Phys1_05-Springs_152e618a-cf17-4e8b-8ac4-57b0bc38c36d

Slide 1 Hooke's Law and Spring Potential Energy Objectives Use Hooke's law to find the spring constant of both springs that came in your kit. Determine the spring potential energy of the smaller spring. Determine if energy is conserved after a collision. Physics Overview Hooke’s Law is defined as a restoring force in which the force needed to stretch or compress a spring is proportional to the amount the spring is stretched (or compressed). The distance that the spring is stretched (or compressed) is always measured from the equilibrium position and the constant of proportionality between the force and distance is known as the spring constant. This spring constant is a property of the spring and in effect measures the stiffness of the spring. A restoring force means that the direction of the force is always oriented so that the object is directed back towards the equilibrium position. This means that depending on the position of the object in relation to the equilibrium position, the spring force may be pointing in different directions. This is depicted in the picture below. The equation for Hooke's Law is shown below. The negative sign indicates the fact that this is a restoring force.

In this lab, the spring constant of two different springs will be discovered. In addition, we will use the spring constant to explore the potential energy of a spring. This energy can be found using the following equation: If you would like to further review Spring Potential Energy, you can watch this video: ConservationOfEnergy

Slide 3 Accelerometer (200 Hz) Remote 1 Ax Ay Az Time (s) 0 1 2 3 4 5 6 7 8 9 10 a (m/s²) -20 -15 -10 -5 0 5 10 15 20 ∆t: 3.90161 s μ: 0.046 m/s² — σ: 0.062 m/s² a: 0.179 m/s s: -0.02 m/s³ (r²: 0.08) μ: -9.806 m/s² — σ: 0.13 m/s² a: -38.260 m/s s: -0.01 m/s³ (r²: 0.00) μ: 0.155 m/s² — σ: 0.045 m/s² a: 0.603 m/s s: -0.00 m/s³ (r²: 0.01)   Force (200 Hz) Remote 1 Time (s) 0 1 2 3 4 5 6 7 8 9 10 Fᵧ (N) -5 -4 -3 -2 -1 0 1 2 3 4 5 ∆t: 3.90065 s μ: -1.981 N — σ: 0.073 N a: -7.726 Ns s: 0.05 N/s (r²: 0.69)  Rezero sensor  Finding the "Known" Value of the Mass Watch the video below to find out how to find the mass of the device. Please note that the iOLab mass will be needed in many future labs and you should remember the procedure you've done here in order to repeat it for those labs. 01 Finding the Mass of the Device

Here are some instructions in words: Take off the plate and attach the screw instead. Turn the device so that the y-axis is pointing downwards. Press record and let it sit there for 1 second. Then use the screw to lift the device. Hold it steady. Find the average force and acceleration (in the direction) once you have picked up the device. This will give you the force due to gravity and the acceleration due to gravity, respectively. Again, since the force of gravity is in the direction, you can uncheck the and the boxes.) Using the gravitational force equation, you can find the mass. Be certain that you include a sceenshot of your own data in your lab report in the "Analysis Mode", while highlighting the region over which you wish to average the data. Be certain to extract meaningful numbers into a clear table and explain in detail how you use the measurements to calculate the mass of your iOLab.

Select Parametric plot mode ( ) and use your mouse to highlight a section of the overlain plots on the bottom. You should remember how to use the parametric plotting tool from the lab on Force and Acceleration. Before moving on, consider the following question: Using Hooke's law, what does the slope of this parametric plot represent? Here is the procedure for this part of the lab: 1. Attach the screw to the force meter and the long spring to the screw. 2. Let the iOLab device hang from the spring. This is the equilibrium position. 3. Stretch the spring from the equilibrium and note which direction the device moves when first released. 4. Allow the device to return to equilibrium. 5. Compress the spring and note which direction the device moves when first released. 6. Use steps 2–4 to explain what a restoring force is. 7. On a horizontal table, while holding onto the end of the spring, press record and roll the cart back and forth. Be careful not to compress the spring all the way. 8. Using the parametric plot option, find the spring constant. Repeat this for a total of 3 trials (the next two slides will enable you to take trials 2 and 3). 9. Use the 3 trials to calculate the mean ( ) and sigma ( ) of the spring constant. You should put the parametric plot from one of the three trials into your lab report as well as a clear explanation of how you used the cursor to extract data points in order to determine the slope (spring constant). You should include a table that shows all three trials of measuring the spring along with the three values you get for the spring constant. Finally, your data table should show the mean ( ) and error on the mean of your spring constant.

Slide 5 Force [Fᵧ] vs Wheel - Position [rᵧ] (100 Hz) Swap axis Wheel - Position (m) -0.06 -0.04 -0.02 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 Force (N) -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 2 4 6 8 10 12 14 16 18 20  Trial 2: Finding the spring constant of the Long Spring Repeat what you just did to find the spring constant of the long spring.

Slide 7 Force [Fᵧ] vs Wheel - Position [rᵧ] (100 Hz) Swap axis Wheel - Position (m) -0.018 -0.016 -0.014 -0.012 -0.010 -0.008 -0.006 -0.004 -0.002 -0.000 0.002 Force (N) -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 2 4 6 8 10 12 14 16 18 20 22  Finding the spring constant of the Short Spring Attach the small spring to the force sensor. Watch the video below to find out how to find the spring constant of the small spring. 01 Small Spring Constant

Here is the procedure for this part of the lab: 1. Push the device into the fixed object. 2. Find the velocity before, the velocity after, and the peak force. 3. Use the peak force and the spring constant to calculate the change in position. 4. Use the spring constant found in the previous slide and the change in position to calculate the spring potential energy. 5. Using the velocity before the collision, find the kinetic energy of the device. (You need the mass of the device for this also.) 6. Using the velocity after the collision, find the kinetic energy of the device. Equations to keep in mind Your data should include the raw data plots with appropriate regions highlighted, tables of numbers used to determine both the MAX kinetic energy and MAX potential energy. You should determine whether your data support these first two numbers being equal.

Slide 9 Error Analysis Using the errors in mass and velocity, find the errors in the starting and ending kinetic energy. Remember to account for the constant. Questions to answer in your lab reports 1. How did you find the spring constant for both springs? 2. Was the slope of the Position vs. Force plots positive or negative? Does this make sense? Why or why not? 3. How did the kinetic energy before the collision, the spring potential energy, and the kinetic energy after the collision compare? Does this match expectations?