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PHYSICS 4A EXAM 4
November 13, 2002
Name:____________________
Rules for Exam:
1. Only Scientific Calculators are allowed!
2. Show your work on non-multiple choice problems. NO WORK=NO CREDIT.
3. Include units with each answer. One point deduction per infraction.
4. Round off to 2 decimal places and circle your final answers.
5. Circle your final answers.
Good Luck!
Scores
Part 1 (16 pts)
Prob 1 (10pts)
Prob 2 (10pts)
Prob 3 (15pts)
Prob 4 (18 pts)
Prob 5 (15 pts)
TOTAL (84 max)
% (out of 84)
For elastic collision (v v ) (v v )
dt p F
d
p p p where p m v dt
d
Conservati on of Momentum
W U K
Work done byNon- conservative forces
U K 0 where U mg(h h )
Conservati on ofMechanical Energy
Mv 2
I
K
2 I
K
W d K
W F dr K
Work Energy Theorem
if F constant W F r F r cos
Work W F dr W d
F ma I
Newton's 2nd Law
a g. m s 32.2ft/s for free fall
s r v r a r
Δ t / t ; t ;
Equations ofMotionfor Constant Accelerat ion
2i i 2f f
EXT ERNAL
i
i
initial final i
i
nc
F i
ROLLING CM
ROTAT IONAL
ROTATIONAL ROTATIONAL
net
ROTATIONAL
f i
o o f i
INITIAL FINAL
i
EXTERNAL
i
CM
ROD
ROD
DISK
HOOP
HOLLOWSPHE RE
SOLIDSPHER E
L L L
dt
d
L
dt
d
L I
L rp sin
rF sin F(leverarm )
r F L r p
Parallel Axis Theorem I I Mh
I ML (ABOUT ENDPOINT)
I ML (ABOUT CENTER OF MASS)
I MR
I MR
I MR
I MR
Multiple choice and short answer questions (4 points each)
- A wheel of outer radius R has an axle of radius R/4. Strings are wrapped as shown around the rim of
the wheel and around the axle. If the string around the rim of the wheel has tension T, then in order to
keep the wheel from turning the tension in the string around the axle must be:
A. 4T
B. 4Tsin
C. T/
D. (T/4)sin
- A particle with linear momentum p =(2 i -4 k )N is at the position r= (-7 i +3 k )m. What is its angular
momentum with respect to the origin?
A. -22 i kgm
2
/s
B. -22 j kgm
2
/s
C. 34 i kgm
2
/s
D. 34 j kgm
2
/s
E. 28 k kgm
2
/s
- A student sits in a spinning stool with her arms folded. When she extends her arms away from her
body, her kinetic energy
A. increases
B. decreases
C. remains the same
- In a lecture demonstration, a bicycle wheel mounted on an axle is spinning with its angular
momentum as indicated. One end of the axle (point A ) is attached to a vertical string, which supports
the weight of the wheel system. As a result the vector L will rotate
A. clockwise in the plane of this paper
B. out of the plane of this paper
C. counterclockwise in the plane of this paper
D. into the plane of this paper
a,b,b,d
3. A hollow sphere of mass m is released from rest such that it rolls without slipping toward the
loop of radius r=1.50m. Calculate the minimum value h such that it barely makes it around
the loop. You may assume that the radius of the sphere is much less than the radius of the
loop (15 points).
4.25m
4. A uniform stick of mass m and length L is supported at the edge of a table on one end (point
A ) and at the fingertip of a Physics 4A student on the other (point B ). The student suddenly
removes the finger from point B. Calculate the angular acceleration of the stick about point
A and the normal force acting at point A just after the finger is removed (18 points).
=1.5g/L
M=mg/
r
h
Sphere
A B
- A 5kg mass hangs from a frictionless pulley of the same mass. Assuming the pulley is a disk
of radius R= 12.5cm calculate the acceleration of the 5kg mass. Note: if you choose the
proper technique, this problem can readily be solved without a free body diagram (
points).
A=(2/3)g
R
