University Physics I: Review for Exam I
Chapter 1&3 : Introduction and Vectors (IV)
IV1.
The position of a particle moving under uniform acceleration is some
function of time and the acceleration. Suppose we write this position
s
=
ka
m
t
n
,
where
k
is a dimensionless constant. Show by dimensional analysis that this
expression is satisfied if
m
= 1 and
n
= 2. Can this analysis give the value of
k
?
IV2
A hydrogen atom has a diameter of approximately 1.06
×
10
–10
m, as
defined by the diameter of the spherical electron cloud around the nucleus. The
hydrogen nucleus has a diameter of approximately
2.40 x 10
–15
m.
(a) For a scale model, represent the diameter of the hydrogen atom by the length
of an American football field (100 yards = 300 feet), and determine the diameter
of the nucleus in millimeters.
(b) The atom is how many times larger in volume than its nucleus?
IV3
A sidewalk is to be constructed around a swimming pool that measures
(10.0
0.1) m by (17.0
0.1) m. If the sidewalk is to measure (1.00
0.01) m
wide by (9.0
0.1) cm thick, what volume of concrete is needed, and what is the
approximate uncertainty of this volume?
IV4
A high fountain of water is located at the center of a circular pool as in
Figure INT4. Not wishing to get his feet wet, a student walks around the pool
and measures its circumference to be 15.0 m. Next, the student stands at the edge
of the pool and uses a protractor to gauge the angle of elevation of the top of the
fountain to be 55.0°. How high is the fountain?
Figure IV4
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University Physics I
Review for Exam I
PHYS 2325
Exam I, Sample Problems
2
IV5.
Consider the two vectors
and
. Calculate
(a)
A
+
B
,
(b)
A
−
B
,
(c) 
A
+
B
,
(d) 
A
−
B
, and
(e) the directions of
A
+
B
and
A
−
B
.
IV6.
You are standing on the ground at the origin of a coordinate system.
An
airplane flies over you with constant velocity parallel to the
x
axis and at a
constant height of 7.60
×
10
3
m. At time
t
= 0 the airplane is directly above
you, so that the vector from you to it is
P
0
=
7.60
×
10
3
m
(
)
ˆ
j
.
At
t
= 30.0 s the
position vector leading from you to the airplane is
P
30
=
8.04
×
10
3
m
(
)
ˆ
i
+
7.60
×
10
3
m
(
)
ˆ
j
.
Determine the magnitude and
orientation of the airplane’s position vector at
t
= 45.0 s.
Chapter 2: Motion in One Dimension (M1D)
M1D1
. An object moves along the
x
axis according to the equation
x
(
t
) =
(3.00
t
2
–
2.00
t +
3.00)
m. Determine
(a) the average speed between
t
= 2.00 s and
t
= 3.00 s,
(b) the instantaneous speed at
t
= 2.00 s and at
t
= 3.00 s,
(c) the average acceleration between
t
= 2.00 s and
t
= 3.00 s, and
(d) the instantaneous acceleration at
t
= 2.00 s and
t
= 3.00 s.
M1D2.
At NASA’s John H. Glenn research center in Cleveland, Ohio, freefall
research is performed by dropping experiment packages from the top of
an evacuated shaft 145 m high.
Free fall imitates the socalled
microgravity environment of a satellite in orbit.
(a) What is the maximum
time interval for free fall if an experiment package were to fall the entire
145 m?
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 Spring '08
 ERSKINE/TSOI
 Acceleration, Force

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