Hookes Law

[deleted-206773]

Hi my name is Nicholas and I have put together the Science buddies mechanical knee. My dad and I purchased the recommended spring 2-1/2" by .072 but this spring is too strong to have the gravity of the hip cause any stretch to it in order to measure Hookes Law. We are going to try and find a spring that allows it to stretch from the gravity and then fine tune the tension to the degree we wish to measure hookes law but we want to make sure that we are performing the science project correctly. You can push down on the hip but it will just spring right back up due to the tension on the spring recommended. Can you confirm that we are still heading in the right direction in purchasing a less tense spring to allow the weight of the hip to stretch the string.
thank you
Nicholas

[kgudger]

Hello and welcome to the forums.

I'm not sure what problem you're having exactly. From reading the experiment, it seems to me that the "leg" should move up and down in the track when the spring is not under pressure. The guitar tuner is used to stretch the spring. The way I understand the experiment, you are supposed to put the leg / knee at a desired angle, then adjust the guitar tuner and spring to hold the leg in that position. Are you saying that any tension on the spring causes the hip to rise to the top of the track? If this is the case, you could also try hanging a weight from the knee. Also, I see the materials suggest using a different (smaller) spring too, so you could do that.

Best, Keith

[deleted-206773]

Thank you for responding. We have put a more stiff spring into the mechanical knee. In order to calculate Hooke's Law my understanding is that I measure the spring at rest which is equal to K and then measure the spring under tension at my desired angle which is X. Is my Force know equal to -K (X) = Force?

[deleted-206773]

My son and I have placed the spring into the mechanical knee and have measured the spring at rest, which I understand is to be K value. We then measurde the spring at the desired knee bend angle 45 degrees and now measure the spring to determine the X by subtracting the spring at rest vs the stretched length and the difference is X.
NOW to calculate "F" force do we use -K*X = F or K * X = F.

[deleted-81235]

Hello,
So, Hooke's law is commonly defined as F=kx, where F represents the force needed to displace the spring, where k represents the spring constant (an intrinsic property specific to each spring), and x represents the total length the spring is displaced by. For example, if we have the spring below, the total force needed to displace the spring's length from 0 (the unaltered spring) to x (the second set up which has a force of F acting downwards on the spring, pulling or extending the spring), would be k*(x-0) or kx. (You will have to subtract the spring's initial length from its final length because Hooke's law relates force to the length that the spring is displaced (extended or compressed) by).


So, in order to calculate the Force, you must know the specific k value of your spring. It's fairly simple to experimentally determine. All you need to do is hang a spring scale (that measures force in Newtons (although it can be another unit, you'll just have to convert it into Newtons in your calculations) vertically, hang your spring on the spring scale's hook, and then hang a weight with a known mass on the other end of the spring. Using a meter stick, measure the new length of the spring and subtract the original length (the length of the spring before the mass was added to the spring) from the new length to get the total displacement (the x of F=kx). Next we need to calculate the force needed to displace the spring. We can do this by using Newton's second law of motion, or F=ma. The downwards force of the mass that we added to the spring was caused by the force of gravity pulling down on the mass which, since it was hooked to the spring, in turn pulled down on and extended the spring. Therefore, the force of gravity that acts on the spring is the same force that causes the spring's displacement (the F in F=kx). We can calculate this force by plugging in values into F=ma, which is commonly used to find the force of gravity on an object. To get this force, you must multiply the weight of the mass (in kg) times the acceleration due to gravity (a constant that is equal to 9.8 m/s^2). Now, we can solve for k by plugging in this value for F and the calculated spring displacement for x into F = kx.

Now, you will be able to calculate the force needed to displace the spring in your model by plugging in the k value we just calculated and by measuring the spring's displaced length, as you did, into F = kx.

The positive and negative signs in the equation F= kx/F =-kx refer to the direction of the force acting on the spring (since force is a vector, it has a numerical value and a direction in which it acts). If the spring is compressed, the force will be acting in the negative direction, and therefore will be negative. If the force causes the spring to expand or lengthen, then the force is acting in the positive direction, therefore giving us a positive force. Essentially, these two equations are the same. If you use my method of using Hooke's Law, you will always end up with the right sign because it involves subtracting the initial length from the final length of the spring, which tells you if the spring is lengthening or compressing.

I hope this helps!
Meg

[deleted-81235]

Hello,
I just saw that you posted this question here as well. I answered it in your newest post, but I'll notify a moderator and ask them to move it into this post so that everything is in one place.

-Meg

Please post again if you have any more questions

[amyC]

Hi -

We apologize if the directions for this project were a little confusing. You do not actually need to calculate the k value in order to follow the procedure exactly. Step 7 of the procedure states that:

7. For each spring, make a graph to show the length of the spring (y-axis) as a function of angle of the knee joint (x-axis).

The important thing to note here is that, according to Hooke's Law, the force in a spring is directly proportional to the displacement (or change in length from equilibrium):

Force = - (spring constant) x (displacement)
F = -kx

What does this tell you? It says that if you make a plot of displacement vs. knee angle, it will have the exact same shape as a plot of force vs. knee angle. If you multiply the displacement by k to calculate force, it will change the vertical scale of the graph, but not the shape. So, if you want to identify general trends like "which knee angle causes the highest force" and "which knee angle causes the lowest force," you can still do that with just a graph of displacement vs. knee angle; and do not actually need to use the k value to calculate force.

If you would like to go the extra step and use the k value to calculate force, you can certainly do so and that would be an impressive addition to your son's final project and display board. To do that, you would need to follow Megara7's advice above about how to calculate the k value.

Amy
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