Chris,+Bret,+Rebecca

=What is the relationship between the mass on a spring and its period of oscillation?= =toc=
 * Group Members:** Rebecca Rabin, Chris Bickel
 * Period 4**
 * Date Completed:** May 23, 2011

-To directly determine the spring constant k of a spring by measuring the elongation of the spring for specific applied forces. -To indirectly determine the spring constant k from measurements of the variation of the period T of oscillation for different values of mass on the end of the spring. -To compare the two values of spring constant k. The relationship between the spring constant k and the m
 * PURPOSE**
 * HYPOTHESIS**

Materials: 1. Springs 2. Tape 3. Clamps and rods 4. Masses 5. Balance 6. Timers 7. Meter stick
 * PROCEDURE**

Set-Up and Methods: 1. Measure equilibrium point of hanger hanging off of he spring. 2. Add masses to hanger and record distance from equilibrium (repeat about 5 times) 3. Record data and graph to find slope (slope = spring constant) 4. Hang masses starting at 10 g on the hanging mass off the spring. 5. Pull it down and let it go. Time how long it takes the spring to oscillate 10 times. 6. Record date and graph to find spring force constant.




 * DATA AND GRAPHS**
 * Calculations**



(2π)^2 / k = slope 1 / k = slope / (2π)^2 k = (2π)^2 / 1.0463 k = 37.73

Percent difference:
 * 37.73-30.501| / 37.73 x 100 = 19.16%

1. Do the data for the displacement of the spring versus the applied force indicate that the data for the spring constant is indeed constant for this range of forces? Although we did have a great percent error, the two spring constants arrived from each method show great similarities. 2. Why is the time for more than one period measured? Human reaction time is not very precise and therefore timing ten oscillations and dividing by the time will be a more accurate average. 3. Discuss the agreement between the k values derived from the two graphs. Which is more accurate? Although each k value derived from the graphs were similar, neither was significantly more accurate to the theoretical value. 4. A spring constant k=8.75 N/m. If the spring is displaced -0.150 m from its equilibrium position, what is the force that the spring exerts? 5. A massless spring has a spring constant of k = 7.85 N/m. A mass m = 0.425 kg is placed on the spring, and it is allowed to oscillate. What is the period T of oscillation?
 * DISCUSSION QUESTIONS**


 * CONCLUSION**

= = =Transverse Standing Waves on a String=
 * Group Members:** Rebecca Rabin, Chris Bickel
 * Period 4**
 * Date Completed:** May 20 2011

What is the relationship between Frequency and the tension of transverse waves traveling in a stretched string? What is the relationship between frequency and harmonic number? What is the relationship between frequency and wavelength?
 * PURPOSE**

We hypothesize that as the tension of the string increases, the resonant frequency of the string will also increase. Also, as the harmonic number increases, the the resonant frequency of the string will also increase. We also hypothesize that as the frequency increases, the wavelength decreases due to the equation. Velocity is a constant so therefore if one variable increases the other variable must decrease to mathematically make this equation correct.
 * HYPOTHESIS**

Materials: 1. Electrically driven Oscillator w/ motor 2. Pulley & table clamp assembly 3. Selection of masses 4. String w/ loop on end for holding masses 5. Electronic Balance
 * PROCEDURE**

Set-Up and Methods 1. Clamp pulley and oscillator (with motor) to opposite ends of table 2. Attach string to oscillator and pull through pulley 3. Hang mass through loop end of string 4. Set the sine generator to its maximum altitude and turn on device 5. Change frequency until string is vibrating with a specific harmonic number. 6. Record frequency and wavelength. 7. Repeat steps 5 & 6 approximately 10 times. 8. Change amount of mass hanging from the end of the string. 9. Find the frequency that causes the string to vibrate with only one antinode at max altitude and record it. 10. Repeat steps 8 & 9 approximately 6 times. Frequency and Harmonic Number, Frequency and wavelength
 * DATA**

Frequency and Tension on string


 * SAMPLE CALCULATIONS**

1. Calculate the tension T that would be required to produce the n=1 standing wave for the red braided string. 2. What would be the effect if the string stretched significantly as the tension increased? How would that have affected the data? //As the tension increased and the string stretched significantly the elastic property of the wave would be affected and therefore change the speed of the wave. Due to the change of the speed, the frequency would be increased and the wavelength decreased.// 3. What is the effect of the type of string on the amount of hanging mass needed to create a set number of nodes? Explain this. //Each type of string has a different its unique elastic property and therefore requires a specific tension force. Therefore, the stronger the string, the higher the mass needed to attain the same tension as a weaker string.// 4. What is the effect of changing frequency on the number of nodes? //By increasing the frequency of a wave, the number of nodes increases as well.// 5. What factors affect the number of nodes in a standing wave? //The frequency of a wave affects the number of nodes however, tension affects the frequency of a wave. Thus, tension and frequency are the factors that affect the number of nodes in a standing wave.//
 * GRAPH**
 * DISCUSSION QUESTIONS**

gggggg The results of our experiment supported our hypothesis. We had predicated that both the relationships between harmonic number and resonant frequency and tension force and frequency were directly related. We also anticipated that frequency and wavelength would be inversely related. As is represented on the graphs of our data, one can tell that these statements remain accurate. gggggg There were almost no sources of error in this lab, as is conclusive from our fantastic r2 value of our trendline equations on our graphs. It is possible that the string’s physical properties had changed slightly due to excessive use, but this is hardly likely. Also, there is a chance we recorded the wrong frequency, although it would have only been off by .1hz. gggggg One very relevant real-life application of this data collection would be in bridge building. From this lab we learned that every material has its own resonant frequency, and that that frequency can change when the tension exerted on that material changes. The material we used in our lab was braided string, and we found that if we set the oscillator to 9.3hz with 9800N tension acting on the string, it would cause the string to vibrate at its maximum altitude. Hypothetically, this scenario could be replicated with any material, including the asphalt used to construct bridge surfaces. Thus, if the correct frequency was directed into the bridge (such as from gusts of wind), it would cause the bridge to oscillate and shake violently, potentially causing it to break. This scenario has occurred in the past with the Tacoma Narrows Bridge, and thus modern bridges undergo extensive testing to ensure safety.
 * CONCLUSION**

