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UC Berkeley Physics 8A Midterm Exam, Fall 2007, Exams of Physics

A midterm exam from the university of california at berkeley's department of physics for physics 8a, held in fall 2007. The exam covers various physics concepts and problems, including torque, buoyancy, mechanical advantage, and rotational motion. Students were required to answer all questions, and were given 100 minutes to complete the exam without the use of books or electronics.

Typology: Exams

2012/2013

Uploaded on 02/12/2013

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University of California at Berkeley
Department of Physics
Physics 8A, Fall2007
Second
Midterm
November 8,2007
6:00PM
You will be
given
100 minutes to work this exam. No books, but
you
may
use a
handwritten note sheet no
larger
than an 8 ll2by I I sheet of paper.
No electronics of any
kind
(calculator,
cell
phone,
iPod, etc) are allowed.
Your
description of the
physics
involved in a
problem
is worth significantly more than
any numerical answer. Show all work, and take
particular
care to explain what
you
are
doing. Write
your
answers directly on the exam, and
if you
have
to use the back of a
sheet
make
sure
to put a note on the front. Do not
use a blue book or scratch
paper.
Each
part
is worth the number of points
indicated. These should
sum to 100
points.
Setup
and explanation are worth almost all of the
points.
Clearly state what
you
are doing and
why. In particular,
make
sure
that
you
explain
what
principles
and conservation rules
you
are applying, and how they relate.
There is a
note
sheet at the back. You
can tear
it off and keep it separate if you'd
like.
NAME:
SID NUMBER:
DISCUSSION SECTION NUMBER:
DISCUSSION SECTION DATE/TIME:
Read the
problems
carefully.
Try to do all the
problems.
If you get
stuck,
go
on to the next
problem.
Don't
give
up! Try
to remain relaxed
and work steadily.
I
2
J
4
total
pf3
pf4
pf5

Partial preview of the text

Download UC Berkeley Physics 8A Midterm Exam, Fall 2007 and more Exams Physics in PDF only on Docsity!

University of California at Berkeley

Departmentof Physics

Physics8A, Fall

SecondMidterm

November8,20076:00PM

You will be given 100minutesto work this exam. No books,but you mayusea

handwrittennotesheetno largerthanan 8 ll2by I I sheetof paper.No electronicsof any

kind (calculator,cell phone,iPod,etc)areallowed.

Your descriptionof the physicsinvolvedin a problemis worth significantlymorethan

anynumericalanswer.Showall work, andtakeparticularcareto explainwhatyou^ are

doing. Write your answersdirectlyon the exam,andif you haveto usethe backof a

sheetmakesureto put a noteon the front. Do not usea bluebook or scratchpaper.

Eachpart is worth the numberof pointsindicated.Theseshouldsumto 100points.Setup

andexplanationareworth almostall of thepoints.Clearlystatewhatyou^ aredoingand

why. In particular,makesurethatyou explainwhatprinciplesandconservationrulesyou

areapplying,andhow theyrelate.

Thereis a notesheetat the back. You cantearit off andkeepit separateif you'd like.

NAME:

SIDNUMBER:

DISCUSSIONSECTIONNUMBER:

DISCUSSIONSECTIONDATE/TIME:

Readthe problemscarefully.

Try to do all the problems.

If you get stuck,go on to the nextproblem.

Don't give up! Try to remainrelaxedandwork steadily.

I

2

J

total

," =H#^ =l,,fl, r,^=H#^ =ly,f*,

F r y ,= l 4 F u F o 3 t r t , F * W = F. i^ F = m i^ p =! C p , l u '^ b = l c o s l a 2+ b 2= c z

sin45o: cos45o:0.71; cos60o: sin30o: 0.50;sin60o: cos30o:0.

W : F x c o s 1 p : d W d t^ K =! ^ r , ( I = m g h^ U = ) * , n = ) C p l r ,

i = f f i l d t^ d = f f i l d t x ( t ) = x o r v o t +! o o t ' v ( t! = v 0 + a : t

l F = m d F = m v 2 l R^ F = m g

p = l m , i , (^) g : 1 0 m / s 2

v'7x1=vl+2ax

1 atm: (^105) N/m

sphericalshellaboutaxis:(2/3)MR

hoopaboutaxis:MR

AK: KrKi AU: UrUi

nr,- nr. 2m"

V t f - = - -.^ l t i - (^). V Z , m r + m 2 m \ + m 2

W:AU+AK+AE6*AE

vrr " ---2!2-ur,*^ !2-!Lr,^ p : F/A m t + m 2 m I + m 2

s - F r = r F s i n l I ' = I + m r 2

L T = l d , T = r x

L = r p s i n | L = I a t L = m r 2 @ 5 =! m '

RotationalInertiasfor radiusR or lengthL:

sphereaboutaxis:(2/5)MR

diskaboutaxis:(l/2)MR

rod aboutperpendicularat midpoint:ML2l|

7 2 2I

f, r' +ygp-rP=constant

  1. Tank drains into a cart (35 points) A tank frlled to a height of 15 m of water standsnext to an (^15) empty 20 kg cart as shown in the figure on the right. At time t: 0,a square0.1 m by 0.1 m hatchon the side of the tank is openedfor exactly one second,allowing water to rush out of the hole and fill the cart. All of the dimensions of the tank are much larger than the size of this hatch, so the water level remains essentiallyunchangedafter the hatch is closed again. The hatch is located 5 m from the bottom of the tank. The densityof water is p: (^) 1000kg/m3. a) Thereis a rock with volume Vn: 0.01 m' sitting at the bottom of the tank. What is the buoyant force on the rock due to the water? b) What is the pressurein the water inside the tank at the sameheight as the hole? State whether you are expressingyour answerin terms of gaugepressureor absolute pressureand be consistentwith your choicefor the rest of this problem. c) What is the speedof the water shooting out horizontally through the hole? d) How much water (in kg) pours from the hole during the 1 secthat the hatch is open? e) Assuming that all of the water that leavesthe tank lands in the cart and none of it spills, how fast doesthe filled cart move to the right after the hatch has (^) been closed? Assumethe cart's wheelsare masslessand frictionless. 1 I I L !;
  1. Mechanical advantage(20 points) 6\rQc+rAy

A 1000Kg car is raised2 m off of the groundusing a hydraulic lift, which consistsof a U-shapedtube that has a small areaAn: 0.001m2^ on the right side^ and alarge arca Ar:2 m' on the left side. A car mechanicexertsa downward force on the right side of the lift with his foot. Assume that the hydraulic fluid has^ the density^ of water: p: 1000kg/m'.

a) What is the pressureof the hydraulic fluid located^ at point C, which is right under^ the car? Statewhether you are expressingyour answerin gaugepressureor absolute pressureand be consistentwith your choice for the rest of this problem. b) What is the pressureof the fluid at point G, located at ground level on the left side of the lift? c) What downward force must the mechanicapply to the lift with his foot to keep the car from fallins?

p o r n t

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