PHIL 150 Lecture Notes - Lecture 10: Omnipotence, Theism

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tanbutterfly665

16 May 2015

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This argument depends upon what we mean by god" and. A traditional theist will argue that when we may closer attention to what we mean by these we will see that premise 1 is nonsense. The stone is question is a stone so heavy that a being that can lift every stone cannot lift it. Does this mean that god is constrained by something outside of. No, because we might think that logic and rationality are internal to god"s will.

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For my Physic class, my teacher assigned us with a project of creating a mechnical cannon, meaning no human, electrical, chemical, pneumatic energy can be applied. I was wondering if you guys have any idea of the type of mechnical mechanism that I should use to fire tennis at both a 8 m and 12 m target. Two ideas that I have right now are either to use some spring loaded mechanism or rubber bands. The rules for the testing are that we will only have two minutes to fire as many shots as possible in the hope that it will land in a trash can at the prementioned distance. We get 3 pt if the ball gets in the can, 2pt if it hits the can but does not drop into it, 1 pt if it hits within a 1/2 meter of the can. As a result, a mortar would be prefered since it is over a relatively short distance where a arc would be greatly favorable. At the same time, the mechanism must not only be accurate but fast. In the two minutes, we must fire as many shots as possible for a max of 15 at each location. So five direct hit would be enough. Since time is of the essence, I was thinking that a spring loaded mechanism would be prefered over rubber bands. Please provide any suggestion on other possible mechanism that would produce better results. Also any help on the overall design of the cannon itself will be greatly appreciated. My idea is to have a tube with a spring attached at the bottom. The firer would first pull down the spring and then the loader would drop the tennis ball, upon which the firer would release the spring. I would also appreciate it if you could explain how to add a aiming mechanism on the mortar. I plan to have it on a base plate with a bipod.

I am so lost onwere to even begin. I just need help trying to find the Ñ² (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 frictionm_s 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 q_c 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 objectâs 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 relatesm_s toq_c.

F_N = NormalForce = mg cos(Î¸)

F_F =Î¼_s x F_N = Î¼_s mg cos(Î¸)

Î£F_x = mA_x = F_Gx - F_F = ?

F_Gx = mgsin(Î¸)

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(W_H). The other component is âpressinginto the hillâ, 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)	Ñ²	Ms	Height(m)	Ñ²	Ms
0.24			0.26
0.25			0.31
0.245			0.345

avg m_s: ______ s : _______ avg m_s: ______ 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)	Ñ²	s	Height(m)	Ñ²	s
0.15			0.23
0.16			0.165
0.16			0.195

avg m_s: ______ s : _______ avg m_s: ______ 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 m_s: ______ s : _______ avg m_s: ______ s : _______

Part 2: KineticFriction

Theory:

You can calculate the coefficient of kinetic friction,m_k, 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 W_H and the force offriction will need to add up such that the block will slide at aconstant speed. Think of Newtonâs 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 m_k using aprocedure similar to the one you used to measurem_s. 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 m_sandm_k!

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 m_k: ______ s : _______ avg m_k: ______ 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 m_s compareto the values of m_k? (Of course, youcan only compare them for the same pairs of materials.)

2. Is the relationship betweenm_sand m_kwhat you expected?

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

4. Could m_k orm_s 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?

PHIL 150 Lecture Notes - Lecture 10: Omnipotence, Theism

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