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PHYS1417 Basics Physics
Problem set 1
Due Date: 5:00 p.m., March 9, 2009
Answer all questions in this problem set.
1.
A river with a water current running at 4 km/hr is
0.25 km wide between parallel banks. A boat
whose speed in still water is 6 km/hr wishes to
cross. In what direction should it be headed so as to
cross the stream
6 km/hr in still water
0.25 km
Water current
Boat
4 km/hr
(a)
in the least possible time,
(b)
to a point directly opposite its starting point?
(c)
Find the time in each case and the distance moved downstream in case (a).
2.
Three uniform thin rods, each of length
L
, are arranged in an inverted
U
, as shown in the figure. The
two rods on the arms of the inverted
U
each has mass
M
; the third rod has mass 3
M
.
(a)
Where is the center of mass of the system? Give your answer with respect to the reference point at
O
.
O
L
L
M
3M
L
M
L
M
3M
L
L
M
(b)
Find the moment of inertia about an axis passing through the center of
the 3
M
rod. The moment of inertia of a rod of mass
m
and length
l
is
2
1
12
ml
when it is rotating about an axis normal to the rod and passing
through its center.
1
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A man throws a disk of radius
R
down a table at
O
as shown in figure (a). The disk slides on the plane
with initial speed
v
0
and initial angular speed
ω
0
, where
R
0
>>
v
0
.
The coefficient of kinetic friction
between the disk and the table is
µ
. The disk slides for a while and then rolls smoothly. The moment of
inertia of the disk about its center is given as
2
2
1
MR
, where
M
is the mass of the disk. The gravitational
acceleration is labeled as
g
.
v
0
0
O
.
v
0
0
O
.
Figure (a)
Figure (b)
(a)
Sketch figure and point out the direction of kinetic friction, which acts on the sliding disk.
(b)
Describe in a few words the motion of the disk when it is sliding. Is the speed of disk increasing or
decreasing? Is the angular speed increasing or decreasing?
(c)
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This note was uploaded on 09/06/2010 for the course BSC PHY1417 taught by Professor Prof during the Spring '08 term at HKU.
 Spring '08
 Prof

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