Term
| Purpose of Experiment 1 : (Two Triangles, a Ruler, and Calipers) |
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Definition
| The purpose of this experiment was to test error propagation. We measure the sides of two triangles, using vernier calipers and a ruler, to test the consistency of pythagoreans theorem. We are unable to "prove" anything experimentally, but we can test it's consistency. This consistency is quantified by the reduced kai squared. |
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| How precise is the ruler? |
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Definition
| The error for the ruler is about 5 mm |
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Term
| What is the precision of the vernier calipers? |
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Definition
| The error for the calipers is roughly 0.02 mm |
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Term
| Suggest a Technique which you could use to measure the length of the side of the triangle more precisely. |
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Definition
| You can measure the side of a triangle more precisely by using a interferometer, it measures the interference of light waves in small increments. |
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Term
Calculate d=pythagoreans then find h-d. Are the measurements consistent with pythagoreans theorem?
h=Measured Side
d=Calculated side |
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Definition
| Calculate d=[(a^2+b^2)^(1/2)] and it's uncertainty. Subtracting h-d gives you the range uncertainty. D in theory should be within c-d given it's uncertainty. |
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Term
| Can this experiment prove Pythagoreans Theorem? |
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Definition
| No, you can not ever experimentally prove any theory. You can only test its consistency. |
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Term
| Explain the purpose of experiment 2: (Pendulum) |
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Definition
| The purpose of the experiment was to determine the value of g using a pendulum as well as why the period of the pendulum does/ or does not depend on certain parameters. |
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Term
| Using a ruler how precisely can you measure the length of the pendulum? |
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Definition
| The error of the ruler is roughly 5 mm |
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Term
| Measure the time for 20 swings of the pendulum. What is it's period: the time for one swing. What is the error of the period? |
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Definition
| 1. Set up the Pendulum 2. Goto >> Lab Templates >> Plane Pendulum 3. Run a test for 20 swings 4. Goto analyze >> statistics (gives you the value of the stddev) 5. In excel determine the uncertainty of the mean period. =STDEV(T)/sqrt(#of periods) T= Avg Period |
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Term
| Why is it important to keep the angle small in this experiment? |
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Definition
| Using small angle approximation we can solve for equations of motion. If the angle were larger, there would be other variables we would have to consider when measuring frequency. Larger angles also affect the approximation that the period is independent from the amplitude. |
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Term
| Would you expect a more precise answer for a longer or shorter pendulum? |
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Definition
1. Use the equation for g on the formula sheet.
2. propagate the error using T and L
3. Both the values of T and L will increase while their values remain the same. This will give you a more precise answer for g. |
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Term
| What affect does the weight of the bob have? Could you use a much heavier bob or lighter one? |
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Definition
| The weight of the bob provides a restoring force on the pendulum. It increases tension but doesn't affect the frequency, period, or length. These variables are unaffected so the value of g remains the same. So you can use any weight for the pendulum. |
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Term
| What are the systematic errors and random errors? |
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Definition
Random Errors: Measuring the length of the pendulum, the stability of the table, air friction.
Systematic Errors: A calibration error in the equipment. i.e. the timer is off or the rulers tic marks are off. |
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Term
| Is the calibration error in the timer systematic or random? Can you overcome this by making more measurements? |
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Definition
| The calibration error of the timer is a systematic error because it is a consistent error that occurs in all measurements. You can not overcome this error, you will need to use a calibrated timer and repeat the collection of date. |
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Term
| Purpose of Experiment 3 (forced harmonic motion) |
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Definition
| We wanted to study the resonance in a system. We did this by measuring the amplitude and phase of a driven mass-and-spring oscillator. These measurements were used to determent the resonance (w0) and quality factor (Q). |
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Term
| What is the uncertainty of the drive frequency? |
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Definition
The drive frequency is A0 and max amp = X0
Error is: 0.005 to 0.01 Hz |
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Term
| How precisely can the variation amplitude be determined? |
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Definition
| The amplitude is determined by adding the mass to the end of the spring and measuring the change in length. The error is 0.5 mm to 1 mm. |
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Term
| How precisely can the phase be measure in this experiment? |
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Definition
| Set the phase as close to 0 degrees as possible. The error is roughly 2.5 to 10 degrees. |
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Term
| Sketch Phase and Frequency |
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Definition
| Phase(y) and Frequency(x) looks like S ranging from 0 90 180 degrees. |
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Term
| Sketch Amplitude and Frequency |
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Definition
| Amplitude (y) Frequency (x) looks like -parabola w0 is the peak. A0 is the start |
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Term
| Measure the resonant frequency using just the mass bar. |
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Definition
1. make sure the magnets aren't dampening the spring.
