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23 Nov 2019

Imagine a hexagonal or octagonal object. Describe how you could usesuch an object to determine both an upper and lower bound for thevalue of pi. Which object will give bounds closer to the actualvalue and why?

Please provide an example using formulas and calculations

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Patrina Schowalter
Patrina SchowalterLv2
27 Feb 2019

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Related textbook solutions

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

Related questions

CHARGING BY INDUCTION:

Conductor A (positively charged) is brought nearby to conductor B(initially uncharged). We will use object A to charge object B byinduction.

In order to successfully charge object B, all of the following mustbe done:

a.) Which object needs to be connected to ground (at some time inthe process) in order for this to work?

Choose one answer:
1. A only
2. B only
3. Both A and B
4. Neither A or B
5. Not enough info

b.) During this connection, electrons will flow:
Choose one answer:
1. From A into the ground
2. From the ground into A
3. From B into the ground
4. From the ground into B
5. From A onto B
6. From B onto A
7. Not enough info

c.) When should B be disconnected to the ground?
Choose one answer:
1. Before A is taken away
2. After A is taken away
3. B will be charged the same way regardless
4. B does not need to be connected to ground at all
5. Not enough info

d.) If A is brought closer to B during this process (rather thanfurther away), then the amount of charge that can be generated on Bis:

Choose one answer:
1. Larger
2. Smaller
3. The same
4. Not enough info

e.) More generally, when charging an object by induction, theinitially uncharged object will always end up:

Choose one answer:
1. Negatively charged
2. Positively charged
3. With the opposite charge as the object used to charge it
4. With the same charge as the object used to charge it
5. There is no general statement that can be made about this

POTENTIAL MISHAPS:
f.) If, during an otherwise correct procedure, A were accidentallytouched to B while B is connected to the ground, then:

*The net charge on A would end up:
Choose one answer:
1. Positive
2. Negative
3. Zero
4. Not enough info

*The net charge on B would end up:
Choose one answer:
1. Positive
2. Negative
3. Zero
4. Not enough info

(Can you see why our attempt to charge B has failed?)

g.) If, during an otherwise correct procedure, B was disconnectedfrom ground only after A was taken far away, then:

*the net charge on A would end up:
Choose one answer:
1. Positive
2. Negative
3. Zero
4. Not enough info

*the net charge on B would end up:
Choose one answer:
1. Positive
2. Negative
3. Zero
4. Not enough info

(Can you see why our attempt to charge B has failed?)

Please refrane from answering if you are unfamiliar with MSExcel and inputing formulas for Cells. Thanks.

NOTE, you may need to save images to desktop to view in a largerscale.

Part b: Collision in Two-Dimensions

The law of conservation of momentum is true for any and everydirection. So, for an isolated system, the momentum in the x, y andz directions or any other direction does not change.

Consider two objects colliding in deep space. Since the two objectstogether can be considered an isolated system, the total momentumof the system (the sum of the momenta of the two objects) isconserved in both the x and y directions. That is

pi-x-total=pf-x-total or pix1+pix2=pfx1+pfx2

pi-y-total=pf-y-total or piy1+piy2=pfy1+pfy2

If we assume object one is moving in the x-direction, object two ismoving in the y-direction and the collision is perfectlyinelastic,
we can rewrite these equations as

m1*vix1=(m1+m2)vfx

m2*viy2=(m1+m2)vfy

These equations can be solved to find the x and y components of theobject's velocity after the collision. The magnitude of vf can befound using the Pythagorean Theorem. The direction of the objectsafter the collision can be found using the inverse cosinefunction

θ=cos-1(vfx/|vf|)

Since cos-1 outputs an angle between 0 and π radians, we must useθnew=2π-θold if vfy is negative to get a correct value. Use thebuilt in function 'if' to find the true value of θ. Afterwards,convert the angle into degrees using the built in function'degrees' .

i) Fill in the missing values in the table on the bottom usingformulas to find each value

This is the half of the tablethat is full so far

A = Mass1

B = Velocity initial 1

C = Mass2

D = Velocity intial 2

E = M2/M1

F = Vi2/Vi1

This is therest of the chart that needs formulas


G =Pi-x

H =Pi-y

I =|Pf|

J =Vf-x

K =Vf-y

L =|Vf|

M =θ

N = θ if Vi2< 0

O = θ(degrees)

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.

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?

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