Physics 2211
Quiz #2
Solutions
Fall 2007
g
Earth
= 9
.
8m
/
s
2
Unless otherwise directed, all springs, cords, and pulleys are ideal, and drag should be neglected.
I
. (16 points) A block of mass
m
is being slid to the right along a horizontal ceiling by an applied force
of magnitude
A
that makes an angle
θ
with the vertical, as illustrated. The coeﬃcient of static friction
between the block and the ceiling is
μ
s
, while the coeﬃcient of kinetic friction is
μ
k
. What is the acceleration
magnitude the block in terms of any or all of
m
,
A
,
μ
s
,
μ
k
, and physical or mathematical constants? (
On
Earth.
)
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
As announced during the quiz, the acceleration may depend on
θ
.
Use Newton’s Second Law. Sketch a Free Body Diagram.
X
F
x
=
A
x

f
k
=
ma
x
⇒
A
sin
θ

μ
k
n
=
ma
x
X
F
y
=
A
y

n

w
=
ma
y
= 0
⇒
n
=
A
cos
θ

mg
Substituting this expression for the normal force,
n
, into the
x
equation above,
A
sin
θ

μ
k
(
A
cos
θ

mg
) =
ma
x
⇒
a
x
=
A
sin
θ

μ
k
(
A
cos
θ

mg
)
m
Quiz #2 Solutions Page 1 of 5
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. (16 points) Zach, of mass
m
, is riding upward in an elevator when the ﬂoor partially breaks free and hangs
at an angle
θ
below the horizontal! Fortunately, the safety system of the elevator detects the problem and
brings the elevator to a stop with acceleration magnitude
a
. Also fortunately, the coeﬃcient of static friction,
μ
s
, is just suﬃcient to prevent Zach from sliding out of the gap as it slows. What is Zach’s apparent weight
as the elevator slows, in terms of any or all of
m
,
θ
,
μ
s
,
a
, and physical or mathematical constants? (
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 Spring '08
 UZER
 Force, Mass, Normal Force, Zach, Solutions Page, µs

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