me with this problem. I've searched all through my textbook, notes, and the Internet, but I keep getting the wrong answer. Here's the question:

If it requires 6 J of work to stretch a particular spring by 2.0 cm from its equilibrium length, how much more work will be required to stretch it an additional 4 cm?

I start by finding k, the spring constant. I do this by using the equation W = 1/2kx^2. I plug in the known values of work and x in the equation, which gives me 30,000 Nm (I changed 2 cm to 0.02 m). Now that I know k, I find the total work to pull the spring down 0.06 m (the original 0.02 m plus the additional 0.04 m). I use the same W = 1/2kx^2 equation, with W being the unknown, k = 30,000 Nm, and x = 0.06. This gave me a W = 54 J. From there, I know that to find the additional work needed to pull down the spring from 0.02 m to 0.06 m I should just subtract 6 J from 54 J, which gives me a final answer of 48 J. However, I keep getting told that this is the wrong answer. Any idea where I'm making my mistake?
 
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  • #2
Your result is correct.

You should double check the units of your spring constant though.

Note that you really do not need to compute the spring constant, it is sufficient to note that
$$
2W_2 = k x_2^2 = k(3x_1)^2 = 9kx_1^2 = 18W_1
$$
and therefore ##W_2 = 9W_1## and ##W_2-W_1 = 8W_1 = 8\cdot 6\ \mathrm{J} = 48\ \mathrm{J}##.
 

1. How do I calculate the work required to stretch a spring by additional distance?

To calculate the work required to stretch a spring by additional distance, you will need to use the formula W = 1/2kx^2, where W is the work, k is the spring constant, and x is the distance the spring is stretched. First, determine the spring constant of your spring, which is a measure of its stiffness. Then, measure the distance the spring is stretched by and plug in the values to the formula to calculate the work required.

2. What is the spring constant and how do I find it?

The spring constant is a measure of the stiffness of a spring. It is represented by the letter k and is measured in units of force per unit distance (N/m). It is typically provided by the manufacturer of the spring, but if you do not have this information, you can find the spring constant by dividing the force applied to the spring by the distance it is stretched.

3. Can I use the same formula to calculate the work for any type of spring?

Yes, the formula W = 1/2kx^2 can be used to calculate the work required to stretch any type of spring, as long as the spring is being stretched by a distance x and the spring constant k is known.

4. How does the work required to stretch a spring change with different spring constants?

The work required to stretch a spring increases as the spring constant increases. This means that the stiffer the spring, the more work is required to stretch it by a certain distance. Conversely, a less stiff spring will require less work to stretch by the same distance.

5. Is there a limit to how much a spring can be stretched and still obey Hooke's Law?

Yes, there is a limit to how much a spring can be stretched and still obey Hooke's Law. This limit is known as the elastic limit and is different for each spring. Once a spring is stretched beyond its elastic limit, it will no longer return to its original length when the applied force is removed, and Hooke's Law will no longer apply.

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