Please answer the questions at the bottom of the page. You will need to also use those simulations provided down below. Any help is greatly appreciated thank you!

Determining the force constant for a spring

Intro: When no force is imparted on a spring it is at its EQUILIBRIUM position. To contract it or expand it takes ELASTIC force. The more it is stretched or compressed (the higher its displacement) the more force must be applied. The force can be described as F = kx (Hooke's Law), where x is the displacement (either compression or extension from the equilibrium position) of one end of the spring, and k is a constant that is unique for each spring. The purpose of this lab will be to explore the behavior of springs and determine their force constants, both qualitatively and quantitatively.

Note that Hooke's law is less of a law, and more of an equation that is pretty accurate when the displacement x falls between certain values. Not all springs follow this ideal behavior. For example, when any spring gets stretched too far it will reach a length that is a maximum, and it can't stretch any farther, regardless of how much more weight you add. Ideally, a force vs displacement graph will be a straight line, but it will start to curve upwards if the spring stretches (or compresses) a lot.

Procedure: You will use the Phet simulations "Hookes Law" and "Masses and Springs." The first ishttps://phet.colorado.edu/sims/html/hookes-law/latest/hookes-law_en.html . Check the boxes on the right to see values for displacement, force, etc... Identify where the equilibrium position is. Set the slider bar on the bottom so that the spring constant (force constant) is 500 N/m and set the applied force slider bar to 10 N. Measure the displacement of the spring. Adding 10 N at a time, record the displacement for several amounts of force (10N, 20N, 30N... ), and graph the result, with F on the y axis, and displacement on the x axis (it is given the variable x anyway). You won't need to ever show this graph to anyone, but just find its slope. How does that compare to the force constant? Do some more experimentation. Try compressing as well as stretching. How does the displacement compare when you COMPRESS with, say, 37 N as opposed to STRETCHING with 37 N?

Go to the second simulation,https://phet.colorado.edu/sims/mass-spring-lab/mass-spring-lab_en.html. You will need to find the force constant of the spring on the left, so you will need to make at least one measurement of displacement with one known weight. (You can check boxes to see lines where the equilibrium positions are, both with and without weights) Find the spring constant by solving F=kx for k, remembering the F is mg.

Now find the mass of the green/ blue (midsize) hanger block. You have by now found k for spring #1 on the left and you can measure the displacement, x, with the ruler. Using Hooke's Law equation you can find F, but this is NOT the mass (see analysis below). Find the mass using F=mg.

You can play around with changing the spring constant and see how the appearance and behavior of the spring changes.

Analysis: The force on the spring is not equal to the mass on it. It is equal to the WEIGHT on it. A 10 g mass has weight/force of 0.01kg * 9.8 m/s² = 0.098 N, for example. Look back at your F vs. x graph. Hooke's law (F=kx) is an equation in the form y = mx + b (b is 0). This is an equation that, when graphed, should produce a straight line whose slope should be the force constant, k! See this video for more about Hooke's Law and a F vs. x curve:https://www.youtube.com/watch?v=O2EZEhBFWQg . Note: here he does an example of solving for force (not too hard, the equation is already solved for F) and x (involves re-arranging the equation). You will have to solve for k (also involves re-arranging the equation). Also note that in his F vs. x graph, the graph flattened out when entering a "plastic region." His object (not a spring) may be more like a piece of taffy once enough force is added and it starts to "break." In this plastic region, the object will essentially continue to stretch out if only tiny amounts of force are added (like taffy) and it gets easier to stretch. This is not the behavior of a spring. With a lot of force added, the spring reaches its length limit where it is more like a straight line instead of coils. It is not reaching a "plastic" limit where the integrity of the material starts to break down. The spring will actually get harder to stretch, and the graph of F vs x will curve up.

Report/Questions:(the Q's for your report in Canvas will be very similar to these)

Hooke's Law:

0. Does a higher force constant / spring constant (k) mean a spring will stretch more or less with the same amount of applied force?

a. more b. less c. same

1. How does the slope of the F vs. x graph compare to the force constant?

a. same b. double c. half d. square of k

2. How does the displacement compare when you COMPRESS with, say, 37 N as opposed to STRETCHING with 37 N?

a. same b. double c. half d. square of stretching x

Masses and Springs:

3. Without doing any math or measurements, just by playing with the simulation, answer this: a spring with a higher spring constant will be.... a. thicker and have higher displacement b. thicker and have lower displacement c. skinnier and have higher displacement d. skinnier and have smaller displacement.

4. What is the default force constant of spring #1, BEFORE YOU CHANGE the value? Hint: solve for k and remember, mass is not force! a. 6 N*m b. 98 kg/m c. 0.2 m/kg d. 10 N/m

5. What is the slope of the graph of F vs. x for spring #1? a. 3 b. 10 c. 6 d. 49

6. What is the relationship of the value of the slope of the F vs. x curve to the value of the force constant? (Hint: By the way, Hooke's law is an equation for a line in the form y = mx + b (b is 0). What variable is m here, F or k? And what is so special about m? Hint for future question you will see very soon: Hooke's law could not be put into a form where x is squared, because the graph of an equation where x is squared will curve upwards)

a. slope is equal to k b. slope is one tenth k c. slope is ten times k. d. slope is half k

7. What units could your force constant be in? a. N*m b. kg/m c. m/kg d. N/m

8. What force does the green/ blue (midsize) block impart on spring #1 on the left? a. 120 N b. 1.5 N c. 0.02 N d. 49 N

9. What is the mass of the green/ blue (midsize) block (use what you know about how to find weight from mass, and work backwards, or just solve the equation for m)? a. ~0.15 kg b. ~0.4 kg c. ~0.05 kg d. ~100 kg

10. Find/remember the equation for potential energy in a spring. If the displacement of your spring doubles from 0.10 m to 0.20 m the potential energy held in your spring: a.) also doubles b.) quadruples c.) increases by a factor of 1.414 d.) is cut in half.

11. You would expect to get a graph that curves upward (not a straight line) for (select all that apply) a. a graph of F vs x for a spring acting ideally b. PE in spring vs x c. A graph of F vs x where there is so much force on the spring that it has stopped acting ideally. d. your graph of F vs. x that only includes small displacements with small masses added.

12. If you were going to use Hooke's Law to calculate the mass of the very heavy block, would it be best to hang it from a spring with high or low force constant? (keep in mind the non-ideal nature of springs, and that they stop following Hooke's Law at some point) a. higher b. lower c. It will never work regardless. There is no hope trying. d. there is no option d. A vote for d is a vote for anarchy.

Bonus: What is the PE in the spring #1 on the left, with initial force constant, at displacement 0.10 m? (This could maybe help you with question number 10.) Hint: Find/ remember an equation for elastic potential energy. a. 0.03 J b. 3.92 J c. 4.12 J d. 12.7 J