Activphysics Activities

Introduction

             The purpose of this activities is to understand the theory of relativity of time and length. In this activities, some of the relativity theories will be simulated in the activities.

Activities

Questions on Relativity of Time

1. The distance of the stationary light clock is shorter than that of the moving clock as shown in picture above.
2. The time of the moving clock is greater relative to a stationary frame of reference than the stationary clock.
3. In the moving frame of reference, the time interval of the light of the moving clock is the same as the stationary clock
4. As the velocity of light clock decreased, the time interval difference will also decrease.
5. delta_t = 1.2 * 6.67 µs = 8.00µs
6. gamma = 7.45 / 6.67 = 1.12

Questions on Relativity of Time

1. The round trip is independent of the velocity
2. The round trip time interval will be longer observed from earth since there will be a value for gamma.
3. It can't be equal since by saying it is equal, it means there is no time dilation.
4. L = 1000 / 1.3 = 769m

Lenses

Purpose
            The purpose of this lab is to be able to analyze the characteristic of a converging lens to the image. In this experiment, a lens with measured focal length will be set in front of a light source and the image obtained from the light source. In this experiment, the distance from lens to light source and the lens from the image is measured. The image is measured when focus is achieved.

Experimental
   
The setup for the lab is as follow

Setup of the lab

different angle of the setup

The shape of the image

Measurement of the image distance

Light source for part 2 using different object

The image of the object used

Data and Analysis

Focal Length = 20cm ± 0.5cm

Object distance (cm)	Image distance (cm)	Object height (cm)	Image Height (cm)	M	Image Type
100	23	5.1	1.7	0.333	Inverted, real
80	24.5	5.1	2	0.392	Inverted, real
60	28	5.1	2.5	0.490	Inverted, real

Conclusion
                Based on the result obtained, the object and image distance is indeed have an inverse relationship as shown in the first graph. On the second graph, we shows that it has linear relationship between the inverse image versus the negative inverse object distance. Since we didn't have the time to complete the actual lab, the image of the 0.5 focal length distance is unknown, but we predicted for it to have inverted, real image but it will be rather difficult to focus the image in the board. Some error that contributes to the accuracy of the graph is the lenses used might have deteriorated a little bit which change the focal length for a little bit.

CD Diffraction

Introduction
          In this experiment, the distance between the grooves of a compact disc will be determined. One of the method to measure it which we are using in this lab is to use the diffraction of the disc. In this experiment, a laser will be used to shine a CD and the diffraction pattern is then measured and the distance of the grooves will then be able to be calculated.

Experimental


First the lab is set up as follow:

Setup of the lab

Measurement that is made in the experiment

The data from the measurement is tabulated below:

Distance from disc to board (cm)	45.2 ± 0.05
Distance of diffraction pattern (cm)	21.25 ± 1.25
Wavelength of laser (nm)	633 ± 1 nm

The data obtained is as calculated to be d = 1485 ± 20 nm

The theoretical distance of the grooves are 1600 nm

From these data, the percent error is calculated to be 7.19%

Conclusion

              

                Based on the data obtained, the distance between the grooves appear to be 1485 ± 20 nm with a percent error of 7.19%. Some of the error that contributes to the percent error is that there is couple of scratches and smudges. Although the percent error is quite high, it is still accurate as the true value is still within uncertainty.

Measuring Human Hair

Introduction
           The purpose of this experiment is to measure human hair using 2 methods. The first one is by using a diffraction from laser and then figure out the distance from it. The other method is by measuring it directly using a micrometer. The accuracy will then be determined by calculating percent difference from the two methods which will give us the uncertainty.

Experimental
          The measurement of width of hair using the laser is set-up as follow:

Hair attached to the hole in the note card

Setup of the experiment using the laser

The interference in the laser observed

The data obtained by the laser experiment is as follow:

Wavelength (nm)	632.8
Distance to the board, L (cm)	180 ± 0.5
Distance of fringes, y (cm)	2.05 ± 0.02

Once the data is taken, the measurement with micrometer is conducted as follow:

Lab partners measuring using the micrometer

The reading of the micrometer

Once the data is taken and calculated, a table for compilation of data is made:

Width of hair using laser (µm)	55.56
Width of hair using micrometer (µm)	70.0
Percent difference	26.0%

Conclusion
             Based on this experiment, the width of human hair is about 62.78µm. The theoretical width of human hair cannot be determined in this case so percent error is impossible to calculate. The width of human hair is impossible to be determined theoretically because the width of hair of a person differs from one another so the theoretical values is actually a range that we cannot use to calculate percent error. The only thing that can be analyzed using the range is that both measurement is inside the range of the human hair width.
           The value that is more relevant to look at is the percent difference of the value of the two methods. By using these two methods, laser and micrometer, we determine it to be 26% difference in the value. Some error that could contributes to this is the fact that the micrometer itself is not a really accurate tool as hair can be as thin as 17 µm which makes it less accurate the smaller it gets. From the laser experiment, it is quite difficult to have the laser perfectly aligned with the board. There will be some angle created from the laser, slit and the board which makes the calculation a little bit off.

