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Physics 2211
Quiz #5
Solutions
Spring 2007
G
= 6
.
673
×
10

11
N
·
m
2
/
kg
2
M
Earth
= 5
.
98
×
10
24
kg
g
Earth
= 9
.
8m
/
s
2
R
Earth
= 6
.
37
×
10
6
m
Unless otherwise directed, all springs and cords are ideal, and drag should be neglected.
I
. (16 points) A block of mass
m
is at rest at the foot of a frictionless ramp. The ramp is in the form of a quarter
circle, with radius
R
. A constant horizontal force of magnitude
F
is applied to the block, as illustrated.
Assuming the force
F
is suﬃcient to raise the block up through a quarter circle, what is its speed when it
has done so? Express your result in terms of any or all of
m
,
R
,
F
, and physical or mathematical constants.
(
On Earth.
)
.
.
.
.
.
.
.
.
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.
.
Use the WorkEnergy Theorem
W
ext
+
W
nc
= Δ
K
+ Δ
U
Let
y
be positive upward and
x
be positive to the right. Choose the
block and the Earth be the system. There are no nonconservative
forces. External forces are the applied force and the normal force.
The normal force does no work, as it is always perpendicular to the
displacement. The only potential energy is that of local gravity,
U
g
=
mgy
.
Z
~
F
·
d~s
=
Z
F
cos
θ ds
=
(
1
2
mv
2
f

1
2
mv
2
i
)
+ (
mgy
f

mgy
i
) =
1
2
mv
2
f
+
mg
Δ
y
as
v
i
= 0. Note that
F
is constant, and cos
θ ds
is
dx
, so
Z
F dx
=
1
2
mv
2
f
+
mg
Δ
y
⇒
FR
=
1
2
mv
2
f
+
mgR
since
R
dx
=
R
and Δ
y
=
R
.
Solving for
v
f
FR

mgR
=
1
2
mv
2
f
⇒
v
f
=
r
2
m
(
F

mg
)
R
Quiz #5 Solutions Page 1 of 5
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. (16 points) A block of mass 2
m
has a massless spring with spring constant
k
attached to its front, parallel
to the ground. This block slides across a frictionless horizontal surface at speed
v
i
toward a stationary block
of mass
m
. What is the maximum compression of the spring during the collision? Express your result in
terms of any or all of
m
,
k
,
v
i
, and physical or mathematical constants. (
On Earth.
)
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
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This homework help was uploaded on 04/09/2008 for the course PHYSICS 2211 taught by Professor Uzer during the Spring '08 term at Georgia Institute of Technology.
 Spring '08
 UZER
 Physics

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