2. Do not turn on the oscillator
3. lightly pull on the mass and record the T
4. Use the equation w0=2pi/T |
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Term
| Measure the spring constant k. explain how you did this. |
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Definition
To measure the k factor use k=mg/A.
To find A measure the spring without the mass and then place the mass and measure the length. The difference of lengths is the Amplitude. |
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Term
| How do you reduce the resonant frequency? |
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Definition
| You can reduce the resonant frequency by adding more mass or using a spring with a smaller k value. |
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Term
| Suppose you wanted to increase the quality factor Q, how do you do this? |
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Definition
| Q=mW0/b Where b is the dampening. Increasing Q brings the system closer to resonant frequency. To do this you must decrease the dampening, you can do this by placing the system in a vacuum which reduces air resistance. |
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Term
| The purpose of experiment 5 (Tilted air-track) |
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Definition
| We wanted to test the position, velocity, and acceleration of the car acted by a constant force. (gravity) |
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Term
| Explain how the sonic ranger works. |
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Definition
| The sonic ranger uses a sound pulse that is emitted by a speaker. The sound hits the object and reflects back to the sensor. The sonic ranger measures the time it takes for the sound to return. |
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Term
| Suppose the air track is tilted at an angle of 0.01 rad from level. What will be the acceleration of the frictionless cart? |
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Definition
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Term
| What is the relationship of the tilt of the track and the acceleration of the cart? Define variables and make sketch. |
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Definition
| As sin(theta) increases the acceleration of the cart increases. |
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Term
| Find the angle if a 1 cm block is placed under 1 leg of the track. |
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Definition
| Using pythagoreans theorem find the length of 1 other side. Then use trig Sin(theta)=o/h o= 1 cm |
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Term
| Find the acceleration if a 1 cm block is placed under 1 leg of the air track. |
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Definition
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| How long will it take the cart to reach the bottom of the track? Assume the distance is 1.5 m from the bottom. |
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Definition
| Using kinematics df=d0+v0t+(1/2)a*t^2 assuming d0 and v0 are 0. d=(1/2)a*t^2 |
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Term
| Make hand drawn plots of position vs time and velocity vs time |
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Definition
| Velocity vs time graph looks like x=y. Position vs time is 1/2 a + parabola below velocity vs. time. |
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Term
| Graph Data for velocity vs time and acceleration vs time |
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Definition
| Assume v0 and a0 is 0. v=(xi-xi-1)/(ti-ti-1) |
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Term
| Purpose of Experiment 7 (Ideal Gas Law) |
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Definition
| The purpose of the experiment was to verify the ideal gas law. We first used the syringe attached to a sensor to test Boyle's law constant Temp PV=PV. We also tested Charle's Law constant volume P/T=P/T. |
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Term
| How precisely can you measure temp in the Charles Law apparatus? How precisely can you measure pressure? |
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Definition
| ΔP=P/500 and ΔT=.003T+.02 these are manufacturers uncertainties. To get the true values open Lab Temp >> Charles Law. Record P and T values. |
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Term
| At what temperature would you have to raise the Charles Law apparatus to double the pressure. |
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Definition
| Pi/Ti=Pf/Tf find Tf when Pf is two times Pi . Tf=2*Ti |
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Term
| What is the error of the thermometer? |
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Definition
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