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With a wooden ruler you measure the length of a rectangular piece of sheet metal to be 13 mm m m . You use micrometer calipers to measure the width of the rectangle and obtain the value 5.98 mm m m . Give your answers to the following questions to the correct number of significant figures.

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Physics: Principles with Applications
7th Edition, 2013
Giancoli
ISBN: 9780321625922

Related questions


Theory: Topics that you should be familiar with are: significantfigures, least count and estimated fraction, systematic and randomerrors, accuracy versus precision, percent difference and percenterror. These topics should have been covered in class already (orperhaps in an introduction to the lab manual or in a handout). Itis assumed that the instructor has discussed how to use the massbalance, etc.
Introduction: The goal of section I of this experiment is tomeasure (to the correct least count and estimated fraction) andcalculate (to the correct number of significant figures) thedensity of a metal ball and compare it to a table of accepteddensities (?=7.8x103 kg/m3).
To accomplish this goal keep in mind that: ? = m/V and Vsphere =(4/3) p r3
In the space below create a data table, show your calculations indetail, and compare your measured answer to accepted values givenabove. (Would you calculate a percent error or a percentdifference?)
1
II. Is g (the acceleration due to gravity) a constant? If so, whatis it?
1) SetuptheFree-FallApparatusasdemonstratedbytheinstructor.
2)MeasurethetimeittakesforthemetalballtofallthroughthesuggesteddisplacementsshowninDataTable 1. Be sure to do 4 trials for each fall and take the averageof your time and displacement. For each trial measure thedisplacement and record your results as precisely as possible. Becareful how you measure the displacement!
Data Table 1
Displacement (meters) Time
Trial 1
___.40___ m .281 s
______.40_ m .284 s
___.40____ m .283 s
____.40___ m .285 s
Average Displacement =.40 m Average time .0285 s
Trial 2
____.60___ m .357 s
____.60___ m .358 s
_____.60__ m .347 s
____.60___ m .347 s
Time (seconds)
Average Displacement = .60 Average Time = .352
Trial3
_.80____ m .402 s
_.80____ m .401 s
_.80______ m .402 S
_.80___ m .401 s
Average Displacement = .80 m Average Time =.401 s

Trial4
__ 1.00____ m .454 s
___1.00____ m .453 s
___1.00____ m .463 s
___1.00____ m .453 s
Average Displacement = 1.00 m Average Time =.455 s
3)PlotDisplacement(usetheaveragedisplacement)asafunctionofTime(usetheaveragetime)usingacomputer software that you know the best. (Does Displacement orTime go on the “vertical” (or y) axis? Make sure that you label theaxes of your graph properly and give the graph a descriptivetitle.), Please include (0,0) point.
4)UsetheCurveFitFunctiontotrytofindthecurvethatistheclosestfitforthegraph.Whichofthefollowing curve types gives the best fit? Try each to findout.
a) linear fit? b) quadratic (power 2)? c) exponential? d) Power?
The curve with the correlation coefficient (R) closest to 1 has theclosest fit. (e.g. 0.997 is better than 0.956)
5)Printthecurvewiththeclosestfit(oneforeachmemberofthelabgroup).Besureyourgraphincludesthe equation for your fit.
6)Canyoudeterminetheexperimentalaccelerationofgravityfromthisgraph?Explainhowandshowyourwork.
7)Ifalinearfunctionisnotthebestfitofyourplotfromstep3),howwouldyouplotdisplacementandtimeso that the resulting plot is linear? Explain. (Ask your instructorfor a hint if you are not sure of what to do, but be sure to thinkabout it for a while before you ask.)
3
8)Printacopyofthegraphforeachlabpartnershowingalinearfittoyourdataandproperlylabeledaxes.
9)Canyoudeterminetheexperimentalaccelerationduetogravityfromthisgraph?Explainandshowyourwork.
10) How do your experimental values of “g” compare with theaccepted value (g = 9.80 m/s2) for the acceleration of gravity?Give a mathematical comparison using what you learned aboutmeasurements previously. (Show work)
4
Question and further procedures
1. What is the greatest source of error in performing theexperiment? Is this error random or systematic? Explain.
2. At this point you should have calculated g in two different ways(A quadratic graph, and a linear graph). Which technique do youthink is best? Do all two techniques give the same answer? If not,which technique do you think has the most error?
3. How might you modify your procedures to determine whether or notg depends on the mass of the falling object? Do the experiment andcalculate g using your favorite technique.
I am so lost onwere to even begin. I just need help trying to find the Ѳ (angle)for part part 1 of the experiment if anyone can just explain how todo that and maybe give me a step-by-step example so I can finishthe rest. Thank you! Experiment 6 ~ Friction