Standing Wave Activity

Purpose
          The purpose of this activity is to be able to determine the velocity of wave in a spring. To do this, two people will hold each end of the spring and the spring will be moved as the procedure in the following picture shows:

Procedure of the activity

Experimental


The data taken is as follow:

The data of 3 different wavelength (on the left) and the time it takes to achieve 10 cycle (on the right)

 By using the data obtained, these calculations are obtained:
Trial 1:
length of string = 3m ;  wavelength = 6m ;  period = 0.9 ± 0.02 s
frequency = 1.11 Hz
v = f * wavelength = 6.66m/s


Trial 2:
length of string = 3m ;  wavelength = 3m ;  period = 0.44 ± 0.02 s
frequency = 2.23 Hz
v = 6.69m/s


Trial 3:
length of string = 3m ;  wavelength = 2m ;  period = 0.24 ± 0.02 s
frequency = 4.17 Hz
v = 8.34m/s

Conclusion
         By using the data obtained, the value for trial 3 seems unreasonable so it is not relevant. Some of the error that could contribute to data being unreliable is that the standing wave for trial 3 is really fast and it is rather difficult to keep track of the number of cycle. Furthermore, the more the nodes in the waves, the more affected it is by the time of human reactions since the timekeeper in this experiment is different from the person who keeps track of the cycle. Based on data 1 and 2, the average velocity appears to be 6.67 ± 0.02 m/s. The uncertainty is quite small but it has the same reason as discussed above that it yields some discrepancy in the values.

         

Lab Quiz: Microwave

Purpose
       The purpose of this lab is to determine the frequency ,dimensions, energy content of the microwaves. We will also determine the number of photons oscillating in the microwave and the pressure the photons exert on the side of the microwave.

Data


Wavelength of microwave = 12 ± 1 cm
Height = 23 ± 1 cm
Width = 35 ± 1 cm
Depth = 35 ± 1 cm
Specific heat of water = 4.186 J/g C
h = planck's constant = 6.626 * 10^(-34) kg m^2/s

for the water:

T_initial = 20 ± 1 C
T_final = 57 ± 1 C
time = 30s
Mass of water = 100g

Data Analysis
c = f*wavelength
f = c / wavelength = 2.59 ± 0.210 GHz

From the calculation above, the frequency is 2.59 ± 0.210 GHz


E = Q = m*c*delta_T =  4.186*100*37 = 15.5 ± 0.570 kJ


Average power of microwave = E/t = 15500/30 = 517 ± 20 W


Number of photon per second = average power / (h * f) = 3.12 * 10^26 ± 2.6 * 10^25


For the pressure of photons exerted on the side of microwave, an assumption that all of the area exerted an equal pressure is made.

Pressure = I / C = power / (Area * C)

Area = 2*( width*depth + width*length + length*depth) = 0.5817 ± 0.0375 m^2

Pressure = power / (Area * C) = 517 / (0.5817 * 3.0*10^8) = 2.98 ± 0.31 µN/m^2

Concave and Convex Mirror

Introduction
          The purpose of this experiment is to observe different types of mirror and how the image of an object will be projected in the mirror. In this experiment, a convex, a concave and a regular mirror will be used on an object to observe the image projected and what happens if the object gets closer or further from the mirror.

Experimental

Convex Mirror

Concave mirror

The image is observed as follow following the diagram below:

convex mirror diagram

concave mirror diagram

	Convex	Concave
ho (cm)	2.2	2.3
hi (cm)	0.7	0.6
do (cm)	5.7	11.7
di (cm)	1.9	3.2
hi/ho	0.318	0.261
di/do	0.333	0.273

Conclusion

            Based on the observation of the experiment, the convex mirror has an image smaller than the actual object. The image is also in an upright position and its further from the actual distance. When the object is moved closer to the mirror, it gets larger than the original spot but the characteristic of upright, smaller than the object and further still apply. When it gets farther, it gets really small compare to the original object. This observation agree with the diagram shown above.

          The concave mirror makes the size of the object larger and upright. It also closer than the actual object. When the object gets further from the mirror, it gets larger until it reaches the focal point where it switch from upright to inverted and getting smaller as it goes further. This is again agree with the diagram. As seen in the diagram , when object is placed far from the focal point, it becomes inverted and smaller. If the object is in between focal point and the mirror, the image will be larger and upright.

           In the case of regular mirror, the distance of the object and the image is the same. The image is upright and the same size as the object.

         The magnification of the mirror from the data table above is obtained by measuring the distance and height with a ruler. The magnification for each mirror is just the ratio between image distance with the object distance or it could also be the ratio of the height image to height object.

       

Length of Pipe

Introduction
              The purpose of this experiment is to be able to determine the length of a pipe by spinning the pipe and recording the sound it creates using a logger pro. The speed of the spin will then be changed to get different frequency from the sound. The length of the pipe will be calculated using the harmonics equation learned in class.

Experiment
       The pipe was spun until a clear tone was heard and then the frequency was measured using logger pro. This procedure was repeated with greater spinning speed and then some data was again taken. Once the data is taken, some calculation was done to determine the length of the pipe.

The data taken is as follow:

Speed	ω(rad/s)	f(Hz)	L(m)
Slow	3859 ± 0.4736	614	0.83
Fast	5068 ± 1.106	806

The calculation that was made are as follow to obtain the length

Conclusion
         In this experiment the length of the pipe is calculated using the concept of harmonics. Since it is an open ended pipes, the anti-nodes has to be at the end. As shown in the picture above, the shape of first harmonics has to be picture 1 while number 2 will have a half wavelength longer. By using the relation of the first harmonics with the frequency and wavelength and the second harmonics, The length of the pipe is determined to be 0.83m. Our group didn't measure the pipe using ruler, but using the data of other group, the length appears to be 0.80m by using ruler. This comes out to have 3.75%. This error occurred probably because the pipe is actually stretched when spun which increase its length to create the sounds. Some rounding in the calculation might also cause the percent error to appear in this experiment.