Bodet (ngb299) – oldfinal 02 JT10 – turner – (57340)
1
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21
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before answering.
001
10.0 points
A train pulls away from a station with a con
stant acceleration of 0
.
6 m
/
s
2
.
A passenger
arrives at a position on the track 6 s after the
end of the train left that position.
What is the slowest constant speed at which
she can run and catch the train?
Correct answer: 7
.
2 m
/
s.
Explanation:
Let :
x
0
= 0 m
,
end of train position
v
0
t
= 0 m
/
s
,
a
t
= 0
.
6 m
/
s
2
,
and
Δ
t
= 6 s
.
After time
t
the train has traveled a dis
tance of
x
t
=
x
0
+
v
0
t
t
+
1
2
a
t
t
2
=
1
2
a
t
t
2
and the passenger a distance of
x
p
=
x
0
+
v
p
(
t

Δ
t
) =
v
p
(
t

Δ
t
)
.
When the passenger overtakes the train,
x
t
=
x
p
v
p
(
t

Δ
t
) =
1
2
a
t
t
2
v
p
=
a
t
t
2
2 (
t

Δ
t
)
.
To minimize
v
p
,
d
dt
a
t
t
2
2 (
t

Δ
t
)
= 0
4 (
t

Δ
t
)
a
t
t

2
a
t
t
2
4 (
t

Δ
t
)
2
= 0
2 (
t

Δ
t
)

t
= 0
t

2
Δ
t
= 0
t
= 2
Δ
t
= 2 (6 s) = 12 s
,
so
v
p
=
a
t
t
2
2 (
t

Δ
t
)
=
a
t
(2
Δ
t
)
2
2
Δ
t
= 2
a
t
Δ
t
= 2 (0
.
6 m
/
s
2
) (6 s) =
7
.
2 m
/
s
.
0
4
8
12
16
0
5
10
15
20
25
30
35
40
45
50
x
(m)
t
(s)
Δ
t
Train
Passenger
The train’s velocity at this time is
v
t
=
a
t
t
= 2
a
t
Δ
t
= 2 (0
.
6 m
/
s
2
) (6 s) = 7
.
2 m
/
s
.
The dashed line (representing the passen
ger’s minimum constant velocity) is tangent
to the train’s acceleration curve, illustrating
the fact that the velocities are equal at the
passenger’s minimum speed.
002
10.0 points
Two bodies are falling with negligible air resis
tance, side by side, above a horizontal plane.
If one of the bodies is given an additional
horizontal acceleration during its descent, it
1.
has the vertical component of its acceler
ation altered.
2.
has the vertical component of its velocity
altered.
3.
strikes the plane at the same time as the
other body.
correct
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Bodet (ngb299) – oldfinal 02 JT10 – turner – (57340)
2
4.
follows a straight line path along the re
sultant acceleration vector.
5.
follows a hyperbolic path.
Explanation:
Because a horizontal acceleration does not
change the vertical velocity of an object, the
two bodies strike the plane at the same time.
003
10.0 points
A man stands in an elevator in the university’s
administration building and is accelerating
upwards.
(During peak hours, this does not
happen very often.)
Elevator
Cable
Choose the correct free body diagram for
the man, where
F
i,j
is the force on the object
i
, from the object
j
.
1.
F
elevator, cable
F
man, elevator
2.
F
F
man, floor
man, earth
correct
3.
F
F
elevator, cable
man, earth
4.
F
man, floor
F
elevator, cable
F
man, earth
5.
F
man, acceleration
6.
F
man, cable
Explanation:
Only the forces acting
directly
on the man
are to be in the free body diagram. Therefore,
the force from the cable should be omitted,
while those from gravity and from the floor’s
normal force should be included.
004
10.0 points
The horizontal surface on which the objects
slide is frictionless.
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 Spring '08
 Turner
 Physics, Force, Friction, kg, tan θ

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