Lab Assignment: Find the Linear Mass Density of the string.
Our Group's Plan: In order to find μ, we must find tension and velocity. To find velocity, we can measure wavelength and frequency. To find tension, we will hang a mass on the string and when the weight becomes still, the forces are balanced and the tension is therefore equal to the force of gravity.
Procedure:
1. We will first find the tension of the string. We found this by hanging a mass on the pulley and making sure the weight was still. Then, the force of tension is equal of to the force of gravity.
2. To find the velocity, we must find the wavelength and frequency.
3. We adjusted the oscillator to the second harmonic.
4. We know the frequency, given by the oscillator, and the wavelength is the length of the string, because it is the second harmonic.
5. We then measured the string to find wavelength.
6. We used the equation v = λf to find the velocity.
7. Now that we have the velocity and tension force we can solve for the Linear Mass Density. The equation is below, followed by pictures of the lab.
1. We will first find the tension of the string. We found this by hanging a mass on the pulley and making sure the weight was still. Then, the force of tension is equal of to the force of gravity.
2. To find the velocity, we must find the wavelength and frequency.
3. We adjusted the oscillator to the second harmonic.
4. We know the frequency, given by the oscillator, and the wavelength is the length of the string, because it is the second harmonic.
5. We then measured the string to find wavelength.
6. We used the equation v = λf to find the velocity.
7. Now that we have the velocity and tension force we can solve for the Linear Mass Density. The equation is below, followed by pictures of the lab.
Credit to Lab Partner Kathleen for the pictures.
Results
After performing the calculations described with both 300g and 350g, we found the Linear Mass Density to be 0.002449 kg/m.
Conclusion
Based on our data and calculations, we can be confident in the value we found for Linear Mass Density. Thinking practically, our number makes physical sense because it is a very small number, as the string has little mass but has a lot of length. We can have even more confidence in our result because we repeated our experiment for two different masses and found very similar values.
Evaluating Procedures
One possible source of uncertainty is if we accurately found the second harmonic. Visually, it looked like there were obvious nodes and antinodes for the second harmonic, but it is possible the frequency was slightly off, making our velocity slightly off. Another possible source of uncertainty is that we didn't take into account the friction force exerted by the pulley, which would affect our tension force calculation.
Improving the Investigation
We could have tested the Linear Mass Density for more than the two masses we actually did. We could have also performed tests at different harmonics and seen if the Linear Mass Density stayed the same.