Purpose:

In this lab, you will make some basic measurements of friction.You will measure the coefficients of staticfriction between several combinations of surfaces using aninclined plane, and you will measure the coefficient ofkinetic friction between two of the combinationsof surfaces you used in the static friction part of thisexperiment.

Part 1: StaticFriction

Theory:

The coefficient of static frictionms can be measured experimentally foran object placed on an inclined plane (a.k.a. ramp, a.k.a. hill).The coefficient of static friction is related to the criticalangle qc for the ramp, at whichthe object just begins to slide. Using what we havecovered in class, you can derive this relationshipyourself! At this critical angle, static friction preventing theobject from sliding down the hill is just exactly equal to thecomponent of the object’s weight along the hill. If the componentof the weight along the hill were just a little greater, it wouldovercome friction, and the object would start to slide down. Thefree body diagram for this situation will look like the figuresketched below. Use this diagram to find an equation that relatesms toqc.

FN = NormalForce = mg cos(θ)

FF =μs x FN = μs mg cos(θ)

ΣFx = mAx = FGx - FF = ?

FGx = mgsin(θ)

Hint #1: the angle q of the incline is the same as theangle between the normal force N and the weightmg. Why?

Hint #2: The weight mg can be broken into twocomponents. One component is along the incline(WH). The other component is “pressinginto the hill”, and is equal in magnitude to the normal forceN. (This is an example of a situation where the normalforce is not equal to the weight!) Remember that you need to usethe normal force to calculate friction, sincef=mN. Now calculate what the angle ofthe incline should be, so that the component of the weight down thehill is just exactly balanced by friction.

Equipment:

For this lab you will need to share the following ramps andblocks with other lab groups:

Ramps Blocks

Aluminum Aluminum

ParticleBoard Brass

StainlessSteel Plexiglass

Plastic Copper

Rubber

Steel

Wood

Experiment:

Test at least 5 different combinations of materials. Record thematerial of the block and the ramp for each combination.

1. Measure and record the length of theinclined plane you will be using. (This is thehypotenuse of the right triangle!)

2. Place the block on the plane and begin tiltingthe plane just until the point when the block begins to slide.

3. Measure the height of the raisedend of the inclined plane at this point. (This is theopposite side of the right triangle!) You cancalculate the angle from the measurements of the two sides.

4. Repeat the height measurement at least 3 timesfor each combination of materials. Record all the measurements inthe table below. Then,

(a) calculate the angle from the measurements of the hypotenuseand opposite side you just obtained

(b) use the equation you derived above in order to calculate thecoefficient of kinetic friction from the angle.

Block: woodenblock Block: cooper

Ramp:particleboard Ramp: particle board

Length of ramp:0.61(m) Length of ramp: 0.61(m)

Height(m)

Ѳ

Ms

Height(m)

Ѳ

Ms

0.24

0.26

0.25

0.31

0.245

0.345

avg ms: ______ s : _______ avg ms: ______ s : _______

Block:aluminum Block:particle board block

Ramp: solidewood Ramp: solide wood

Length of ramp:0.605(m) Length of ramp: 0.605(m)

Height(m)

Ѳ

s

Height(m)

Ѳ

s

0.15

0.23

0.16

0.165

0.16

0.195

avg ms: ______ s : _______ avg ms: ______ s : _______

5. Remember that in class we said that friction does not dependon surface area. You can easily test whether or not this iscorrect. Choose a block/ramp combination not already tested, andmake sure the block is not a cube or cylinder. Place the block sothat the side with the larger surface area is in contact with theboard. Now measure the angle at which the block just begins toslide (by measuring the hypotenuse and opposite sides of thecorresponding right triangle). As before, calculate the coefficientof friction from the angle you measured, using your equation.Repeat this process with the side of the block with the smallersurface area in contact with the board. Enter this data in thesmall tables below.

