Problem 1 Multiple Choice 5 points'

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Sample Exam I Solutions Physics 211 Fall
2005 Professors A. Dominguez and G. Snow

Problem 1 Multiple Choice (5 points.)   You are
holding an object which weighs 98 Newtons. What
is its mass?    
Mass Weight / g 98 Newtons / (9.8 m/s2) 10
kg   a) 0.1 kg b) 0.98 kg
c) 1.0 kg d) 10 kg
e) 98 kg f) 980 kg
2
H
Need only think of upward part of bounce
v2 vup2 2 g h
Solve for vup
h
0
vdown
vup
Given vdown 3 vup vdown2 (9 ? 2gh) v02 2
g H Solve for H
0
No math needed here. You want the top of the
second bounce to be at height h, so top of first
bounce must be at H 9h. Hence you must drop
from 9 ? 9h 81h to achieve this.
3
Problem
3 Multiple Choice (8 points.) A train car is
accelerating to the right with an acceleration
of 5.66 m/s2. A simple pendulum suspended from
the ceiling of the train car does not swing but
makes a constant angle ? with the vertical as
shown at right. The angle ? is
a) 10o b) 22o
c) 30o d) 45o
e) 54o f) 60o
a
q
m
y
T
?
The y-component of T supports the weight of the
ball, the x-component of T provides the
acceleration of the ball.
T cos(?)
?
x
T sin(?)
mg
x T sin(?) max , ax is given y T cos(?) mg
may 0 , or T cos(?) mg Divide top equation
by bottom equation, Ts and ms cancel. sin(?)
ax ----------
tan(?) ------- cos(?)
g
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Problem 4 --
Multiple Choice (8 points.) A simple pendulum is
made of a 0.1 kg mass attached to a 2 m long
cord. The pendulum is hung vertically and it
swings back and forth in a circular arc. Point B
is the lowest point of its path. Its speed as it
passes through B is 8 m/s. What is the tension
in the string at point B?
a) 0.0 N b) 0.98 N c) 2.2
N d) 3.2 N e) 4.2 N
f) 9.8 N
T
v
mg


v 2 T mg m
-------- , since v 2/R is masss centripetal
acceleration R
v 2 T mg m --------- 4.2
N, since m, g, v, and R are given.
R
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Problem 5 -- Partial Credit. (20 points.) A
soccer ball is kicked from the ground (point A)
with an initial velocity of v0 72 km/hr
directed at 30o above the horizontal. A vertical
wall is located a horizontal distance of 30 m
away, and the ball strikes the wall at a height
h above the ground. Neglect air
resistance.     Part A. (5 points.) What are the
horizontal and vertical components of the ball's
velocity in m/s (!!) at point A?           v x,0
____________________m/s
v y,0 ______________________m/s   Part
B. (5 points.) How much time does it take for the
ball to hit the wall?             Time to reach
wall ___________________________s.   Part C. (5
points.) What is the height h?           Height h
___________________________________m. Part D.
(5 points.) What is the speed of the ball just
before it hits the wall?               Speed at
the wall ___________________________ m/s.
h
30o
A
30 m
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Problem 6 Partial
Credit (25 points.) Parts D. and E. on next
page! There are two masses, m1 2 kg and m2 4
kg, attached to a string draped over a
frictionless, massless pulley which is attached
to the ceiling. As the masses move, the pulley
wheel turns with the string i.e. the string
does not slip over the pulley wheel. At t 0,
you observe m1 moving DOWN and m2 moving UP with
initial speed v0 2 m/s.   Part A. (5 points.)
There is an extremely light fly riding on the
edge of the pulley wheel (Radius 0.5 m) as
shown in the figure. At t 0, what is the
magnitude of the fly's centripetal
acceleration?         Centripetal acceleration
______________________ m/s2.   Part B. (5
points.) In the space below, draw separate
free-body diagrams for m1 and m2 showing all the
forces acting on each mass.                  
Part C. (7 points.) Write Newtons 2nd law, ?F
ma, separately for the motion of m1 and m2 in the
vertical direction, and then find the
acceleration (magnitude and direction) of the
mass m1.                     Acceleration
magnitude _________________m/s2, Direction
____________ (up or down)
Fly

R
m1
v0
v0
m2
y
m2
T
x
m2g
Negative since m2 is heavier
Up
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Problem 6 --
continued.   Part D. (4 points.) How much higher
(in meters) does m2 go above its position at t
0? (You can assume that mass m2 has enough
string above it so that it does NOT run into the
pulley wheel.)                             Distan
ce ______________________________ m.   Part E.
(4 points.) At the instant when m2 has reached
its highest position and momentarily comes to
rest, what is the tension in the
string?                                 Tension
_______________________________ N.
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Problem 7 Partial Credit (22
points.)   A particle of mass m is moving in
three dimensions. Its motion is described by the
following position vector for t gt 0   Part A.
(7 points.) Find the velocity vector as a
function of time.               Part B. (7
points.) Find the acceleration vector as a
function of time.               Part C. (8
points.) Describe the acceleration. Is it
constant? And is it confined to a particular
spatial plane? Make three sketches of the
acceleration ax vs. t ay vs. t and az vs. t
for t gt 0.
The acceleration is not constant due to the time
dependence in the y-direction. The acceleration
is in the x-y plane, constant in the x-direction,
linearly increasing in the y-direction. There is
no acceleration in the z-direction.
az
ay
ay 6t m/s2
az 0 m/s2
0
t
t