Spring Constant Lab

AP Physics 1 Name _ Joelle Calugay______
An experiment to obtain and compare the spring constants of 3 strings (soft, medium, and hard) obtained in 2 ways (using the energy chapter and the dynamics chapter), to confirm that Hooke’s Law is valid over a range of initial displacements, and to find the acceleration due to gravity on unknown Planet X.
Problem: What are the spring constants of 3 strings (soft, medium, and hard) and how do they compare?
Theory: To find the spring constants of each string, we can calculate the velocity that the string is moving at with the equation: v= d/t
Since the mass will experience both kinetic and elastic potential energy, and since energy is conserved, you can set both equations equal to each other and solve for the spring constant
EPE= 1/2kx2 KE= 1/2mv2 1/2kx2=1/2mv2
We can also find the spring constants of each string using Hooke’s Law, F=-kx

Materials: 3 different strings (soft, medium, and hard), lab stand, hooked masses, stopwatch, and meterstick
Procedure:
1. Determine a mass to hang on the lab stand, which happened to be 100 g, or .1 kg.
2. Find the distance it travels from equilibrium for a hanging mass on a soft string.
3. Find the time it takes to travel the distance.
4. Calculate the velocity using v=d/t.
5. Using velocity, plug it into the equation, 1/2kx2=1/2mv2
6. Since Fg=mg, and F=Fg, F=mg, so F=-kx becomes mg=-kx, and we can solve for k.
7. Repeat steps 2-6 for the medium and hard strings.
8. To find acceleration due to gravity on Planet X, we can use mg=-kx using one of the constants we found and solve for g.

String
Distance
Time
Spring Constant
Soft
.73m
1.44s
1.34
Medium
.33m
.64s
2.97
Hard
.16m
.34s
6.13

Distance
Time
Acceleration
Planet X (medium string)
.21m
.62s
6.2 m/s2

Conclusion:
Based on this lab, I found out that you can find the spring constant in a mass-string system using both equations from the energy and dynamics chapter. I also found out that the amplitude does not affect the period because T=2π and the amplitude is not used in the equation, therefore, it does not affect the system. During the calculation process, there could’ve been human error such as not getting the time exact.

Questions:
1. Which factors can affect the results?
Factors such as thermal energy and friction can make this lab incorrect. Having the energy not being entirely conserved because of the missing factors could potentially change what the answer is supposed to be.
2. Can we apply the major result in daily life? Explain.
We could apply the major result in daily life. When playing with a slinky or any type of string and attach a ball to it, you can apply what you learned about how the softness of the string can differentiate the constant of others. When you see a mass hanging on a spring moving up and down continuously, you can apply what has been learned from this lab to that moment as well.