Block (larger end) :_________ Block (smaller end):__________

Ramp:_______________ Ramp: ________________

Length of ramp:______(m) Length of ramp: ______(m)

Height(m)

s

Height(m)

s

avg ms: ______ s : _______ avg ms: ______ s : _______

Part 2: KineticFriction

Theory:

You can calculate the coefficient of kinetic friction,mk, using a variation of the methodyou used for the coefficient of static friction. For thecoefficient of kinetic friction, you can use the same free bodydiagram as the one drawn on the first page. But now, thecombination of WH and the force offriction will need to add up such that the block will slide at aconstant speed. Think of Newton’s first and second laws when youset up this equation. Derive a relationship between the criticalangle and the coefficient of kinetic friction.

Experiment:

You can measure mk using aprocedure similar to the one you used to measurems. This time, just pick twocombinations of materials. The combinations you pick for this partof the experiment have to be combinations you alreadyused for the static friction part of the experiment, because thepoint is to compare msandmk!

1. Measure and record the length ofthe inclined plane you will be using.

2. Raise the plane high enough for the blockto begin moving. Begin lowering the plane just until the pointwhen the block begins to slow down. (Alternatively, raise theboard while tapping the block until block moves at a constantrate.)

3. Measure the height of the raisedend of the inclined plane at this point.

4. Repeat the height measurement at least 3times for each combination of materials. Record all themeasurements in the table below. Then,

(a) calculate the angle from the measurements of the hypotenuseand opposite side you just obtained

(b) use the equation you derived above in order to calculate thecoefficient of kinetic friction from the angle.

Block (from part 1) :_________ Block (from part 1):__________

Ramp:_______________ Ramp: ________________

Length of ramp:______(m) Length of ramp: ______(m)

Height(m)

k

Height(m)

k

avg mk: ______ s : _______ avg mk: ______ s : _______

Analysis:

Calculate the mean value and standard deviation of thecoefficient of static friction that you measured, for each set ofmaterials.

ramp/board

pair

Standard

deviation

(larger end)

(smaller end)

Calculate the mean value and standard deviation of thecoefficient of kinetic friction that you measured, for each set ofmaterials.

ramp/board

pair

Standard

deviation

Questions:

1. How do the values of ms compareto the values of mk? (Of course, youcan only compare them for the same pairs of materials.)

2. Is the relationship betweenmsand mkwhat you expected?

3. Of the two parts of the experiment, measurement ofmsand measurement ofmk, which had more sources of error?What were some of the sources of error?

4. Could mk orms ever be greater than 1? Explain whyor why not.

5. Is the coefficient of friction the same as when the block wasstanding on its larger (or smaller) end?

6. Think about your results. Do they make sense when youconsider your everyday experiences?

If a virtual image is formed 9.0 cm along the principal axis from aconvex mirror of focal length –15.0 cm, how far is the object fromthe mirror?

2. A woman looking in a makeup mirror sees her face at twice itsactual size and right-side up. If she is 26.0 cm from the mirror,what is its focal length?

3. Which of the following best describes the image of a concavemirror when the object is at a distance greater than twice thefocal point distance from the mirror?
a. virtual, upright and magnification greater than one
b. real, inverted and magnification less than one
c. virtual, upright and magnification less than one
d. real, inverted and magnification greater than one

4. A convex mirror with focal length of ?18 cm forms an image 12 cmbehind the surface. Where is the object located as measured fromthe surface?