=Levers - Static Equilibrium= What is the relationship between the torques acting on an object at equilibrium?
 * PURPOSE **

The torques acting on an object at equilibrium will be equal. According to the second condition of equilibrium, the net torque must equal to 0 thus the torques acting on an object must be equal.
 * HYPOTHESIS **

Materials: 1. Meterstick 2. Pivot 3. Knife-edge level clamps 4. 3 mass hangers 5. Set of masses 6. Unknown mass 7. Balance 8. String 9. Masking tape
 * PROCEDURE **

1. Find the center of mass (COM) of the meter stick. 2. Use level clamp to keep meter stick on the pivot at the fulcrum. 3. Clamp two different masses to meter stick. 4. Use excel spreadsheet to determine proper distances of each mass to maintain equilibrium.
 * Set-Up and Methods: **
 * Trial 1 **

1. Find the COM of the meter stick and make fulcrum. 2. Use level clamp to keep meter stick on the pivot at the fulcrum. 3. Clamp three different masses to meter stick. 4. Use excel spreadsheet to determine proper distances of each mass to maintain equilibrium.
 * Trial 2**

1. Find point at least 20 cm off of COM to make fulcrum. 2. Use level clamp to keep meter stick on the pivot at the fulcrum. 3. Clamp two different masses to meter stick. 4. Use excel spreadsheet to determine proper distances of each mass to maintain equilibrium.
 * Trial 3**

1. Find point at least 20 cm off of COM to make fulcrum. 2. Use level clamp to keep meter stick on the pivot at the fulcrum. 3. Clamp one mass to meter stick. 4. Use excel spreadsheet to determine proper distance of mass to maintain equilibrium.
 * Trial 4**

1. Find point at least 20 cm off of COM to make fulcrum. 2. Use level clamp to keep meter stick on the pivot at the fulcrum. 3. Clamp unknown mass to meter stick at distance that maintains equilibrium. 4. Use excel spreadsheet with chosen distance to solve for weight of unknown mass.
 * Trial 5**

1. Set up by teacher. 2. Measure angle of tension, length of beam, and distance of mass from beam. 3. Use excel spreadsheet with given information to solve for torque.
 * Trial 6**


 * DATA:**

TRIAL 1: Two different masses with the fulcrum at the center of mass of the meter stick (COM). TRIAL 2: Three different masses with the fulcrum at COM. TRIAL 3: Two different masses with the fulcrum at least 20 cm off COM. TRIAL 4: One mass with the fulcrum at least 20 cm off of COM. TRIAL 5: One object of unknown mass, everything else to be determined by you. TRIAL 6: A single mass supported by a tension at an upward angle and a wall.
 * DIAGRAM AND CALCULATIONS**
 * ANALYSIS QUESTIONS**
 * 1. Does it get easier or harder to rotate a stick as a mass gets father from the pivot point?** It gets harder to rotate a stick as a mass gets farther from the pivot point.
 * 2. Does the weight of the mass increase as you move the mass away from the pivot point (your index finger)?** The weight of the mass does not increase because the equation for weight (w=mg) does not change based on position.
 * 3. Why is more mass required to balance the meter stick as you move another mass farther from the pivot?** To maintain equilibrium the torque forces on each side of the pivot must be equal as well. Therefore as the position of one mass becomes farther from the pivot point, the force on that side of the meter stick will become greater. To equal each side, more force (mass) must be added to balance the meter stick.
 * 4. Why must the mass of the hangers and clamps be taken into account in this experiment?** Due to their additional mass onto the meter stick, the hangers and clamps both produce a force. If these equations are not taken into account, we will not be able to solve for torque accurately.
 * 5. If you are playing seesaw with your younger sibling (who weighs much less than you), what can you do the balance the seesaw? Mention at least two things.** To balance this specific seesaw, the older sibling who weighs more could move closer to the center of the seesaw (fulcrum) or they could change the fulcrum of the seesaw closer to the edge in which the older sibling would be sitting.
 * 6. What kept the meter stick in equilibrium in the fourth trial? In other words, what counterbalanced the unknown mass?** In this trial, the pivot point was not at the center of mass and therefore the longer side had more force then the shorter side. Due to this the unknown mass was placed on the shorter side, adding force, and maintaining equilibrium. Thus, the counterbalance for the unknown mass was the lengths of the meter stick on each side of the pivot point.

From our data, we were able to prove our hypothesis correct. Our hypothesis that the torques will be equal was correct. From our data the net torque was 0 and both sides were equal to each other.
 * CONCLUSION**

There were very few sources of error in this lab, which is why we were able to get such accurate results. Our percent error was very minimal and very close to 0. We were able to use our givens to find the approximate lever arm for trials 1, 2, 3, 4.

The lab shows off a few ways for real life scenarios. In case you are trying to make a scaffold safe to walk around from edge to edge. You will able create the example and find the lever arm for the person to try to figure out far it is safe for the person to walk. Also in case you are trying to hold a sign at the end of a beam, you will able to figure out the lever arm where the wire must be placed to keep everything in place and not moving.