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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
- 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 !;
- 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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