5. A convex mirror with a focal length of ?18 cm forms an image 15cm behind the surface. If the object height is 1.2 cm what is theimage height?

6. An object placed 14 cm from a concave mirror produces a realimage 8.0 cm from the mirror. If the object is now moved to a newposition 18.0 cm from the mirror, where is the new image located asmeasured from the mirror?

7. When the reflection of an object is seen in a concave mirror theimage will:

8. A candle is 40.0 cm in front of a convex spherical mirror ofradius of curvature 70.0 cm. What are the image distance and themagnification, respectively?

9. An object is 16.0 cm from the surface of a spherical Christmastree ornament that is 8.00 cm in diameter. What is themagnification of the image?

10. A solid glass sphere with a radius of 6.00 cm and index ofrefraction of 1.50 has a small coin embedded 3.00 cm from the frontsurface of the sphere. For the viewer looking at the coin throughthe glass, at what distance from the front surface of the glassdoes the coin’s image appear to be located?

11. A glass block, for which n = 1.52, has a blemish located 4.5 cmfrom one surface. At what distance from that surface does the imageof the blemish appear to the outside observer?

12. An object of length 2.00 cm is inside a plastic block withindex of refraction 1.50. If the object is viewed from directlyabove, what is the length of its image?

13. An object is placed at a distance of 25 cm from a thin convexlens along its axis. The lens has a focal length of 10 cm. What arethe values, respectively, of the image distance andmagnification?
14. An object is placed at a distance of 50 cm from a thin lensalong the axis. If a real image forms at a distance of 35 cm fromthe lens, on the opposite side from the object, what is the focallength of the lens?

15. A contact lens is made of plastic with an index of refraction1.50. The lens has an outer radius of curvature of +2.0 cm and aninner radius of curvature of +2.5 cm. What is its focallength?

16. A Young’s double slit has a slit separation of 2.50 ? 10?5 m onwhich a monochromatic light beam is directed. The resultant brightfringes on a screen 2.00 m from the double slit are separated by2.30 ? 10?2 m. What is the wavelength of this beam? (1 nm = 10?9m)

17. A Young’s double-slit apparatus is set up so that a screen ispositioned 1.9 m from the double slits, and the spacing between thetwo slits is 0.040 mm. What is the distance between alternatingbright fringes on the screen if the light source has a wavelengthof 630 nm? (1 nm = 10?9 m)

18. The blue tint of a coated camera lens is largely caused by whateffects?

19. What is the minimum thickness of a glycerin film (n = 1.47) onwhich light of wavelength 650 nm shines that results inconstructive interference of the reflected light? Assume the filmis surrounded front and back by air.

20. Light of wavelength 560 nm is incident on a slit of width 0.150mm, and a diffraction pattern is produced on a screen that is 2.00m from the slit. What is the width of the central bright fringe? (1nm = 10?9 m)

21. Light of wavelength 610 nm is incident on a slit of width 0.25mm, and a diffraction pattern is produced on a screen that is 1.5 mfrom the slit. What is the distance of the second dark fringe fromthe center of the bright fringe? (1 nm = 10?9 m)

22. A multiple slit diffraction grating has a slit separation of2.50 ? 10?6 m. Find the wavelength of the monochromatic light thatwill have its second order bright fringe diffracted through anangle of 38.0°. (1 nm = 10?9 m)

23. A diffraction grating with 12 000 lines/cm will exhibit thefirst order maximum for light of wavelength 510 nm at what angle?(1 nm = 10?9 m)

24. A beam of unpolarized light in air strikes a flat piece ofglass at an angle of incidence of 58.0°. If the reflected beam iscompletely polarized, what is the index of refraction of theglass?

25. A beam of polarized light of intensity I0 passes through asheet of ideal polarizing material. The polarization axis of thebeam and the transmission axis of the sheet differ by 45°. What isthe intensity of the emerging light?

26. At what angle is the sun above the horizon if its light isfound to be completely polarized when it is reflected from the topsurface of a slab of glass (n = 1.65)?

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